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\begin{document}
\title[APPENDIX]{Appendix}

%\keywords{Classical method, Bayesian method, Generalized variable method,
%General class of exponentiated generalized inverted exponential
%distributions, Reliability}
%\subjclass[2010]{62F03, 62F10, 62F15, 62F40}
%\date{submitted on \today}
%\maketitle


\section{Appendix}



%TCIMACRO{\TeXButton{TeX field}{\tiny}}%
%BeginExpansion
\tiny%
%EndExpansion

\begin{center}
\begin{tabular}{lcccccccc}
\multicolumn{9}{l}{Table 5.3(a) Classical and Generalized Point Estimates of 
$R_{1,3}$ when the \ {Common}\ {Scale}} \\ 
\multicolumn{9}{l}{\ \ \ \ \ \ \ \ \ \ \ \ \ \ {\ \ \ Parameter }$\lambda $
is known {$(\lambda =3)$}} \\ 
&  &  &  &  &  &  &  &  \\ \hline
Sample size & Parameters & Reliability &  & \multicolumn{3}{c}{Classical} & 
& Generalized \\ \cline{1-3}\cline{5-7}\cline{9-9}
\multicolumn{1}{c}{$n$} & $\mathbf{\beta }$ & $R_{1,3}$ &  & $\widehat{R}%
_{s,k}^{M}$ & $\widehat{R}_{s,k}^{U}$ & $\widehat{R}_{s,k}^{\ast }$ &  & $%
\widehat{R}_{s,k}^{G}$ \\ \cline{1-3}\cline{5-7}\cline{9-9}
\multicolumn{1}{c}{$10$} & $(4,2)$ & $0.5429$ &  & $0.5595$ & $0.5488$ & $%
0.5480$ &  & $0.5450$ \\ 
\multicolumn{1}{c}{} &  &  &  & $0.0135$ & $0.0138$ & $0.0088$ &  & $0.0056$
\\ 
\multicolumn{1}{c}{$15$} &  &  &  & $0.5521$ & $0.5444$ & $0.5450$ &  & $%
0.5446$ \\ 
\multicolumn{1}{c}{} &  &  &  & $0.0086$ & $0.0090$ & $0.0061$ &  & $0.0062$
\\ 
\multicolumn{1}{c}{$25$} &  &  &  & $0.5485$ & $0.5439$ & $0.5447$ &  & $%
0.5446$ \\ 
\multicolumn{1}{c}{} &  &  &  & $0.0050$ & $0.0051$ & $0.0040$ &  & $0.0040$
\\ 
\multicolumn{1}{c}{$35$} &  &  &  & $0.5461$ & $0.5429$ & $0.5435$ &  & $%
0.5434$ \\ 
\multicolumn{1}{c}{} &  &  &  & $0.0036$ & $0.0036$ & $0.0031$ &  & $0.0031$
\\ \hline
\multicolumn{1}{c}{$10$} & $(4,4)$ & $0.7500$ &  & $0.7522$ & $0.7521$ & $%
0.7389$ &  & $0.7392$ \\ 
\multicolumn{1}{c}{} &  &  &  & $0.0091$ & $0.0102$ & $0.0049$ &  & $0.0049$
\\ 
\multicolumn{1}{c}{$15$} &  &  &  & $0.7518$ & $0.7517$ & $0.7421$ &  & $%
0.7423$ \\ 
\multicolumn{1}{c}{} &  &  &  & $0.0060$ & $0.0065$ & $0.0039$ &  & $0.0039$
\\ 
\multicolumn{1}{c}{$25$} &  &  &  & $0.7502$ & $0.7501$ & $0.7441$ &  & $%
0.7442$ \\ 
\multicolumn{1}{c}{} &  &  &  & $0.0038$ & $0.0040$ & $0.0029$ &  & $0.0029$
\\ 
\multicolumn{1}{c}{$35$} &  &  &  & $0.7505$ & $0.7504$ & $0.7459$ &  & $%
0.7459$ \\ 
\multicolumn{1}{c}{} &  &  &  & $0.0026$ & $0.0027$ & $0.0021$ &  & $0.0021$
\\ \hline
\multicolumn{1}{c}{$10$} & $(4,6)$ & $0.8476$ &  & $0.8453$ & $0.8499$ & $%
0.8345$ &  & $0.8348$ \\ 
\multicolumn{1}{c}{} &  &  &  & $0.0053$ & $0.0057$ & $0.0026$ &  & $0.0026$
\\ 
\multicolumn{1}{c}{$15$} &  &  &  & $0.8449$ & $0.8480$ & $0.8367$ &  & $%
0.8370$ \\ 
\multicolumn{1}{c}{} &  &  &  & $0.0036$ & $0.0038$ & $0.0022$ &  & $0.0022$
\\ 
\multicolumn{1}{c}{$25$} &  &  &  & $0.8462$ & $0.8481$ & $0.8405$ &  & $%
0.8406$ \\ 
\multicolumn{1}{c}{} &  &  &  & $0.0023$ & $0.0024$ & $0.0017$ &  & $0.0017$
\\ 
\multicolumn{1}{c}{$35$} &  &  &  & $0.8454$ & $0.8467$ & $0.8412$ &  & $%
0.8412$ \\ 
\multicolumn{1}{c}{} &  &  &  & $0.0017$ & $0.0017$ & $0.0013$ &  & $0.0013$
\\ \hline
\multicolumn{1}{c}{$10$} & $(4,8)$ & $0.9000$ &  & $0.8954$ & $0.9015$ & $%
0.8880$ &  & $0.8885$ \\ 
\multicolumn{1}{c}{} &  &  &  & $0.0033$ & $0.0034$ & $0.0015$ &  & $0.0015$
\\ 
\multicolumn{1}{c}{$15$} &  &  &  & $0.8941$ & $0.8982$ & $0.8886$ &  & $%
0.8888$ \\ 
\multicolumn{1}{c}{} &  &  &  & $0.0023$ & $0.0023$ & $0.0013$ &  & $0.0013$
\\ 
\multicolumn{1}{c}{$25$} &  &  &  & $0.8974$ & $0.8999$ & $0.8929$ &  & $%
0.8929$ \\ 
\multicolumn{1}{c}{} &  &  &  & $0.0013$ & $0.0013$ & $0.0009$ &  & $0.0009$
\\ 
\multicolumn{1}{c}{$35$} &  &  &  & $0.8992$ & $0.9010$ & $0.8954$ &  & $%
0.8955$ \\ 
\multicolumn{1}{c}{} &  &  &  & $0.0009$ & $0.0009$ & $0.0007$ &  & $0.0007$
\\ \hline
\end{tabular}

\begin{tabular}{lcccccccc}
\multicolumn{9}{l}{Table 5.3(b) {Bayesian Point Estimates of $R_{1,3}$ when
the Common Scale Parameter $\lambda $ is Known $(\lambda =3)$}} \\ 
&  &  &  &  &  &  &  &  \\ \hline
Sample size & Parameters & Reliability & \multicolumn{6}{c}{Bayesian} \\ 
\hline
\multicolumn{1}{c}{$n$} & $\mathbf{\beta }$ & $R_{1,3}$ & $\widehat{R}%
_{s,k}^{SE}$ & $\widehat{R}_{s,k}^{LINEX}$ & $^{SE}\widehat{R}_{s,k}^{Lin}$
& $^{LINEX}\widehat{R}_{s,k}^{Lin}$ & $^{SE}\widehat{R}_{s,k}^{MCMC}$ & $%
^{LINEX}\widehat{R}_{s,k}^{MCMC}$ \\ \hline
\multicolumn{1}{c}{$10$} & $(4,2)$ & $0.5429$ & $0.5593$ & $0.5489$ & $%
0.5486 $ & $0.5454$ & $0.5454$ & $0.5454$ \\ 
\multicolumn{1}{c}{} &  &  & $0.0145$ & $0.0138$ & $0.0088$ & $0.0056$ & $%
0.0138$ & $0.0017$ \\ 
\multicolumn{1}{c}{$15$} &  &  & $0.5521$ & $0.5444$ & $0.5450$ & $0.5446$ & 
$0.5446$ & $0.5446$ \\ 
\multicolumn{1}{c}{} &  &  & $0.0086$ & $0.0090$ & $0.0061$ & $0.0062$ & $%
0.0138$ & $0.0138$ \\ 
\multicolumn{1}{c}{$25$} &  &  & $0.5485$ & $0.5439$ & $0.5447$ & $0.5446$ & 
$0.5446$ & $0.5446$ \\ 
\multicolumn{1}{c}{} &  &  & $0.0050$ & $0.0051$ & $0.0040$ & $0.0040$ & $%
0.0138$ & $0.0138$ \\ 
\multicolumn{1}{c}{$35$} &  &  & $0.5461$ & $0.5429$ & $0.5435$ & $0.5434$ & 
$0.5454$ & $0.5429$ \\ 
\multicolumn{1}{c}{} &  &  & $0.0036$ & $0.0036$ & $0.0031$ & $0.0031$ & $%
0.0031$ & $0.0031$ \\ \hline
\multicolumn{1}{c}{$10$} & $(4,4)$ & $0.7500$ & $0.7522$ & $0.7521$ & $%
0.7389 $ & $0.7392$ & $0.5461$ & $0.5450$ \\ 
\multicolumn{1}{c}{} &  &  & $0.0091$ & $0.0102$ & $0.0049$ & $0.0049$ & $%
0.0031$ & $0.0031$ \\ 
\multicolumn{1}{c}{$15$} &  &  & $0.7518$ & $0.7517$ & $0.7421$ & $0.7423$ & 
$0.5454$ & $0.5461$ \\ 
\multicolumn{1}{c}{} &  &  & $0.0060$ & $0.0065$ & $0.0039$ & $0.0039$ & $%
0.0039$ & $0.0039$ \\ 
\multicolumn{1}{c}{$25$} &  &  & $0.7502$ & $0.7501$ & $0.7441$ & $0.7442$ & 
$0.5444$ & $0.7504$ \\ 
\multicolumn{1}{c}{} &  &  & $0.0038$ & $0.0040$ & $0.0029$ & $0.0029$ & $%
0.0029$ & $0.0017$ \\ 
\multicolumn{1}{c}{$35$} &  &  & $0.7505$ & $0.7504$ & $0.7459$ & $0.7459$ & 
$0.7504$ & $0.7504$ \\ 
\multicolumn{1}{c}{} &  &  & $0.0026$ & $0.0027$ & $0.0021$ & $0.0021$ & $%
0.0029$ & $0.0029$ \\ \hline
\multicolumn{1}{c}{$10$} & $(4,6)$ & $0.8476$ & $0.8453$ & $0.8499$ & $%
0.8345 $ & $0.8348$ & $0.7442$ & $0.7442$ \\ 
\multicolumn{1}{c}{} &  &  & $0.0053$ & $0.0057$ & $0.0026$ & $0.0026$ & $%
0.0029$ & $0.0029$ \\ 
\multicolumn{1}{c}{$15$} &  &  & $0.8449$ & $0.8480$ & $0.8367$ & $0.8370$ & 
$0.8370$ & $0.8370$ \\ 
\multicolumn{1}{c}{} &  &  & $0.0036$ & $0.0038$ & $0.0022$ & $0.0022$ & $%
0.0029$ & $0.0017$ \\ 
\multicolumn{1}{c}{$25$} &  &  & $0.8462$ & $0.8481$ & $0.8405$ & $0.8406$ & 
$0.7442$ & $0.7442$ \\ 
\multicolumn{1}{c}{} &  &  & $0.0023$ & $0.0024$ & $0.0017$ & $0.0017$ & $%
0.0017$ & $0.0029$ \\ 
\multicolumn{1}{c}{$35$} &  &  & $0.8454$ & $0.8467$ & $0.8412$ & $0.8412$ & 
$0.8370$ & $0.8370$ \\ 
\multicolumn{1}{c}{} &  &  & $0.0017$ & $0.0017$ & $0.0013$ & $0.0013$ & $%
0.0057$ & $0.0057$ \\ \hline
\multicolumn{1}{c}{$10$} & $(4,8)$ & $0.9000$ & $0.8954$ & $0.9015$ & $%
0.8880 $ & $0.8885$ & $0.8449$ & $0.8449$ \\ 
\multicolumn{1}{c}{} &  &  & $0.0033$ & $0.0034$ & $0.0015$ & $0.0015$ & $%
0.0057$ & $0.0057$ \\ 
\multicolumn{1}{c}{$15$} &  &  & $0.8941$ & $0.8982$ & $0.8886$ & $0.8888$ & 
$0.8941$ & $0.8941$ \\ 
\multicolumn{1}{c}{} &  &  & $0.0023$ & $0.0023$ & $0.0013$ & $0.0013$ & $%
0.0023$ & $0.0007$ \\ 
\multicolumn{1}{c}{$25$} &  &  & $0.8974$ & $0.8999$ & $0.8929$ & $0.8929$ & 
$0.8992$ & $0.8992$ \\ 
\multicolumn{1}{c}{} &  &  & $0.0013$ & $0.0013$ & $0.0009$ & $0.0009$ & $%
0.0007$ & $0.0007$ \\ 
\multicolumn{1}{c}{$35$} &  &  & $0.8992$ & $0.9010$ & $0.8954$ & $0.8955$ & 
$0.8955$ & $0.8955$ \\ 
\multicolumn{1}{c}{} &  &  & $0.0009$ & $0.0009$ & $0.0007$ & $0.0007$ & $%
0.0023$ & $0.0007$ \\ \hline
\end{tabular}

\begin{tabular}{lccccccc}
\multicolumn{8}{l}{Table 5.3(c) Classical and generalized interval estimates
of $R_{1,3}$ when the common scale parameter $\lambda $ is known $(\lambda
=3)$} \\ 
&  &  &  &  &  &  &  \\ \hline
Sample size & Parameters & Reliability & \multicolumn{3}{c}{Classical} &  & 
Generalized \\ \cline{1-6}\cline{8-8}
\multicolumn{1}{c}{$n$} & $\mathbf{\beta }$ & $R_{1,3}$ & ACI & PBCI & BTCI
&  & GCI \\ \cline{1-3}\cline{4-6}\cline{8-8}
\multicolumn{1}{c}{$10$} & $(4,2)$ & $0.5429$ & $(0.3475,0.7704)$ & $%
(0.3459,0.7745)$ & $(0.3474,0.7733)$ &  & $(0.3591,0.7319)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.4229/0.9092$ & $0.4230/0.9070$ & $%
0.4230/0.9091$ &  & $0.3728/0.9552$ \\ 
\multicolumn{1}{c}{$15$} &  &  & $(0.3764,0.7269)$ & $(0.3721,0.7261)$ & $%
(0.3765,0.7270)$ &  & $(0.3844,0.7030)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.3506/0.9228$ & $0.3498/0.9201$ & $%
0.3501/0.9212$ &  & $0.3186/0.9476$ \\ 
\multicolumn{1}{c}{$25$} &  &  & $(0.4109,0.6860)$ & $(0.4095,0.6840)$ & $%
(0.4100,0.6862)$ &  & $(0.4152,0.6726)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.2752/0.9412$ & $0.2725/0.9422$ & $%
0.2735/0.9410$ &  & $0.2573/0.9520$ \\ 
\multicolumn{1}{c}{$35$} &  &  & $(0.4293,0.6630)$ & $(0.4278,0.6622)$ & $%
(0.4292,0.6638)$ &  & $(0.4321,0.6538)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.2336/0.9400$ & $0.2331/0.9401$ & $%
0.2333/0.9395$ &  & $0.2217/0.9456$ \\ \hline
\multicolumn{1}{c}{$10$} & $(4,4)$ & $0.7500$ & $(0.5698,0.9346)$ & $%
(0.5648,0.9326)$ & $(0.5658,0.9336)$ &  & $(0.5763,0.8872)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.3648/0.9076$ & $0.3635/0.9065$ & $%
0.3644/0.9070$ &  & $0.3109/0.9692$ \\ 
\multicolumn{1}{c}{$15$} &  &  & $(0.5998,0.9038)$ & $(0.5988,0.9030)$ & $%
(0.5998,0.9033)$ &  & $(0.6022,0.8712)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.3040/0.9212$ & $0.3035/0.9200$ & $%
0.3025/0.9211$ &  & $0.2690/0.9588$ \\ 
\multicolumn{1}{c}{$25$} &  &  & $(0.6304,0.8700)$ & $(0.6300,0.8701)$ & $%
(0.6302,0.8705)$ &  & $(0.6307,0.8505)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.2395/0.9312$ & $0.2394/0.9300$ & $%
0.2388/0.9310$ &  & $0.2197/0.9568$ \\ 
\multicolumn{1}{c}{$35$} &  &  & $(0.6486,0.8524)$ & $(0.6477,0.8511)$ & $%
(0.6478,0.8520)$ &  & $(0.6480,0.8385)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.2038/0.9416$ & $0.2033/0.9410$ & $%
0.2028/0.9405$ &  & $0.1905/0.9552$ \\ \hline
\multicolumn{1}{c}{$10$} & $(4,6)$ & $0.8476$ & $(0.7036,0.9869)$ & $%
(0.7030,0.9861)$ & $(0.7031,0.9861)$ &  & $(0.7097,0.9431)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.2833/0.8892$ & $0.2828/0.8878$ & $%
0.2830/0.8890$ &  & $0.2334/0.9832$ \\ 
\multicolumn{1}{c}{$15$} &  &  & $(0.7269,0.9628)$ & $(0.7255,0.9618)$ & $%
(0.7263,0.9629)$ &  & $(0.7290,0.9323$ \\ 
\multicolumn{1}{c}{} &  &  & $0.2359/0.9068$ & $0.2355/0.9063$ & $%
0.2360/0.9065$ &  & $0.2033/0.9712$ \\ 
\multicolumn{1}{c}{$25$} &  &  & $(0.7541,0.9384)$ & $(0.7538,0.9378)$ & $%
(0.7540,0.9380)$ &  & $(0.7532,0.9196)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.1843/0.9224$ & $0.1837/0.9219$ & $%
0.1838/0.9225$ &  & $0.1664/0.9628$ \\ 
\multicolumn{1}{c}{$35$} &  &  & $(0.7667,0.9241)$ & $(0.7665,0.9237)$ & $%
(0.7670,0.9240)$ &  & $(0.7656,0.9109$ \\ 
\multicolumn{1}{c}{} &  &  & $0.1574/0.9336$ & $0.1565/0.9330$ & $%
0.1570/0.9340$ &  & $0.1453/0.9564$ \\ \hline
\multicolumn{1}{c}{$10$} & $(4,8)$ & $0.9000$ & $(0.7862,1.0046)$ & $%
(0.7858,1.0044)$ & $(0.7860,1.0040)$ &  & $(0.7941,0.9667)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.2183/0.8844$ & $0.2178/0.8840$ & $%
0.2180/0.8840$ &  & $0.1726/0.9824$ \\ 
\multicolumn{1}{c}{$15$} &  &  & $(0.8024,0.9857)$ & $(0.8017,0.9844)$ & $%
(0.8019,0.9851)$ &  & $(0.8064,0.9593)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.1834/0.9116$ & $0.1831/0.9109$ & $%
0.1833/0.9115$ &  & $0.1528/0.9768$ \\ 
\multicolumn{1}{c}{$25$} &  &  & $(0.8269,0.9679)$ & $(0.8258,0.9677)$ & $%
(0.8255,0.9677)$ &  & $(0.8264,0.9514)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.1410/0.9188$ & $0.1405/0.9177$ & $%
0.1405/0.9177$ &  & $0.1250/0.9708$ \\ 
\multicolumn{1}{c}{$35$} &  &  & $(0.8399,0.9585)$ & $(0.8387,0.9578)$ & $%
(0.8389,0.9584)$ &  & $(0.8384,0.9465)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.1186/0.9352$ & $0.1179/0.9348$ & $%
0.1179/0.9350$ &  & $0.1081/0.9660$ \\ \hline
\end{tabular}

\begin{tabular}{lcccccc}
\multicolumn{7}{l}{Table 5.3(d) Bayesian interval estimates of $R_{1,3}$
when the common scale parameter $\lambda $ is known $(\lambda =3)$} \\ 
&  &  &  &  &  &  \\ \hline
Sample size & Parameters & Reliability & \multicolumn{4}{c}{Bayesian} \\ 
\hline
\multicolumn{1}{c}{$n$} & $\mathbf{\beta }$ & $R_{1,3}$ & $^{SE}\text{BCI}%
^{MCMC}$ & $^{SE}$HDPI$^{MCMC}$ & $^{LINEX}\text{BCI}^{MCMC}$ & $^{LINEX}$%
HPDI$^{MCMC}$ \\ \cline{1-3}\cline{4-7}
\multicolumn{1}{c}{$10$} & $(4,2)$ & $0.5429$ & $(0.3475,0.7704)$ & $%
(0.3459,0.7745)$ & $(0.3474,0.7733)$ & $(0.3591,0.7319)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.4229/0.9092$ & $0.4230/0.9070$ & $%
0.4230/0.9091$ & $0.3728/0.9552$ \\ 
\multicolumn{1}{c}{$15$} &  &  & $(0.3764,0.7269)$ & $(0.3721,0.7261)$ & $%
(0.3765,0.7270)$ & $(0.3844,0.7030)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.3506/0.9228$ & $0.3498/0.9201$ & $%
0.3501/0.9212$ & $0.3186/0.9476$ \\ 
\multicolumn{1}{c}{$25$} &  &  & $(0.4109,0.6860)$ & $(0.4095,0.6840)$ & $%
(0.4100,0.6862)$ & $(0.4152,0.6726)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.2752/0.9412$ & $0.2725/0.9422$ & $%
0.2735/0.9410$ & $0.2573/0.9520$ \\ 
\multicolumn{1}{c}{$35$} &  &  & $(0.4293,0.6630)$ & $(0.4278,0.6622)$ & $%
(0.4292,0.6638)$ & $(0.4321,0.6538)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.2336/0.9400$ & $0.2331/0.9401$ & $%
0.2333/0.9395$ & $0.2217/0.9456$ \\ \hline
\multicolumn{1}{c}{$10$} & $(4,4)$ & $0.7500$ & $(0.5698,0.9346)$ & $%
(0.5648,0.9326)$ & $(0.5658,0.9336)$ & $(0.5763,0.8872)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.3648/0.9076$ & $0.3635/0.9065$ & $%
0.3644/0.9070$ & $0.3109/0.9692$ \\ 
\multicolumn{1}{c}{$15$} &  &  & $(0.5998,0.9038)$ & $(0.5988,0.9030)$ & $%
(0.5998,0.9033)$ & $(0.6022,0.8712)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.3040/0.9212$ & $0.3035/0.9200$ & $%
0.3025/0.9211$ & $0.2690/0.9588$ \\ 
\multicolumn{1}{c}{$25$} &  &  & $(0.6304,0.8700)$ & $(0.6300,0.8701)$ & $%
(0.6302,0.8705)$ & $(0.6307,0.8505)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.2395/0.9312$ & $0.2394/0.9300$ & $%
0.2388/0.9310$ & $0.2197/0.9568$ \\ 
\multicolumn{1}{c}{$35$} &  &  & $(0.6486,0.8524)$ & $(0.6477,0.8511)$ & $%
(0.6478,0.8520)$ & $(0.6480,0.8385)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.2038/0.9416$ & $0.2033/0.9410$ & $%
0.2028/0.9405$ & $0.1905/0.9552$ \\ \hline
\multicolumn{1}{c}{$10$} & $(4,6)$ & $0.8476$ & $(0.7036,0.9869)$ & $%
(0.7030,0.9861)$ & $(0.7031,0.9861)$ & $(0.7097,0.9431)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.2833/0.8892$ & $0.2828/0.8878$ & $%
0.2830/0.8890$ & $0.2334/0.9832$ \\ 
\multicolumn{1}{c}{$15$} &  &  & $(0.7269,0.9628)$ & $(0.7255,0.9618)$ & $%
(0.7263,0.9629)$ & $(0.7290,0.9323$ \\ 
\multicolumn{1}{c}{} &  &  & $0.2359/0.9068$ & $0.2355/0.9063$ & $%
0.2360/0.9065$ & $0.2033/0.9712$ \\ 
\multicolumn{1}{c}{$25$} &  &  & $(0.7541,0.9384)$ & $(0.7538,0.9378)$ & $%
(0.7540,0.9380)$ & $(0.7532,0.9196)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.1843/0.9224$ & $0.1837/0.9219$ & $%
0.1838/0.9225$ & $0.1664/0.9628$ \\ 
\multicolumn{1}{c}{$35$} &  &  & $(0.7667,0.9241)$ & $(0.7665,0.9237)$ & $%
(0.7670,0.9240)$ & $(0.7656,0.9109$ \\ 
\multicolumn{1}{c}{} &  &  & $0.1574/0.9336$ & $0.1565/0.9330$ & $%
0.1570/0.9340$ & $0.1453/0.9564$ \\ \hline
\multicolumn{1}{c}{$10$} & $(4,8)$ & $0.9000$ & $(0.7862,1.0046)$ & $%
(0.7858,1.0044)$ & $(0.7860,1.0040)$ & $(0.7941,0.9667)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.2183/0.8844$ & $0.2178/0.8840$ & $%
0.2180/0.8840$ & $0.1726/0.9824$ \\ 
\multicolumn{1}{c}{$15$} &  &  & $(0.8024,0.9857)$ & $(0.8017,0.9844)$ & $%
(0.8019,0.9851)$ & $(0.8064,0.9593)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.1834/0.9116$ & $0.1831/0.9109$ & $%
0.1833/0.9115$ & $0.1528/0.9768$ \\ 
\multicolumn{1}{c}{$25$} &  &  & $(0.8269,0.9679)$ & $(0.8258,0.9677)$ & $%
(0.8255,0.9677)$ & $(0.8264,0.9514)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.1410/0.9188$ & $0.1405/0.9177$ & $%
0.1405/0.9177$ & $0.1250/0.9708$ \\ 
\multicolumn{1}{c}{$35$} &  &  & $(0.8399,0.9585)$ & $(0.8387,0.9578)$ & $%
(0.8389,0.9584)$ & $(0.8384,0.9465)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.1186/0.9352$ & $0.1179/0.9348$ & $%
0.1179/0.9350$ & $0.1081/0.9660$ \\ \hline
\end{tabular}

\begin{tabular}{ccccccccc}
\multicolumn{9}{l}{Table 5.4(a) Classical and generalized point estimates of 
$R_{2,4}$ when the common\ scale} \\ 
\multicolumn{9}{l}{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ parameter $\lambda $ is
known $(\lambda =3)$} \\ 
&  &  &  &  &  &  &  &  \\ \hline
Sample size & Parameters & Reliability &  & \multicolumn{3}{c}{Classical} & 
\multicolumn{1}{c}{} & \multicolumn{1}{c}{Generalized} \\ 
\cline{1-3}\cline{5-7}\cline{9-9}
$n$ & $\mathbf{\beta }$ & $R_{2,4}$ &  & $\widehat{R}_{s,k}^{M}$ & $\widehat{%
R}_{s,k}^{U}$ & $\widehat{R}_{s,k}^{\ast }$ &  & $\widehat{R}_{s,k}^{G}$ \\ 
\cline{1-3}\cline{5-7}\cline{9-9}
$10$ &  & $0.3905$ &  & $0.4071$ & $0.3905$ & $0.3982$ &  & $0.3989$ \\ 
&  &  &  & $0.0108$ & $0.0108$ & $0.0066$ &  & $0.0066$ \\ 
$15$ &  &  &  & $0.3998$ & $0.3886$ & $0.3952$ &  & $0.3956$ \\ 
&  &  &  & $0.0064$ & $0.0064$ & $0.0046$ &  & $0.0046$ \\ 
$25$ &  &  &  & $0.3980$ & $0.3913$ & $0.3955$ &  & $0.3957$ \\ 
&  &  &  & $0.0038$ & $0.0038$ & $0.0031$ &  & $0.0031$ \\ 
$35$ &  &  &  & $0.3957$ & $0.3909$ & $0.3942$ &  & $0.3942$ \\ 
&  &  &  & $0.0029$ & $0.0029$ & $0.0025$ &  & $0.0025$ \\ \hline
$10$ &  & $0.6000$ &  & $0.6085$ & $0.5986$ & $0.5950$ &  & $0.5953$ \\ 
&  &  &  & $0.0115$ & $0.0126$ & $0.0059$ &  & $0.0059$ \\ 
$15$ &  &  &  & $0.6074$ & $0.6006$ & $0.5981$ &  & $0.5983$ \\ 
&  &  &  & $0.0077$ & $0.0081$ & $0.0047$ &  & $0.0047$ \\ 
$25$ &  &  &  & $0.6045$ & $0.6004$ & $0.5989$ &  & $0.5990$ \\ 
&  &  &  & $0.0048$ & $0.0050$ & $0.0036$ &  & $0.0036$ \\ 
$35$ &  &  &  & $0.6031$ & $0.6001$ & $0.5992$ &  & $0.5992$ \\ 
&  &  &  & $0.0034$ & $0.0035$ & $0.0027$ &  & $0.0027$ \\ \hline
$10$ &  & $0.7229$ &  & $0.7267$ & $0.7235$ & $0.7130$ &  & $0.7129$ \\ 
&  &  &  & $0.0093$ & $0.0105$ & $0.0043$ &  & $0.0042$ \\ 
$15$ &  &  &  & $0.7257$ & $0.7235$ & $0.7158$ &  & $0.7158$ \\ 
&  &  &  & $0.0064$ & $0.0069$ & $0.0036$ &  & $0.0036$ \\ 
$25$ &  &  &  & $0.7246$ & $0.7232$ & $0.7181$ &  & $0.7181$ \\ 
&  &  &  & $0.0040$ & $0.0042$ & $0.0027$ &  & $0.0027$ \\ 
$35$ &  &  &  & $0.7239$ & $0.7229$ & $0.7192$ &  & $0.7192$ \\ 
&  &  &  & $0.0029$ & $0.0030$ & $0.0022$ &  & $0.0022$ \\ \hline
$10$ &  & $0.8000$ &  & $0.7995$ & $0.8005$ & $0.7880$ &  & $0.7878$ \\ 
&  &  &  & $0.0070$ & $0.0077$ & $0.0029$ &  & $0.0029$ \\ 
$15$ &  &  &  & $0.8016$ & $0.8024$ & $0.7922$ &  & $0.7921$ \\ 
&  &  &  & $0.0048$ & $0.0052$ & $0.0025$ &  & $0.0025$ \\ 
$25$ &  &  &  & $0.7989$ & $0.7992$ & $0.7929$ &  & $0.7928$ \\ 
&  &  &  & $0.0030$ & $0.0031$ & $0.0019$ &  & $0.0019$ \\ 
$35$ &  &  &  & $0.7998$ & $0.8000$ & $0.7952$ &  & $0.7952$ \\ 
&  &  &  & $0.0020$ & $0.0021$ & $0.0015$ &  & $0.0015$ \\ \hline
\end{tabular}

\begin{tabular}{ccccccccc}
\multicolumn{9}{l}{Table 5.4(b) Bayesian point estimates of $R_{2,4}$ when
the common\ scale parameter $\lambda $ is known $(\lambda =3)$} \\ 
&  &  &  &  &  &  &  &  \\ \hline
Sample size & Parameters & Reliability & \multicolumn{6}{c}{Bayesian} \\ 
\hline
$n$ & $\mathbf{\beta }$ & $R_{2,4}$ & $\widehat{R}_{s,k}^{SE}$ & $\widehat{R}%
_{s,k}^{LINEX}$ & $^{SE}\widehat{R}_{s,k}^{Lin}$ & $^{LINEX}\widehat{R}%
_{s,k}^{Lin}$ & $^{SE}\widehat{R}_{s,k}^{MCMC}$ & $^{LINEX}\widehat{R}%
_{s,k}^{MCMC}$ \\ \hline
$10$ &  & $0.3905$ & $0.4071$ & $0.3905$ & $0.3982$ & $0.3989$ & $0.3982$ & $%
0.3982$ \\ 
&  &  & $0.0108$ & $0.0108$ & $0.0066$ & $0.0066$ & $0.0046$ & $0.0077$ \\ 
$15$ &  &  & $0.3998$ & $0.3886$ & $0.3952$ & $0.3956$ & $0.3982$ & $0.3982$
\\ 
&  &  & $0.0064$ & $0.0064$ & $0.0046$ & $0.0046$ & $0.0046$ & $0.0077$ \\ 
$25$ &  &  & $0.3980$ & $0.3913$ & $0.3955$ & $0.3957$ & $0.3982$ & $0.5950$
\\ 
&  &  & $0.0038$ & $0.0038$ & $0.0031$ & $0.0031$ & $0.0025$ & $0.0031$ \\ 
$35$ &  &  & $0.3957$ & $0.3909$ & $0.3942$ & $0.3942$ & $0.3942$ & $0.3942$
\\ 
&  &  & $0.0029$ & $0.0029$ & $0.0025$ & $0.0025$ & $0.0025$ & $0.5986$ \\ 
\hline
$10$ &  & $0.6000$ & $0.6085$ & $0.5986$ & $0.5950$ & $0.5953$ & $0.3942$ & $%
0.5950$ \\ 
&  &  & $0.0115$ & $0.0126$ & $0.0059$ & $0.0059$ & $0.0025$ & $0.0025$ \\ 
$15$ &  &  & $0.6074$ & $0.6006$ & $0.5981$ & $0.5983$ & $0.5983$ & $0.0025$
\\ 
&  &  & $0.0077$ & $0.0081$ & $0.0047$ & $0.0047$ & $0.0047$ & $0.0077$ \\ 
$25$ &  &  & $0.6045$ & $0.6004$ & $0.5989$ & $0.5990$ & $0.5992$ & $0.5992$
\\ 
&  &  & $0.0048$ & $0.0050$ & $0.0036$ & $0.0036$ & $0.0025$ & $0.0025$ \\ 
$35$ &  &  & $0.6031$ & $0.6001$ & $0.5992$ & $0.5992$ & $0.5992$ & $0.5992$
\\ 
&  &  & $0.0034$ & $0.0035$ & $0.0027$ & $0.0027$ & $0.0025$ & $0.0042$ \\ 
\hline
$10$ &  & $0.7229$ & $0.7267$ & $0.7235$ & $0.7130$ & $0.7129$ & $0.5992$ & $%
0.7192$ \\ 
&  &  & $0.0093$ & $0.0105$ & $0.0043$ & $0.0042$ & $0.0042$ & $0.0042$ \\ 
$15$ &  &  & $0.7257$ & $0.7235$ & $0.7158$ & $0.7158$ & $0.5992$ & $0.7192$
\\ 
&  &  & $0.0064$ & $0.0069$ & $0.0036$ & $0.0036$ & $0.0042$ & $0.0042$ \\ 
$25$ &  &  & $0.7246$ & $0.7232$ & $0.7181$ & $0.7181$ & $0.5992$ & $0.7192$
\\ 
&  &  & $0.0040$ & $0.0042$ & $0.0027$ & $0.0027$ & $0.0027$ & $0.0042$ \\ 
$35$ &  &  & $0.7239$ & $0.7229$ & $0.7192$ & $0.7192$ & $0.7181$ & $0.7181$
\\ 
&  &  & $0.0029$ & $0.0030$ & $0.0022$ & $0.0022$ & $0.0019$ & $0.0019$ \\ 
\hline
$10$ &  & $0.8000$ & $0.7995$ & $0.8005$ & $0.7880$ & $0.7878$ & $0.7181$ & $%
0.7181$ \\ 
&  &  & $0.0070$ & $0.0077$ & $0.0029$ & $0.0029$ & $0.0027$ & $0.0018$ \\ 
$15$ &  &  & $0.8016$ & $0.8024$ & $0.7922$ & $0.7921$ & $0.7181$ & $0.7880$
\\ 
&  &  & $0.0048$ & $0.0052$ & $0.0025$ & $0.0025$ & $0.0019$ & $0.0042$ \\ 
$25$ &  &  & $0.7989$ & $0.7992$ & $0.7929$ & $0.7928$ & $0.7952$ & $0.7880$
\\ 
&  &  & $0.0030$ & $0.0031$ & $0.0019$ & $0.0019$ & $0.0019$ & $0.0017$ \\ 
$35$ &  &  & $0.7998$ & $0.8000$ & $0.7952$ & $0.7952$ & $0.7953$ & $(0.7952$
\\ 
&  &  & $0.0020$ & $0.0021$ & $0.0015$ & $0.0015$ & $0.0019$ & $0.0019$ \\ 
\hline
\end{tabular}

\begin{tabular}{cccccccc}
\multicolumn{8}{l}{Table 5.4(c) Classical and generalized interval estimates
of $R_{2,4}$ when the common\ scale parameter $\lambda $ is known $(\lambda
=3)$} \\ 
&  &  &  &  &  &  &  \\ \hline
Sample size & Parameters & Reliability & \multicolumn{3}{c}{Classical} &  & 
Generalized \\ \cline{1-6}\cline{8-8}
$n$ & $\mathbf{\beta }$ & $R_{2,4}$ & ACI & PBCI & BTCI &  & GCI \\ 
\cline{1-3}\cline{4-6}\cline{8-8}
$10$ &  & $0.3905$ & $(0.2182,0.5960)$ & $(0.2180,0.5959)$ & $(0.218,0.5949)$
&  & $(0.2340,0.5663)$ \\ 
&  &  & $0.3779/0.9272$ & $0.3770/0.9270$ & $0.3775/0.9265$ &  & $%
0.3322/0.9548$ \\ 
$15$ &  &  & $(0.2447,0.5550)$ & $(0.2444,0.5555)$ & $(0.2441,0.5548)$ &  & $%
(0.2553,0.5375)$ \\ 
&  &  & $0.3103/0.9432$ & $0.3100/0.9428$ & $0.3103/0.9432$ &  & $%
0.2822/0.9604$ \\ 
$25$ &  &  & $(0.2771,0.5190)$ & $(0.2758,0.5188)$ & $(0.2765,0.5175)$ &  & $%
(0.2830,0.5100)$ \\ 
&  &  & $0.2419/0.9448$ & $0.2415/0.9440$ & $0.2410/0.9440$ &  & $%
0.2269/0.9556$ \\ 
$35$ &  &  & $(0.2935,0.4980)$ & $(0.2930,0.4975)$ & $(0.2933,0.4977)$ &  & $%
(0.2975,0.4920)$ \\ 
&  &  & $0.2045/0.9412$ & $0.2044/0.9412$ & $0.2040/0.9410$ &  & $%
0.1945/0.9432$ \\ \hline
$10$ &  & $0.6000$ & $(0.4018,0.8153)$ & $(0.4015,0.8150)$ & $%
(0.4010,0.8152) $ &  & $(0.4172,0.7667)$ \\ 
&  &  & $0.4134/0.9200$ & $0.4130/0.9189$ & $0.4128/0.9190$ &  & $%
0.3495/0.9672$ \\ 
$15$ &  &  & $(0.4357,0.7790)$ & $(0.4351,0.7777)$ & $(0.4355,0.7788)$ &  & $%
(0.4447,0.7467)$ \\ 
&  &  & $0.3432/0.9372$ & $0.3429/0.9365$ & $0.3425/0.9365$ &  & $%
0.3020/0.9716$ \\ 
$25$ &  &  & $(0.4699,0.7391)$ & $(0.4688,0.7389)$ & $(0.4688,0.7389)$ &  & $%
(0.4740,0.7206)$ \\ 
&  &  & $0.2692/0.9364$ & $0.2689/0.9365$ & $0.2687/0.9360$ &  & $%
0.2466/0.9572$ \\ 
$35$ &  &  & $(0.4886,0.7175)$ & $(0.4883,0.7177)$ & $(0.4885,0.7170)$ &  & $%
(0.4911,0.7047)$ \\ 
&  &  & $0.2289/0.9480$ & $0.2282/0.9479$ & $0.2284/0.9477$ &  & $%
0.2136/0.9576$ \\ \hline
$10$ &  & $0.7229$ & $(0.5394,0.9141)$ & $(0.5388,0.9138)$ & $%
(0.5389,0.9138) $ &  & $(0.5537,0.8601)$ \\ 
&  &  & $0.3747/0.9032$ & $0.3739/0.9031$ & $0.3744/0.9030$ &  & $%
0.3065/0.9752$ \\ 
$15$ &  &  & $(0.5699,0.8816)$ & $(0.5688,0.8810)$ & $(0.5688,0.8811)$ &  & $%
(0.5776,0.8450)$ \\ 
&  &  & $0.3117/0.9172$ & $0.3111/0.9165$ & $0.3115/0.9165$ &  & $%
0.2674/0.9700$ \\ 
$25$ &  &  & $(0.6019,0.8472)$ & $(0.6018,0.8468)$ & $(0.6010,0.8468)$ &  & $%
(0.6051,0.8254)$ \\ 
&  &  & $0.2452/0.9308$ & $0.2444/0.9300$ & $0.2449/0.9300$ &  & $%
0.2203/0.9596$ \\ 
$35$ &  &  & $(0.6196,0.8283)$ & $(0.6190,0.8280)$ & $(0.6195,0.8282)$ &  & $%
(0.6209,0.8127)$ \\ 
&  &  & $0.2087/0.9332$ & $0.2085/0.9331$ & $0.2080/0.9328$ &  & $%
0.1918/0.9540$ \\ \hline
$10$ &  & $0.8000$ & $(0.6376,0.9614)$ & $(0.6372,0.9601)$ & $%
(0.6365,0.9610) $ &  & $(0.6531,0.9092)$ \\ 
&  &  & $0.3238/0.8992$ & $0.3228/0.8985$ & $0.3230/0.8960$ &  & $%
0.2561/0.9844$ \\ 
$15$ &  &  & $(0.6680,0.9353)$ & $(0.6677,0.9344)$ & $(0.6677,0.9350)$ &  & $%
(0.6750,0.8988)$ \\ 
&  &  & $0.2674/0.9040$ & $0.2670/0.9039$ & $0.2666/0.9033$ &  & $%
0.2239/0.9664$ \\ 
$25$ &  &  & $(0.6929,0.9048)$ & $(0.6920,0.9040)$ & $(0.6918,0.9040)$ &  & $%
(0.6961,0.8826)$ \\ 
&  &  & $0.2119/0.9252$ & $0.2111/0.9248$ & $0.2108/0.9238$ &  & $%
0.1866/0.9648$ \\ 
$35$ &  &  & $(0.7098,0.8897)$ & $(0.7098,0.8897)$ & $(0.7088,0.8885)$ &  & $%
(0.7110,0.8739)$ \\ 
&  &  & $0.1799/0.9372$ & $0.1799/0.9372$ & $0.1789/0.9365$ &  & $%
0.1630/0.9628$ \\ \hline
\end{tabular}

\begin{tabular}{ccccccc}
\hline
\multicolumn{7}{l}{Table 5.4(d) Bayesian interval estimates of $R_{2,4}$
when the common\ scale parameter $\lambda $ is known $(\lambda =3)$} \\ 
&  &  &  &  &  &  \\ \hline
Sample size & Parameters & Reliability & \multicolumn{4}{c}{Bayesian} \\ 
\hline
$n$ & $\mathbf{\beta }$ & $R_{2,4}$ & $^{SE}\text{BCI}^{MCMC}$ & $^{SE}$HDPI$%
^{MCMC}$ & $^{LINEX}\text{BCI}^{MCMC}$ & $^{LINEX}$HPDI$^{MCMC}$ \\ 
\cline{1-3}\cline{4-7}
$10$ &  & $0.3905$ & $(0.2182,0.5960)$ & $(0.2180,0.5959)$ & $(0.218,0.5949)$
& $(0.2340,0.5663)$ \\ 
&  &  & $0.3779/0.9272$ & $0.3770/0.9270$ & $0.3775/0.9265$ & $0.3322/0.9548$
\\ 
$15$ &  &  & $(0.2447,0.5550)$ & $(0.2444,0.5555)$ & $(0.2441,0.5548)$ & $%
(0.2553,0.5375)$ \\ 
&  &  & $0.3103/0.9432$ & $0.3100/0.9428$ & $0.3103/0.9432$ & $0.2822/0.9604$
\\ 
$25$ &  &  & $(0.2771,0.5190)$ & $(0.2758,0.5188)$ & $(0.2765,0.5175)$ & $%
(0.2830,0.5100)$ \\ 
&  &  & $0.2419/0.9448$ & $0.2415/0.9440$ & $0.2410/0.9440$ & $0.2269/0.9556$
\\ 
$35$ &  &  & $(0.2935,0.4980)$ & $(0.2930,0.4975)$ & $(0.2933,0.4977)$ & $%
(0.2975,0.4920)$ \\ 
&  &  & $0.2045/0.9412$ & $0.2044/0.9412$ & $0.2040/0.9410$ & $0.1945/0.9432$
\\ \hline
$10$ &  & $0.6000$ & $(0.4018,0.8153)$ & $(0.4015,0.8150)$ & $%
(0.4010,0.8152) $ & $(0.4172,0.7667)$ \\ 
&  &  & $0.4134/0.9200$ & $0.4130/0.9189$ & $0.4128/0.9190$ & $0.3495/0.9672$
\\ 
$15$ &  &  & $(0.4357,0.7790)$ & $(0.4351,0.7777)$ & $(0.4355,0.7788)$ & $%
(0.4447,0.7467)$ \\ 
&  &  & $0.3432/0.9372$ & $0.3429/0.9365$ & $0.3425/0.9365$ & $0.3020/0.9716$
\\ 
$25$ &  &  & $(0.4699,0.7391)$ & $(0.4688,0.7389)$ & $(0.4688,0.7389)$ & $%
(0.4740,0.7206)$ \\ 
&  &  & $0.2692/0.9364$ & $0.2689/0.9365$ & $0.2687/0.9360$ & $0.2466/0.9572$
\\ 
$35$ &  &  & $(0.4886,0.7175)$ & $(0.4883,0.7177)$ & $(0.4885,0.7170)$ & $%
(0.4911,0.7047)$ \\ 
&  &  & $0.2289/0.9480$ & $0.2282/0.9479$ & $0.2284/0.9477$ & $0.2136/0.9576$
\\ \hline
$10$ &  & $0.7229$ & $(0.5394,0.9141)$ & $(0.5388,0.9138)$ & $%
(0.5389,0.9138) $ & $(0.5537,0.8601)$ \\ 
&  &  & $0.3747/0.9032$ & $0.3739/0.9031$ & $0.3744/0.9030$ & $0.3065/0.9752$
\\ 
$15$ &  &  & $(0.5699,0.8816)$ & $(0.5688,0.8810)$ & $(0.5688,0.8811)$ & $%
(0.5776,0.8450)$ \\ 
&  &  & $0.3117/0.9172$ & $0.3111/0.9165$ & $0.3115/0.9165$ & $0.2674/0.9700$
\\ 
$25$ &  &  & $(0.6019,0.8472)$ & $(0.6018,0.8468)$ & $(0.6010,0.8468)$ & $%
(0.6051,0.8254)$ \\ 
&  &  & $0.2452/0.9308$ & $0.2444/0.9300$ & $0.2449/0.9300$ & $0.2203/0.9596$
\\ 
$35$ &  &  & $(0.6196,0.8283)$ & $(0.6190,0.8280)$ & $(0.6195,0.8282)$ & $%
(0.6209,0.8127)$ \\ 
&  &  & $0.2087/0.9332$ & $0.2085/0.9331$ & $0.2080/0.9328$ & $0.1918/0.9540$
\\ \hline
$10$ &  & $0.8000$ & $(0.6376,0.9614)$ & $(0.6372,0.9601)$ & $%
(0.6365,0.9610) $ & $(0.6531,0.9092)$ \\ 
&  &  & $0.3238/0.8992$ & $0.3228/0.8985$ & $0.3230/0.8960$ & $0.2561/0.9844$
\\ 
$15$ &  &  & $(0.6680,0.9353)$ & $(0.6677,0.9344)$ & $(0.6677,0.9350)$ & $%
(0.6750,0.8988)$ \\ 
&  &  & $0.2674/0.9040$ & $0.2670/0.9039$ & $0.2666/0.9033$ & $0.2239/0.9664$
\\ 
$25$ &  &  & $(0.6929,0.9048)$ & $(0.6920,0.9040)$ & $(0.6918,0.9040)$ & $%
(0.6961,0.8826)$ \\ 
&  &  & $0.2119/0.9252$ & $0.2111/0.9248$ & $0.2108/0.9238$ & $0.1866/0.9648$
\\ 
$35$ &  &  & $(0.7098,0.8897)$ & $(0.7098,0.8897)$ & $(0.7088,0.8885)$ & $%
(0.7110,0.8739)$ \\ 
&  &  & $0.1799/0.9372$ & $0.1799/0.9372$ & $0.1789/0.9365$ & $0.1630/0.9628$
\\ \hline
\end{tabular}
\end{center}

\bigskip

\bigskip

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\begin{center}
\begin{tabular}{lcccccccc}
\multicolumn{9}{l}{Table 5.5(a) Classical and generalized point estimates of 
$R_{1,3}$ when the common scale} \\ 
\multicolumn{9}{l}{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ parameter $\lambda $ is
known $(\lambda =10)$} \\ 
&  &  &  &  &  &  &  &  \\ \hline
Sample size & Parameters & Reliability &  & \multicolumn{3}{c}{Classical} & 
& Generalized \\ \cline{1-3}\cline{5-7}\cline{9-9}
\multicolumn{1}{c}{$n$} & $\mathbf{\beta }$ & $R_{1,3}$ &  & $\widehat{R}%
_{s,k}^{M}$ & $\widehat{R}_{s,k}^{U}$ & $\widehat{R}_{s,k}^{\ast }$ &  & $%
\widehat{R}_{s,k}^{G}$ \\ \cline{1-3}\cline{5-7}\cline{9-9}
\multicolumn{1}{c}{$10$} & $(4,2)$ & $0.5429$ &  & $0.5590$ & $0.5483$ & $%
0.5478$ &  & $0.5473$ \\ 
\multicolumn{1}{c}{} &  &  &  & $0.0128$ & $0.0138$ & $0.0078$ &  & $0.0079$
\\ 
\multicolumn{1}{c}{$15$} &  &  &  & $0.5517$ & $0.5442$ & $0.5449$ &  & $%
0.5446$ \\ 
\multicolumn{1}{c}{} &  &  &  & $0.0086$ & $0.0090$ & $0.0061$ &  & $0.0062$
\\ 
\multicolumn{1}{c}{$25$} &  &  &  & $0.5485$ & $0.5439$ & $0.5447$ &  & $%
0.5446$ \\ 
\multicolumn{1}{c}{} &  &  &  & $0.0050$ & $0.0051$ & $0.0040$ &  & $0.0040$
\\ 
\multicolumn{1}{c}{$35$} &  &  &  & $0.5461$ & $0.5429$ & $0.5435$ &  & $%
0.5434$ \\ 
\multicolumn{1}{c}{} &  &  &  & $0.0036$ & $0.0036$ & $0.0031$ &  & $0.0031$
\\ \hline
\multicolumn{1}{c}{$10$} & $(4,4)$ & $0.7500$ &  & $0.7522$ & $0.7521$ & $%
0.7389$ &  & $0.7392$ \\ 
\multicolumn{1}{c}{} &  &  &  & $0.0091$ & $0.0102$ & $0.0049$ &  & $0.0049$
\\ 
\multicolumn{1}{c}{$15$} &  &  &  & $0.7518$ & $0.7517$ & $0.7421$ &  & $%
0.7423$ \\ 
\multicolumn{1}{c}{} &  &  &  & $0.0060$ & $0.0065$ & $0.0039$ &  & $0.0039$
\\ 
\multicolumn{1}{c}{$25$} &  &  &  & $0.7502$ & $0.7501$ & $0.7441$ &  & $%
0.7442$ \\ 
\multicolumn{1}{c}{} &  &  &  & $0.0038$ & $0.0040$ & $0.0029$ &  & $0.0029$
\\ 
\multicolumn{1}{c}{$35$} &  &  &  & $0.7505$ & $0.7504$ & $0.7459$ &  & $%
0.7459$ \\ 
\multicolumn{1}{c}{} &  &  &  & $0.0026$ & $0.0027$ & $0.0021$ &  & $0.0021$
\\ \hline
\multicolumn{1}{c}{$10$} & $(4,6)$ & $0.8476$ &  & $0.8453$ & $0.8499$ & $%
0.8345$ &  & $0.8348$ \\ 
\multicolumn{1}{c}{} &  &  &  & $0.0053$ & $0.0057$ & $0.0026$ &  & $0.0026$
\\ 
\multicolumn{1}{c}{$15$} &  &  &  & $0.8449$ & $0.8480$ & $0.8367$ &  & $%
0.8370$ \\ 
\multicolumn{1}{c}{} &  &  &  & $0.0036$ & $0.0038$ & $0.0022$ &  & $0.0022$
\\ 
\multicolumn{1}{c}{$25$} &  &  &  & $0.8462$ & $0.8481$ & $0.8405$ &  & $%
0.8406$ \\ 
\multicolumn{1}{c}{} &  &  &  & $0.0023$ & $0.0024$ & $0.0017$ &  & $0.0017$
\\ 
\multicolumn{1}{c}{$35$} &  &  &  & $0.8454$ & $0.8467$ & $0.8412$ &  & $%
0.8412$ \\ 
\multicolumn{1}{c}{} &  &  &  & $0.0017$ & $0.0017$ & $0.0013$ &  & $0.0013$
\\ \hline
\multicolumn{1}{c}{$10$} & $(4,8)$ & $0.9000$ &  & $0.8954$ & $0.9015$ & $%
0.8880$ &  & $0.8885$ \\ 
\multicolumn{1}{c}{} &  &  &  & $0.0033$ & $0.0034$ & $0.0015$ &  & $0.0015$
\\ 
\multicolumn{1}{c}{$15$} &  &  &  & $0.8941$ & $0.8982$ & $0.8886$ &  & $%
0.8888$ \\ 
\multicolumn{1}{c}{} &  &  &  & $0.0023$ & $0.0023$ & $0.0013$ &  & $0.0013$
\\ 
\multicolumn{1}{c}{$25$} &  &  &  & $0.8974$ & $0.8999$ & $0.8929$ &  & $%
0.8929$ \\ 
\multicolumn{1}{c}{} &  &  &  & $0.0013$ & $0.0013$ & $0.0009$ &  & $0.0009$
\\ 
\multicolumn{1}{c}{$35$} &  &  &  & $0.8992$ & $0.9010$ & $0.8954$ &  & $%
0.8955$ \\ 
\multicolumn{1}{c}{} &  &  &  & $0.0009$ & $0.0009$ & $0.0007$ &  & $0.0007$
\\ \hline
\end{tabular}

\begin{tabular}{lcccccccc}
\multicolumn{9}{l}{Table 5.5(b) Bayesian point estimates of $R_{1,3}$ when
the common scale parameter $\lambda $ is known $(\lambda =10)$} \\ 
&  &  &  &  &  &  &  &  \\ \hline
Sample size & Parameters & Reliability & \multicolumn{6}{c}{Bayesian} \\ 
\hline
\multicolumn{1}{c}{$n$} & $\mathbf{\beta }$ & $R_{1,3}$ & $\widehat{R}%
_{s,k}^{SE}$ & $\widehat{R}_{s,k}^{LINEX}$ & $^{SE}\widehat{R}_{s,k}^{Lin}$
& $^{LINEX}\widehat{R}_{s,k}^{Lin}$ & $^{SE}\widehat{R}_{s,k}^{MCMC}$ & $%
^{LINEX}\widehat{R}_{s,k}^{MCMC}$ \\ \hline
\multicolumn{1}{c}{$10$} & $(4,2)$ & $0.5429$ & $0.5590$ & $0.5483$ & $%
0.5478 $ & $0.5473$ & $0.5473$ & $0.3475$ \\ 
\multicolumn{1}{c}{} &  &  & $0.0128$ & $0.0138$ & $0.0078$ & $0.0079$ & $%
0.0061$ & $0.0061$ \\ 
\multicolumn{1}{c}{$15$} &  &  & $0.5517$ & $0.5442$ & $0.5449$ & $0.5446$ & 
$0.5473$ & $0.3764$ \\ 
\multicolumn{1}{c}{} &  &  & $0.0086$ & $0.0090$ & $0.0061$ & $0.0062$ & $%
0.0061$ & $0.0061$ \\ 
\multicolumn{1}{c}{$25$} &  &  & $0.5485$ & $0.5439$ & $0.5447$ & $0.5446$ & 
$(0.5590$ & $0.4109$ \\ 
\multicolumn{1}{c}{} &  &  & $0.0050$ & $0.0051$ & $0.0040$ & $0.0040$ & $%
0.0061$ & $0.0061$ \\ 
\multicolumn{1}{c}{$35$} &  &  & $0.5461$ & $0.5429$ & $0.5435$ & $0.5434$ & 
$0.5590$ & $0.4293$ \\ 
\multicolumn{1}{c}{} &  &  & $0.0036$ & $0.0036$ & $0.0031$ & $0.0031$ & $%
0.0031$ & $0.0031$ \\ \hline
\multicolumn{1}{c}{$10$} & $(4,4)$ & $0.7500$ & $0.7522$ & $0.7521$ & $%
0.7389 $ & $0.7392$ & $0.5473$ & $0.5429$ \\ 
\multicolumn{1}{c}{} &  &  & $0.0091$ & $0.0102$ & $0.0049$ & $0.0049$ & $%
0.0031$ & $0.0031$ \\ 
\multicolumn{1}{c}{$15$} &  &  & $0.7518$ & $0.7517$ & $0.7421$ & $0.7423$ & 
$0.5590$ & $0.5429$ \\ 
\multicolumn{1}{c}{} &  &  & $0.0060$ & $0.0065$ & $0.0039$ & $0.0039$ & $%
0.0031$ & $0.0031$ \\ 
\multicolumn{1}{c}{$25$} &  &  & $0.7502$ & $0.7501$ & $0.7441$ & $0.7442$ & 
$0.7501$ & $0.5429$ \\ 
\multicolumn{1}{c}{} &  &  & $0.0038$ & $0.0040$ & $0.0029$ & $0.0029$ & $%
0.0029$ & $0.0022$ \\ 
\multicolumn{1}{c}{$35$} &  &  & $0.7505$ & $0.7504$ & $0.7459$ & $0.7459$ & 
$0.7501$ & $0.7502$ \\ 
\multicolumn{1}{c}{} &  &  & $0.0026$ & $0.0027$ & $0.0021$ & $0.0021$ & $%
0.0029$ & $0.0029$ \\ \hline
\multicolumn{1}{c}{$10$} & $(4,6)$ & $0.8476$ & $0.8453$ & $0.8499$ & $%
0.8345 $ & $0.8348$ & $0.7442$ & $0.7459$ \\ 
\multicolumn{1}{c}{} &  &  & $0.0053$ & $0.0057$ & $0.0026$ & $0.0026$ & $%
0.0029$ & $0.0029$ \\ 
\multicolumn{1}{c}{$15$} &  &  & $0.8449$ & $0.8480$ & $0.8367$ & $0.8370$ & 
$0.8370$ & $0.7502$ \\ 
\multicolumn{1}{c}{} &  &  & $0.0036$ & $0.0038$ & $0.0022$ & $0.0022$ & $%
0.0029$ & $0.0029$ \\ 
\multicolumn{1}{c}{$25$} &  &  & $0.8462$ & $0.8481$ & $0.8405$ & $0.8406$ & 
$0.7442$ & $0.7459$ \\ 
\multicolumn{1}{c}{} &  &  & $0.0023$ & $0.0024$ & $0.0017$ & $0.0017$ & $%
0.0029$ & $0.0022$ \\ 
\multicolumn{1}{c}{$35$} &  &  & $0.8454$ & $0.8467$ & $0.8412$ & $0.8412$ & 
$0.7502$ & $0.7459$ \\ 
\multicolumn{1}{c}{} &  &  & $0.0017$ & $0.0017$ & $0.0013$ & $0.0013$ & $%
0.8954$ & $0.0022$ \\ \hline
\multicolumn{1}{c}{$10$} & $(4,8)$ & $0.9000$ & $0.8954$ & $0.9015$ & $%
0.8880 $ & $0.8885$ & $0.7502$ & $0.7502$ \\ 
\multicolumn{1}{c}{} &  &  & $0.0033$ & $0.0034$ & $0.0015$ & $0.0015$ & $%
0.8954$ & $0.0022$ \\ 
\multicolumn{1}{c}{$15$} &  &  & $0.8941$ & $0.8982$ & $0.8886$ & $0.8888$ & 
$0.8954$ & $0.8954$ \\ 
\multicolumn{1}{c}{} &  &  & $0.0023$ & $0.0023$ & $0.0013$ & $0.0013$ & $%
0.0009$ & $0.0009$ \\ 
\multicolumn{1}{c}{$25$} &  &  & $0.8974$ & $0.8999$ & $0.8929$ & $0.8929$ & 
$(0.8269,$ & $0.8269$ \\ 
\multicolumn{1}{c}{} &  &  & $0.0013$ & $0.0013$ & $0.0009$ & $0.0009$ & $%
0.0009$ & $0.0013$ \\ 
\multicolumn{1}{c}{$35$} &  &  & $0.8992$ & $0.9010$ & $0.8954$ & $0.8955$ & 
$(0.8269,$ & $0.8399$ \\ 
\multicolumn{1}{c}{} &  &  & $0.0009$ & $0.0009$ & $0.0007$ & $0.0007$ & $%
0.0009$ & $0.0013$ \\ \hline
\end{tabular}

\begin{tabular}{lccccccc}
\multicolumn{8}{l}{Table 5.5(c) Classical and generalized interval estimates
of $R_{1,3}$ when the common scale parameter $\lambda $ is known $(\lambda
=10)$} \\ 
&  &  &  &  &  &  &  \\ \hline
Sample size & Parameters & Reliability & \multicolumn{3}{c}{Classical} & 
\multicolumn{1}{c}{} & \multicolumn{1}{c}{Generalized} \\ 
\cline{1-6}\cline{8-8}
\multicolumn{1}{c}{$n$} & $\mathbf{\beta }$ & $R_{1,3}$ & ACI & PBCI & BTCI
&  & GCI \\ \cline{1-3}\cline{4-6}\cline{8-8}
\multicolumn{1}{c}{$10$} & $(4,2)$ & $0.5429$ & $(0.3475,0.7704)$ & $%
(0.3470,0.7700)$ & $(0.3471,0.7700)$ &  & $(0.3591,0.7319)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.4229/0.9092$ & $0.4230/0.9100$ & $%
0.4228/0.9090$ &  & $0.3728/0.9552$ \\ 
\multicolumn{1}{c}{$15$} &  &  & $(0.3764,0.7269)$ & $(0.3760,0.7260)$ & $%
(0.3760,0.7266)$ &  & $(0.3844,0.7030)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.3506/0.9228$ & $0.3501/0.9222$ & $%
0.3501/0.9223$ &  & $0.3186/0.9476$ \\ 
\multicolumn{1}{c}{$25$} &  &  & $(0.4109,0.6860)$ & $(0.4100,0.6858)$ & $%
(0.4101,0.6857)$ &  & $(0.4152,0.6726)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.2752/0.9412$ & $0.2751/0.9401$ & $%
0.2747/0.9401$ &  & $0.2573/0.9520$ \\ 
\multicolumn{1}{c}{$35$} &  &  & $(0.4293,0.6630)$ & $(0.4289,0.6628)$ & $%
(0.4289,0.6625)$ &  & $(0.4321,0.6538)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.2336/0.9400$ & $0.2335/0.9389$ & $%
0.2333/0.9387$ &  & $0.2217/0.9456$ \\ \hline
\multicolumn{1}{c}{$10$} & $(4,4)$ & $0.7500$ & $(0.5698,0.9346)$ & $%
(0.5695,0.9340)$ & $(0.5693,0.9344)$ &  & $(0.5763,0.8872)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.3648/0.9076$ & $0.3641/0.9074$ & $%
0.3644/0.9070$ &  & $0.3109/0.9692$ \\ 
\multicolumn{1}{c}{$15$} &  &  & $(0.5998,0.9038)$ & $(0.5993,0.9035)$ & $%
(0.5995,0.9031)$ &  & $(0.6022,0.8712)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.3040/0.9212$ & $0.3035/0.9210$ & $%
0.3035/0.9209$ &  & $0.2690/0.9588$ \\ 
\multicolumn{1}{c}{$25$} &  &  & $(0.6304,0.8700)$ & $(0.6301,0.8698)$ & $%
(0.6298,0.8697)$ &  & $(0.6307,0.8505)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.2395/0.9312$ & $0.2393/0.9308$ & $%
0.2394/0.9301$ &  & $0.2197/0.9568$ \\ 
\multicolumn{1}{c}{$35$} &  &  & $(0.6486,0.8524)$ & $0.6481,0.8521)$ & $%
0.6481,0.8520)$ &  & $(0.6480,0.8385)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.2038/0.9416$ & $0.2031/0.9413$ & $%
0.2031/0.9410$ &  & $0.1905/0.9552$ \\ \hline
\multicolumn{1}{c}{$10$} & $(4,6)$ & $0.8476$ & $(0.7036,0.9869)$ & $%
(0.7028,0.9861)$ & $(0.7033,0.9850)$ &  & $(0.7097,0.9431)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.2833/0.8892$ & $0.2830/0.8889$ & $%
0.2830/0.8889$ &  & $0.2334/0.9832$ \\ 
\multicolumn{1}{c}{$15$} &  &  & $(0.7269,0.9628)$ & $(0.7261,0.9625)$ & $%
(0.7263,0.9621)$ &  & $(0.7290,0.9323$ \\ 
\multicolumn{1}{c}{} &  &  & $0.2359/0.9068$ & $0.2350/0.9061$ & $%
0.2355/0.9065$ &  & $0.2033/0.9712$ \\ 
\multicolumn{1}{c}{$25$} &  &  & $(0.7541,0.9384)$ & $(0.7539,0.9380)$ & $%
(0.7539,0.9384)$ &  & $(0.7532,0.9196)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.1843/0.9224$ & $0.1838/0.9218$ & $%
0.1843/0.9220$ &  & $0.1664/0.9628$ \\ 
\multicolumn{1}{c}{$35$} &  &  & $(0.7667,0.9241)$ & $(0.7661,0.9228)$ & $%
(0.7666,0.9240)$ &  & $(0.7656,0.9109$ \\ 
\multicolumn{1}{c}{} &  &  & $0.1574/0.9336$ & $0.1571/0.9332$ & $%
0.1571/0.9331$ &  & $0.1453/0.9564$ \\ \hline
\multicolumn{1}{c}{$10$} & $(4,8)$ & $0.9000$ & $(0.7862,1.0046)$ & $%
(0.7859,1.0044)$ & $(0.7860,1.0040)$ &  & $(0.7941,0.9667)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.2183/0.8844$ & $0.2181/0.8840$ & $%
0.2180/0.8844$ &  & $0.1726/0.9824$ \\ 
\multicolumn{1}{c}{$15$} &  &  & $(0.8024,0.9857)$ & $(0.8022,0.9851)$ & $%
(0.8020,0.9857)$ &  & $(0.8064,0.9593)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.1834/0.9116$ & $0.1830/0.9111$ & $%
0.1834/0.9101$ &  & $0.1528/0.9768$ \\ 
\multicolumn{1}{c}{$25$} &  &  & $(0.8269,0.9679)$ & $(0.8264,0.9674)$ & $%
(0.8266,0.9676)$ &  & $(0.8264,0.9514)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.1410/0.9188$ & $0.1408/0.9185$ & $%
0.1409/0.9183$ &  & $0.1250/0.9708$ \\ 
\multicolumn{1}{c}{$35$} &  &  & $(0.8399,0.9585)$ & $(0.8395,0.9581)$ & $%
(0.8391,0.9581)$ &  & $(0.8384,0.9465)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.1186/0.9352$ & $0.1180/0.9350$ & $%
0.1182/0.9348$ &  & $0.1081/0.9660$ \\ \hline
\end{tabular}

\begin{tabular}{lcccccc}
\multicolumn{7}{l}{Table 5.5(d) \ Bayesian interval estimates of $R_{1,3}$
when the common scale parameter $\lambda $ is known $(\lambda =10)$} \\ 
&  &  &  &  &  &  \\ \hline
Sample size & Parameters & Reliability & \multicolumn{4}{c}{Bayesian} \\ 
\hline
\multicolumn{1}{c}{$n$} & $\mathbf{\beta }$ & $R_{1,3}$ & $^{SE}\text{BCI}%
^{MCMC}$ & $^{SE}$HDPI$^{MCMC}$ & $^{LINEX}\text{BCI}^{MCMC}$ & $^{LINEX}$%
HPDI$^{MCMC}$ \\ \cline{1-3}\cline{4-7}
\multicolumn{1}{c}{$10$} & $(4,2)$ & $0.5429$ & $(0.3475,0.7704)$ & $%
(0.3470,0.7700)$ & $(0.3471,0.7700)$ & $(0.3591,0.7319)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.4229/0.9092$ & $0.4230/0.9100$ & $%
0.4228/0.9090$ & $0.3728/0.9552$ \\ 
\multicolumn{1}{c}{$15$} &  &  & $(0.3764,0.7269)$ & $(0.3760,0.7260)$ & $%
(0.3760,0.7266)$ & $(0.3844,0.7030)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.3506/0.9228$ & $0.3501/0.9222$ & $%
0.3501/0.9223$ & $0.3186/0.9476$ \\ 
\multicolumn{1}{c}{$25$} &  &  & $(0.4109,0.6860)$ & $(0.4100,0.6858)$ & $%
(0.4101,0.6857)$ & $(0.4152,0.6726)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.2752/0.9412$ & $0.2751/0.9401$ & $%
0.2747/0.9401$ & $0.2573/0.9520$ \\ 
\multicolumn{1}{c}{$35$} &  &  & $(0.4293,0.6630)$ & $(0.4289,0.6628)$ & $%
(0.4289,0.6625)$ & $(0.4321,0.6538)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.2336/0.9400$ & $0.2335/0.9389$ & $%
0.2333/0.9387$ & $0.2217/0.9456$ \\ \hline
\multicolumn{1}{c}{$10$} & $(4,4)$ & $0.7500$ & $(0.5698,0.9346)$ & $%
(0.5695,0.9340)$ & $(0.5693,0.9344)$ & $(0.5763,0.8872)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.3648/0.9076$ & $0.3641/0.9074$ & $%
0.3644/0.9070$ & $0.3109/0.9692$ \\ 
\multicolumn{1}{c}{$15$} &  &  & $(0.5998,0.9038)$ & $(0.5993,0.9035)$ & $%
(0.5995,0.9031)$ & $(0.6022,0.8712)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.3040/0.9212$ & $0.3035/0.9210$ & $%
0.3035/0.9209$ & $0.2690/0.9588$ \\ 
\multicolumn{1}{c}{$25$} &  &  & $(0.6304,0.8700)$ & $(0.6301,0.8698)$ & $%
(0.6298,0.8697)$ & $(0.6307,0.8505)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.2395/0.9312$ & $0.2393/0.9308$ & $%
0.2394/0.9301$ & $0.2197/0.9568$ \\ 
\multicolumn{1}{c}{$35$} &  &  & $(0.6486,0.8524)$ & $0.6481,0.8521)$ & $%
0.6481,0.8520)$ & $(0.6480,0.8385)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.2038/0.9416$ & $0.2031/0.9413$ & $%
0.2031/0.9410$ & $0.1905/0.9552$ \\ \hline
\multicolumn{1}{c}{$10$} & $(4,6)$ & $0.8476$ & $(0.7036,0.9869)$ & $%
(0.7028,0.9861)$ & $(0.7033,0.9850)$ & $(0.7097,0.9431)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.2833/0.8892$ & $0.2830/0.8889$ & $%
0.2830/0.8889$ & $0.2334/0.9832$ \\ 
\multicolumn{1}{c}{$15$} &  &  & $(0.7269,0.9628)$ & $(0.7261,0.9625)$ & $%
(0.7263,0.9621)$ & $(0.7290,0.9323$ \\ 
\multicolumn{1}{c}{} &  &  & $0.2359/0.9068$ & $0.2350/0.9061$ & $%
0.2355/0.9065$ & $0.2033/0.9712$ \\ 
\multicolumn{1}{c}{$25$} &  &  & $(0.7541,0.9384)$ & $(0.7539,0.9380)$ & $%
(0.7539,0.9384)$ & $(0.7532,0.9196)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.1843/0.9224$ & $0.1838/0.9218$ & $%
0.1843/0.9220$ & $0.1664/0.9628$ \\ 
\multicolumn{1}{c}{$35$} &  &  & $(0.7667,0.9241)$ & $(0.7661,0.9228)$ & $%
(0.7666,0.9240)$ & $(0.7656,0.9109$ \\ 
\multicolumn{1}{c}{} &  &  & $0.1574/0.9336$ & $0.1571/0.9332$ & $%
0.1571/0.9331$ & $0.1453/0.9564$ \\ \hline
\multicolumn{1}{c}{$10$} & $(4,8)$ & $0.9000$ & $(0.7862,1.0046)$ & $%
(0.7859,1.0044)$ & $(0.7860,1.0040)$ & $(0.7941,0.9667)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.2183/0.8844$ & $0.2181/0.8840$ & $%
0.2180/0.8844$ & $0.1726/0.9824$ \\ 
\multicolumn{1}{c}{$15$} &  &  & $(0.8024,0.9857)$ & $(0.8022,0.9851)$ & $%
(0.8020,0.9857)$ & $(0.8064,0.9593)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.1834/0.9116$ & $0.1830/0.9111$ & $%
0.1834/0.9101$ & $0.1528/0.9768$ \\ 
\multicolumn{1}{c}{$25$} &  &  & $(0.8269,0.9679)$ & $(0.8264,0.9674)$ & $%
(0.8266,0.9676)$ & $(0.8264,0.9514)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.1410/0.9188$ & $0.1408/0.9185$ & $%
0.1409/0.9183$ & $0.1250/0.9708$ \\ 
\multicolumn{1}{c}{$35$} &  &  & $(0.8399,0.9585)$ & $(0.8395,0.9581)$ & $%
(0.8391,0.9581)$ & $(0.8384,0.9465)$ \\ 
\multicolumn{1}{c}{} &  &  & $0.1186/0.9352$ & $0.1180/0.9350$ & $%
0.1182/0.9348$ & $0.1081/0.9660$ \\ \hline
\end{tabular}

\begin{tabular}{ccccccccc}
\multicolumn{9}{l}{Table 5.6(a) Classical and generalized point estimates of 
$R_{2,4}$ when the common scale} \\ 
\multicolumn{9}{l}{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ parameter $\lambda $ is
known $(\lambda =10)$} \\ 
&  &  &  &  &  &  &  &  \\ \hline
Sample size & Parameters & Reliability & \multicolumn{4}{c}{Classical} &  & 
Generalized \\ \cline{1-3}\cline{5-7}\cline{9-9}
$n$ & $\mathbf{\beta }$ & $R_{2,4}$ &  & $\widehat{R}_{s,k}^{M}$ & $\widehat{%
R}_{s,k}^{U}$ & $\widehat{R}_{s,k}^{\ast }$ &  & $\widehat{R}_{s,k}^{G}$ \\ 
\cline{1-3}\cline{5-7}\cline{9-9}
$10$ & $(4,2)$ & $0.3905$ &  & $0.4071$ & $0.3905$ & $0.3982$ &  & $0.3989$
\\ 
&  &  &  & $0.0108$ & $0.0108$ & $0.0066$ &  & $0.0066$ \\ 
$15$ &  &  &  & $0.3998$ & $0.3886$ & $0.3952$ &  & $0.3956$ \\ 
&  &  &  & $0.0064$ & $0.0064$ & $0.0046$ &  & $0.0046$ \\ 
$25$ &  &  &  & $0.3980$ & $0.3913$ & $0.3955$ &  & $0.3957$ \\ 
&  &  &  & $0.0038$ & $0.0038$ & $0.0031$ &  & $0.0031$ \\ 
$35$ &  &  &  & $0.3957$ & $0.3909$ & $0.3942$ &  & $0.3942$ \\ 
&  &  &  & $0.0029$ & $0.0029$ & $0.0025$ &  & $0.0025$ \\ \hline
$10$ & $(4,4)$ & $0.6000$ &  & $0.6085$ & $0.5986$ & $0.5950$ &  & $0.5953$
\\ 
&  &  &  & $0.0115$ & $0.0126$ & $0.0059$ &  & $0.0059$ \\ 
$15$ &  &  &  & $0.6074$ & $0.6006$ & $0.5981$ &  & $0.5983$ \\ 
&  &  &  & $0.0077$ & $0.0081$ & $0.0047$ &  & $0.0047$ \\ 
$25$ &  &  &  & $0.6045$ & $0.6004$ & $0.5989$ &  & $0.5990$ \\ 
&  &  &  & $0.0048$ & $0.0050$ & $0.0036$ &  & $0.0036$ \\ 
$35$ &  &  &  & $0.6031$ & $0.6001$ & $0.5992$ &  & $0.5992$ \\ 
&  &  &  & $0.0034$ & $0.0035$ & $0.0027$ &  & $0.0027$ \\ \hline
$10$ & $(4,6)$ & $0.7229$ &  & $0.7267$ & $0.7235$ & $0.7130$ &  & $0.7129$
\\ 
&  &  &  & $0.0093$ & $0.0105$ & $0.0043$ &  & $0.0042$ \\ 
$15$ &  &  &  & $0.7257$ & $0.7235$ & $0.7158$ &  & $0.7158$ \\ 
&  &  &  & $0.0064$ & $0.0069$ & $0.0036$ &  & $0.0036$ \\ 
$25$ &  &  &  & $0.7246$ & $0.7232$ & $0.7181$ &  & $0.7181$ \\ 
&  &  &  & $0.0040$ & $0.0042$ & $0.0027$ &  & $0.0027$ \\ 
$35$ &  &  &  & $0.7239$ & $0.7229$ & $0.7192$ &  & $0.7192$ \\ 
&  &  &  & $0.0029$ & $0.0030$ & $0.0022$ &  & $0.0022$ \\ \hline
$10$ & $(4,8)$ & $0.8000$ &  & $0.7995$ & $0.8005$ & $0.7880$ &  & $0.7878$
\\ 
&  &  &  & $0.0070$ & $0.0077$ & $0.0029$ &  & $0.0029$ \\ 
$15$ &  &  &  & $0.8016$ & $0.8024$ & $0.7922$ &  & $0.7921$ \\ 
&  &  &  & $0.0048$ & $0.0052$ & $0.0025$ &  & $0.0025$ \\ 
$25$ &  &  &  & $0.7989$ & $0.7992$ & $0.7929$ &  & $0.7928$ \\ 
&  &  &  & $0.0030$ & $0.0031$ & $0.0019$ &  & $0.0019$ \\ 
$35$ &  &  &  & $0.7998$ & $0.8000$ & $0.7952$ &  & $0.7952$ \\ 
&  &  &  & $0.0020$ & $0.0021$ & $0.0015$ &  & $0.0015$ \\ \hline
\end{tabular}

\begin{tabular}{ccccccccc}
\multicolumn{9}{l}{Table 5.6(b) Bayesian point estimates of $R_{2,4}$ when
the common scale parameter $\lambda $ is known $(\lambda =10)$} \\ 
&  &  &  &  &  &  &  &  \\ \hline
Sample size & Parameters & Reliability & \multicolumn{6}{c}{Bayesian} \\ 
\hline
$n$ & $\mathbf{\beta }$ & $R_{2,4}$ & $\widehat{R}_{s,k}^{SE}$ & $\widehat{R}%
_{s,k}^{LINEX}$ & $^{SE}\widehat{R}_{s,k}^{Lin}$ & $^{LINEX}\widehat{R}%
_{s,k}^{Lin}$ & $^{SE}\widehat{R}_{s,k}^{MCMC}$ & $^{LINEX}\widehat{R}%
_{s,k}^{MCMC}$ \\ \hline
$10$ & $(4,2)$ & $0.3905$ & $0.4071$ & $0.3905$ & $0.3982$ & $0.3989$ & $%
0.3982$ & $0.3989$ \\ 
&  &  & $0.0108$ & $0.0108$ & $0.0066$ & $0.0066$ & $0.0066$ & $0.0066$ \\ 
$15$ &  &  & $0.3998$ & $0.3886$ & $0.3952$ & $0.3956$ & $0.3952$ & $0.3956$
\\ 
&  &  & $0.0064$ & $0.0064$ & $0.0046$ & $0.0046$ & $0.0046$ & $0.0046$ \\ 
$25$ &  &  & $0.3980$ & $0.3913$ & $0.3955$ & $0.3957$ & $0.3980$ & $0.3958$
\\ 
&  &  & $0.0038$ & $0.0038$ & $0.0031$ & $0.0031$ & $0.0038$ & $0.0040$ \\ 
$35$ &  &  & $0.3957$ & $0.3909$ & $0.3942$ & $0.3942$ & $0.3957$ & $0.3958$
\\ 
&  &  & $0.0029$ & $0.0029$ & $0.0025$ & $0.0025$ & $0.0029$ & $0.0022$ \\ 
\hline
$10$ & $(4,4)$ & $0.6000$ & $0.6085$ & $0.5986$ & $0.5950$ & $0.5953$ & $%
0.5953$ & $0.5953$ \\ 
&  &  & $0.0115$ & $0.0126$ & $0.0059$ & $0.0059$ & $0.0059$ & $0.0060$ \\ 
$15$ &  &  & $0.6074$ & $0.6006$ & $0.5981$ & $0.5983$ & $0.5983$ & $0.5987$
\\ 
&  &  & $0.0077$ & $0.0081$ & $0.0047$ & $0.0047$ & $0.0048$ & $0.0047$ \\ 
$25$ &  &  & $0.6045$ & $0.6004$ & $0.5989$ & $0.5990$ & $0.5990$ & $0.5990$
\\ 
&  &  & $0.0048$ & $0.0050$ & $0.0036$ & $0.0036$ & $0.0037$ & $0.0038$ \\ 
$35$ &  &  & $0.6031$ & $0.6001$ & $0.5992$ & $0.5992$ & $0.5989$ & $0.5992$
\\ 
&  &  & $0.0034$ & $0.0035$ & $0.0027$ & $0.0027$ & $0.0027$ & $0.0097$ \\ 
\hline
$10$ & $(4,6)$ & $0.7229$ & $0.7267$ & $0.7235$ & $0.7130$ & $0.7129$ & $%
0.7129$ & $0.7129$ \\ 
&  &  & $0.0093$ & $0.0105$ & $0.0043$ & $0.0042$ & $0.0042$ & $0.0042$ \\ 
$15$ &  &  & $0.7257$ & $0.7235$ & $0.7158$ & $0.7158$ & $0.7159$ & $0.7159$
\\ 
&  &  & $0.0064$ & $0.0069$ & $0.0036$ & $0.0036$ & $0.0036$ & $0.0036$ \\ 
$25$ &  &  & $0.7246$ & $0.7232$ & $0.7181$ & $0.7181$ & $0.7232$ & $0.7232$
\\ 
&  &  & $0.0040$ & $0.0042$ & $0.0027$ & $0.0027$ & $0.0042$ & $0.0042$ \\ 
$35$ &  &  & $0.7239$ & $0.7229$ & $0.7192$ & $0.7192$ & $0.7192$ & $0.7192$
\\ 
&  &  & $0.0029$ & $0.0030$ & $0.0022$ & $0.0022$ & $0.0029$ & $0.0029$ \\ 
\hline
$10$ & $(4,8)$ & $0.8000$ & $0.7995$ & $0.8005$ & $0.7880$ & $0.7878$ & $%
0.7878$ & $0.7879$ \\ 
&  &  & $0.0070$ & $0.0077$ & $0.0029$ & $0.0029$ & $0.0077$ & $0.0077$ \\ 
$15$ &  &  & $0.8016$ & $0.8024$ & $0.7922$ & $0.7921$ & $0.7921$ & $0.7921$
\\ 
&  &  & $0.0048$ & $0.0052$ & $0.0025$ & $0.0025$ & $0.0025$ & $0.0026$ \\ 
$25$ &  &  & $0.7989$ & $0.7992$ & $0.7929$ & $0.7928$ & $0.7992$ & $0.7992$
\\ 
&  &  & $0.0030$ & $0.0031$ & $0.0019$ & $0.0019$ & $0.0019$ & $0.0019$ \\ 
$35$ &  &  & $0.7998$ & $0.8000$ & $0.7952$ & $0.7952$ & $0.7953$ & $0.7954$
\\ 
&  &  & $0.0020$ & $0.0021$ & $0.0015$ & $0.0015$ & $0.0015$ & $0.0015$ \\ 
\hline
\end{tabular}

\begin{tabular}{cccccccc}
\multicolumn{8}{l}{Table 5.6(c) Classical and generalized interval estimates
of $R_{2,4}$ when the common scale parameter $\lambda $ is known $(\lambda
=10)$} \\ 
&  &  &  &  &  &  &  \\ \hline
Sample size & Parameters & Reliability & \multicolumn{3}{c}{Classical} &  & 
Generalized \\ \cline{1-6}\cline{8-8}
$n$ & $\mathbf{\beta }$ & $R_{2,4}$ & ACI & PBCI & BTCI &  & GCI \\ 
\cline{1-3}\cline{4-6}\cline{8-8}
$10$ & $(4,2)$ & $0.3905$ & $(0.2182,0.5960)$ & $(0.2180,0.5959)$ & $%
(0.2178,0.5959)$ &  & $(0.2340,0.5663)$ \\ 
&  &  & $0.3778/0.9271$ & $0.3779/0.9272$ & $0.3773/0.9271$ &  & $%
0.3322/0.9548$ \\ 
$15$ &  &  & $(0.2443,0.5550)$ & $(0.2447,0.5550)$ & $(0.2444,0.5549)$ &  & $%
(0.2553,0.5375)$ \\ 
&  &  & $0.3103/0.9432$ & $0.3098/0.9430$ & $0.3100/0.9430$ &  & $%
0.2822/0.9604$ \\ 
$25$ &  &  & $(0.2771,0.5190)$ & $(0.2767,0.5189)$ & $(0.2770,0.5189)$ &  & $%
(0.2830,0.5100)$ \\ 
&  &  & $0.2419/0.9448$ & $0.2411/0.9444$ & $0.2411/0.9445$ &  & $%
0.2269/0.9556$ \\ 
$35$ &  &  & $(0.2935,0.4980)$ & $(0.2931,0.4979)$ & $(0.2932,0.4982)$ &  & $%
(0.2975,0.4920)$ \\ 
&  &  & $0.2045/0.9412$ & $0.2043/0.9401$ & $0.2041/0.9411$ &  & $%
0.1945/0.9432$ \\ \hline
$10$ & $(4,4)$ & $0.6000$ & $(0.4018,0.8153)$ & $(0.4012,0.8151)$ & $%
(0.4017,0.8153)$ &  & $(0.4172,0.7667)$ \\ 
&  &  & $0.4134/0.9200$ & $0.4130/0.9197$ & $0.4134/0.9203$ &  & $%
0.3495/0.9672$ \\ 
$15$ &  &  & $(0.4357,0.7790)$ & $(0.4355,0.7789)$ & $(0.4356,0.7791)$ &  & $%
(0.4447,0.7467)$ \\ 
&  &  & $0.3432/0.9372$ & $0.3430/0.9370$ & $0.3431/0.9372$ &  & $%
0.3020/0.9716$ \\ 
$25$ &  &  & $(0.4699,0.7391)$ & $(0.4691,0.7388)$ & $(0.4693,0.7390)$ &  & $%
(0.4740,0.7206)$ \\ 
&  &  & $0.2692/0.9364$ & $0.2688/0.9361$ & $0.2691/0.9361$ &  & $%
0.2466/0.9572$ \\ 
$35$ &  &  & $(0.4886,0.7175)$ & $(0.4885,0.7175)$ & $(0.4885,0.7175)$ &  & $%
(0.4911,0.7047)$ \\ 
&  &  & $0.2289/0.9480$ & $0.2283/0.9478$ & $0.2284/0.9475$ &  & $%
0.2136/0.9576$ \\ \hline
$10$ & $(4,6)$ & $0.7229$ & $(0.5394,0.9141)$ & $(0.5391,0.9140)$ & $%
(0.5391,0.9140)$ &  & $(0.5537,0.8601)$ \\ 
&  &  & $0.3747/0.9032$ & $0.3742/0.9031$ & $0.3744/0.9030$ &  & $%
0.3065/0.9752$ \\ 
$15$ &  &  & $(0.5699,0.8816)$ & $(0.5695,0.8811)$ & $(0.5697,0.8815)$ &  & $%
(0.5776,0.8450)$ \\ 
&  &  & $0.3117/0.9172$ & $0.3112/0.9170$ & $0.3116/0.9170$ &  & $%
0.2674/0.9700$ \\ 
$25$ &  &  & $(0.6019,0.8472)$ & $(0.6009,0.8467)$ & $(0.6011,0.8470)$ &  & $%
(0.6051,0.8254)$ \\ 
&  &  & $0.2452/0.9308$ & $0.2451/0.9303$ & $0.2450/0.9300$ &  & $%
0.2203/0.9596$ \\ 
$35$ &  &  & $(0.6196,0.8283)$ & $(0.6191,0.8282)$ & $(0.6195,0.8280)$ &  & $%
(0.6209,0.8127)$ \\ 
&  &  & $0.2087/0.9332$ & $0.2088/0.9333$ & $0.2080/0.9330$ &  & $%
0.1918/0.9540$ \\ \hline
$10$ & $(4,8)$ & $0.8000$ & $(0.6376,0.9614)$ & $(0.6371,0.9611)$ & $%
(0.6371,0.9614)$ &  & $(0.6531,0.9092)$ \\ 
&  &  & $0.3238/0.8992$ & $0.3233/0.8989$ & $0.3233/0.8992$ &  & $%
0.2561/0.9844$ \\ 
$15$ &  &  & $(0.6680,0.9353)$ & $(0.6678,0.9350)$ & $(0.6680,0.9352)$ &  & $%
(0.6750,0.8988)$ \\ 
&  &  & $0.2674/0.9040$ & $0.2671/0.9037$ & $0.2673/0.9040$ &  & $%
0.2239/0.9664$ \\ 
$25$ &  &  & $(0.6929,0.9048)$ & $(0.6928,0.9041)$ & $(0.6929,0.9045$ &  & $%
(0.6961,0.8826)$ \\ 
&  &  & $0.2119/0.9252$ & $0.2111/0.9251$ & $0.2111/0.9250$ &  & $%
0.1866/0.9648$ \\ 
$35$ &  &  & $(0.7098,0.8897)$ & $(0.7092,0.8892)$ & $(0.7099,0.8897)$ &  & $%
(0.7110,0.8739)$ \\ 
&  &  & $0.1799/0.9372$ & $0.1793/0.9371$ & $0.1799/0.9371$ &  & $%
0.1630/0.9628$ \\ \hline
\end{tabular}

\begin{tabular}{ccccccc}
\multicolumn{7}{l}{Table 5.6(d) Bayesian interval estimates of $R_{2,4}$
when the common scale parameter $\lambda $ is known $(\lambda =10)$} \\ 
&  &  &  &  &  &  \\ \hline
Sample size & Parameters & Reliability & \multicolumn{4}{c}{Bayesian} \\ 
\hline
$n$ & $\mathbf{\beta }$ & $R_{2,4}$ & $^{SE}\text{BCI}^{MCMC}$ & $^{SE}$HDPI$%
^{MCMC}$ & $^{LINEX}\text{BCI}^{MCMC}$ & $^{LINEX}$HPDI$^{MCMC}$ \\ 
\cline{1-3}\cline{4-7}
$10$ & $(4,2)$ & $0.3905$ & $(0.2182,0.5960)$ & $(0.2180,0.5959)$ & $%
(0.2178,0.5959)$ & $(0.2340,0.5663)$ \\ 
&  &  & $0.3778/0.9271$ & $0.3779/0.9272$ & $0.3773/0.9271$ & $0.3322/0.9548$
\\ 
$15$ &  &  & $(0.2443,0.5550)$ & $(0.2447,0.5550)$ & $(0.2444,0.5549)$ & $%
(0.2553,0.5375)$ \\ 
&  &  & $0.3103/0.9432$ & $0.3098/0.9430$ & $0.3100/0.9430$ & $0.2822/0.9604$
\\ 
$25$ &  &  & $(0.2771,0.5190)$ & $(0.2767,0.5189)$ & $(0.2770,0.5189)$ & $%
(0.2830,0.5100)$ \\ 
&  &  & $0.2419/0.9448$ & $0.2411/0.9444$ & $0.2411/0.9445$ & $0.2269/0.9556$
\\ 
$35$ &  &  & $(0.2935,0.4980)$ & $(0.2931,0.4979)$ & $(0.2932,0.4982)$ & $%
(0.2975,0.4920)$ \\ 
&  &  & $0.2045/0.9412$ & $0.2043/0.9401$ & $0.2041/0.9411$ & $0.1945/0.9432$
\\ \hline
$10$ & $(4,4)$ & $0.6000$ & $(0.4018,0.8153)$ & $(0.4012,0.8151)$ & $%
(0.4017,0.8153)$ & $(0.4172,0.7667)$ \\ 
&  &  & $0.4134/0.9200$ & $0.4130/0.9197$ & $0.4134/0.9203$ & $0.3495/0.9672$
\\ 
$15$ &  &  & $(0.4357,0.7790)$ & $(0.4355,0.7789)$ & $(0.4356,0.7791)$ & $%
(0.4447,0.7467)$ \\ 
&  &  & $0.3432/0.9372$ & $0.3430/0.9370$ & $0.3431/0.9372$ & $0.3020/0.9716$
\\ 
$25$ &  &  & $(0.4699,0.7391)$ & $(0.4691,0.7388)$ & $(0.4693,0.7390)$ & $%
(0.4740,0.7206)$ \\ 
&  &  & $0.2692/0.9364$ & $0.2688/0.9361$ & $0.2691/0.9361$ & $0.2466/0.9572$
\\ 
$35$ &  &  & $(0.4886,0.7175)$ & $(0.4885,0.7175)$ & $(0.4885,0.7175)$ & $%
(0.4911,0.7047)$ \\ 
&  &  & $0.2289/0.9480$ & $0.2283/0.9478$ & $0.2284/0.9475$ & $0.2136/0.9576$
\\ \hline
$10$ & $(4,6)$ & $0.7229$ & $(0.5394,0.9141)$ & $(0.5391,0.9140)$ & $%
(0.5391,0.9140)$ & $(0.5537,0.8601)$ \\ 
&  &  & $0.3747/0.9032$ & $0.3742/0.9031$ & $0.3744/0.9030$ & $0.3065/0.9752$
\\ 
$15$ &  &  & $(0.5699,0.8816)$ & $(0.5695,0.8811)$ & $(0.5697,0.8815)$ & $%
(0.5776,0.8450)$ \\ 
&  &  & $0.3117/0.9172$ & $0.3112/0.9170$ & $0.3116/0.9170$ & $0.2674/0.9700$
\\ 
$25$ &  &  & $(0.6019,0.8472)$ & $(0.6009,0.8467)$ & $(0.6011,0.8470)$ & $%
(0.6051,0.8254)$ \\ 
&  &  & $0.2452/0.9308$ & $0.2451/0.9303$ & $0.2450/0.9300$ & $0.2203/0.9596$
\\ 
$35$ &  &  & $(0.6196,0.8283)$ & $(0.6191,0.8282)$ & $(0.6195,0.8280)$ & $%
(0.6209,0.8127)$ \\ 
&  &  & $0.2087/0.9332$ & $0.2088/0.9333$ & $0.2080/0.9330$ & $0.1918/0.9540$
\\ \hline
$10$ & $(4,8)$ & $0.8000$ & $(0.6376,0.9614)$ & $(0.6371,0.9611)$ & $%
(0.6371,0.9614)$ & $(0.6531,0.9092)$ \\ 
&  &  & $0.3238/0.8992$ & $0.3233/0.8989$ & $0.3233/0.8992$ & $0.2561/0.9844$
\\ 
$15$ &  &  & $(0.6680,0.9353)$ & $(0.6678,0.9350)$ & $(0.6680,0.9352)$ & $%
(0.6750,0.8988)$ \\ 
&  &  & $0.2674/0.9040$ & $0.2671/0.9037$ & $0.2673/0.9040$ & $0.2239/0.9664$
\\ 
$25$ &  &  & $(0.6929,0.9048)$ & $(0.6928,0.9041)$ & $(0.6929,0.9045$ & $%
(0.6961,0.8826)$ \\ 
&  &  & $0.2119/0.9252$ & $0.2111/0.9251$ & $0.2111/0.9250$ & $0.1866/0.9648$
\\ 
$35$ &  &  & $(0.7098,0.8897)$ & $(0.7092,0.8892)$ & $(0.7099,0.8897)$ & $%
(0.7110,0.8739)$ \\ 
&  &  & $0.1799/0.9372$ & $0.1793/0.9371$ & $0.1799/0.9371$ & $0.1630/0.9628$
\\ \hline
\end{tabular}

\bigskip

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\begin{center}
\bigskip\ \ 
\begin{tabular}{lcccccccccccc}
\multicolumn{13}{l}{Table 5.7(a) Empirical (true) Type-I error rates for
testing $\ H_{0}:R_{s,k}\leq R_{0}\,\ $vs.$\ \ H_{a}:R_{s,k}>R_{0}$ when
nominal\ } \\ 
\multicolumn{13}{l}{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (intended) level is $%
\gamma =0.05$\ with the known common scale parameter $\lambda =3$} \\ 
&  &  &  &  &  &  &  &  &  &  &  &  \\ \hline
$n$ & $\mathbf{\beta }$ & $R_{1,3}$ & $R_{0}$ & Generalized & Bayesian & 
Classical &  & $R_{2,4}$ & $R_{0}$ & Generalized & Bayesian & Classical \\ 
\hline
$10$ & $(4,2)$ & $0.5429$ & $0.50$ & $0.0490$ & $0.0059$ & $0.0070$ &  & $%
0.3905$ & $0.35$ & $0.0510$ & $0.0510$ & $0.0145$ \\ 
$15$ &  &  &  & $0.0450$ & $0.0050$ & $0.0058$ &  &  &  & $0.0489$ & $0.0541$
& $0.0125$ \\ 
$25$ &  &  &  & $0.0510$ & $0.0480$ & $0.0060$ &  &  &  & $0.0485$ & $0.0478$
& $0.0128$ \\ 
$35$ &  &  &  & $0.0491$ & $0.0480$ & $0.0063$ &  &  &  & $0.0510$ & $0.0478$
& $0.088$ \\ \hline
$10$ & $(4,4)$ & $0.7500$ & $0.70$ & $0.0481$ & $0.0030$ & $0.0031$ &  & $%
0.6000$ & $0.55$ & $0.0510$ & $0.0510$ & $0.0412$ \\ 
$15$ &  &  &  & $0.0510$ & $0.0500$ & $0.0281$ &  &  &  & $0.0478$ & $0.0510$
& $0.0415$ \\ 
$25$ &  &  &  & $0.0503$ & $0.0050$ & $0.0017$ &  &  &  & $0.0512$ & $0.0478$
& $0.0325$ \\ 
$35$ &  &  &  & $0.0540$ & $0.0570$ & $0.0125$ &  &  &  & $0.0499$ & $0.0510$
& $0.0324$ \\ \hline
$10$ & $(4,6)$ & $0.8476$ & $0.80$ & $0.0479$ & $0.0590$ & $0.0254$ &  & $%
0.7229$ & $0.65$ & $0.0510$ & $0.0541$ & $0.0254$ \\ 
$15$ &  &  &  & $0.0486$ & $0.0480$ & $0.0123$ &  &  &  & $0.0502$ & $0.0499$
& $0.0213$ \\ 
$25$ &  &  &  & $0.0512$ & $0.0480$ & $0.0325$ &  &  &  & $0.0513$ & $0.0499$
& $0.0215$ \\ 
$35$ &  &  &  & $0.01487$ & $0.0059$ & $0.0327$ &  &  &  & $0.0499$ & $%
0.0510 $ & $0.0113$ \\ \hline
$10$ & $(4,8)$ & $0.9000$ & $0.85$ & $0.0489$ & $0.0590$ & $0.0400$ &  & $%
0.8000$ & $0.75$ & $0.0501$ & $0.0541$ & $0.0413$ \\ 
$15$ &  &  &  & $0.0466$ & $0.0570$ & $0.0328$ &  &  &  & $0.4888$ & $0.0510$
& $0.0077$ \\ 
$25$ &  &  &  & $0.0485$ & $0.0059$ & $0.0214$ &  &  &  & $0.4789$ & $0.0541$
& $0.0012$ \\ 
$35$ &  &  &  & $0.0512$ & $0.0059$ & $0.0415$ &  &  &  & $0.0541$ & $0.0510$
& $0.0045$ \\ \hline
\end{tabular}

\begin{tabular}{lcccccccccccc}
\multicolumn{13}{l}{Table 5.7(b) Empirical (true) Type-I error rates for
testing $\ H_{0}:R_{s,k}\leq R_{0}\,\ $vs.$\ \ H_{a}:R_{s,k}>R_{0}$ when
nominal\ } \\ 
\multicolumn{13}{l}{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (intended) level is $%
\gamma =0.05$\ with the known common scale parameter $\lambda =10$} \\ 
&  &  &  &  &  &  &  &  &  &  &  &  \\ \hline
$n$ & $\mathbf{\beta }$ & $R_{1,3}$ & $R_{0}$ & Generalized & Bayesian & 
Classical &  & $R_{2,4}$ & $R_{0}$ & Generalized & Bayesian & Classical \\ 
\hline
$10$ & $(4,2)$ & $0.5429$ & $0.50$ & $0.0511$ & $0.0478$ & $0.0012$ &  & $%
0.3905$ & $0.35$ & $0.0512$ & $0.0498$ & $0.0124$ \\ 
$15$ &  &  &  & $0.0513$ & $0.0231$ & $0.0045$ &  &  &  & $0.0548$ & $0.0088$
& $0.0128$ \\ 
$25$ &  &  &  & $0.0489$ & $0.0478$ & $0.0078$ &  &  &  & $0.0510$ & $0.0145$
& $0.0088$ \\ 
$35$ &  &  &  & $0.0485$ & $0.0511$ & $0.0099$ &  &  &  & $0.0555$ & $0.0498$
& $0.0099$ \\ \hline
$10$ & $(4,4)$ & $0.7500$ & $0.70$ & $0.0478$ & $0.0231$ & $0.0012$ &  & $%
0.6000$ & $0.55$ & $0.0478$ & $0.0128$ & $0.0100$ \\ 
$15$ &  &  &  & $0.0498$ & $0.0222$ & $0.0100$ &  &  &  & $0.0498$ & $0.0145$
& $0.0099$ \\ 
$25$ &  &  &  & $0.0478$ & $0.0125$ & $0.0125$ &  &  &  & $0.0457$ & $0.0145$
& $0.0145$ \\ 
$35$ &  &  &  & $0.0456$ & $0.0231$ & $0.0123$ &  &  &  & $0.0498$ & $0.0145$
& $0.0179$ \\ \hline
$10$ & $(4,6)$ & $0.8476$ & $0.80$ & $0.0511$ & $0.0511$ & $0.0236$ &  & $%
0.7229$ & $0.65$ & $0.0478$ & $0.0400$ & $0.0258$ \\ 
$15$ &  &  &  & $0.0509$ & $0.0222$ & $0.0223$ &  &  &  & $0.0513$ & $0.0088$
& $0.0248$ \\ 
$25$ &  &  &  & $0.0478$ & $0.0222$ & $0.0145$ &  &  &  & $0.0511$ & $0.0145$
& $0.0325$ \\ 
$35$ &  &  &  & $0.0499$ & $0.0222$ & $0.0128$ &  &  &  & $0.0547$ & $0.0547$
& $0.0125$ \\ \hline
$10$ & $(4,8)$ & $0.9000$ & $0.85$ & $0.0456$ & $0.0511$ & $0.0222$ &  & $%
0.8000$ & $0.75$ & $0.0555$ & $0.0498$ & $0.0410$ \\ 
$15$ &  &  &  & $0.0477$ & $0.0478$ & $0.0114$ &  &  &  & $0.0547$ & $0.0400$
& $0.0124$ \\ 
$25$ &  &  &  & $0.0518$ & $0.0231$ & $0.0231$ &  &  &  & $0.0512$ & $0.0400$
& $0.0400$ \\ 
$35$ &  &  &  & $0.0498$ & $0.0231$ & $0.0224$ &  &  &  & $0.0478$ & $0.0478$
& $0.0128$ \\ \hline
\end{tabular}

\bigskip

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\end{center}

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\begin{center}
\begin{tabular}{lcccccccccc}
\multicolumn{11}{l}{Table 5.8(a)$\ $Comparison of powers for testing $\
H_{0}:R_{1,3}\leq 0.5429\ $vs $H_{a}:R_{1,3}>0.5429$} \\ 
\multicolumn{11}{l}{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ without and after\
adjusting the size at $\gamma =0.05$ when the common parameter} \\ 
\multicolumn{11}{l}{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ is known $(\lambda =3)$%
} \\ 
&  &  &  &  &  &  &  &  &  &  \\ \hline
\multicolumn{3}{c}{Parameters} &  & \multicolumn{3}{c}{Without adjusting the
size} &  & \multicolumn{3}{c}{After adjusting the size} \\ 
\cline{1-3}\cline{5-7}\cline{9-11}
$n$ & $\mathbf{\beta }$ & $R_{1,3}$ &  & Generalized & Bayesian & Classical
&  & Generalized & Bayesian & Classical \\ \cline{1-3}\cline{5-7}\cline{9-11}
$10$ & $(4,2)$ & $0.5429$ &  & $0.1151$ & $0.0630$ & $0.0630$ &  & $0.0500$
& $0.0500$ & $0.0500$ \\ 
$15$ &  &  &  & $0.1142$ & $0.1217$ & $0.0592$ &  & $0.1138$ & $0.0500$ & $%
0.0612$ \\ 
$25$ &  &  &  & $0.1178$ & $0.1217$ & $0.0698$ &  & $0.1161$ & $0.0500$ & $%
0.0789$ \\ 
$35$ &  &  &  & $0.1154$ & $0.0630$ & $0.0657$ &  & $0.1175$ & $0.0754$ & $%
0.0754$ \\ \hline
$10$ & $(4,4)$ & $0.7500$ &  & $0.2481$ & $0.1125$ & $0.1125$ &  & $0.2400$
& $0.0754$ & $0.1145$ \\ 
$15$ &  &  &  & $0.2441$ & $0.1125$ & $0.1127$ &  & $0.2389$ & $0.0500$ & $%
0.1189$ \\ 
$25$ &  &  &  & $0.2145$ & $0.0630$ & $0.1217$ &  & $0.2082$ & $0.0754$ & $%
0.1245$ \\ 
$35$ &  &  &  & $0.2345$ & $0.2569$ & $0.1354$ &  & $0.2333$ & $0.0500$ & $%
0.1256$ \\ \hline
$10$ & $(4,6)$ & $0.8476$ &  & $0.5879$ & $0.2569$ & $0.2569$ &  & $0.5414$
& $0.0754$ & $0.2456$ \\ 
$15$ &  &  &  & $0.5789$ & $0.2569$ & $0.3512$ &  & $0.5412$ & $0.3542$ & $%
0.2889$ \\ 
$25$ &  &  &  & $0.5887$ & $0.3489$ & $0.3489$ &  & $0.5879$ & $0.3542$ & $%
0.3542$ \\ 
$35$ &  &  &  & $0.5456$ & $0.4415$ & $0.4415$ &  & $0.5312$ & $0.5312$ & $%
0.4412$ \\ \hline
$10$ & $(4,8)$ & $0.9000$ &  & $0.8011$ & $0.4415$ & $0.6123$ &  & $0.7889$
& $0.5312$ & $0.5555$ \\ 
$15$ &  &  &  & $0.8951$ & $0.4415$ & $0.6879$ &  & $0.8045$ & $0.5312$ & $%
0.6415$ \\ 
$25$ &  &  &  & $0.8561$ & $0.6879$ & $0.7412$ &  & $0.8412$ & $0.6889$ & $%
0.6889$ \\ 
$35$ &  &  &  & $0.8893$ & $0.6879$ & $0.7425$ &  & $0.8745$ & $0.6889$ & $%
0.7850$ \\ \hline
\end{tabular}

\begin{tabular}{lcccccccccc}
\multicolumn{11}{l}{Table 5.8(b)$\ $Comparison of powers for testing $\
H_{0}:R_{2,4}\leq 0.0.5429\ $vs $H_{a}:R_{2,4}>0.5429$} \\ 
\multicolumn{11}{l}{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ without and after\
adjusting the size at $\gamma =0.05$ when the common scale parameter} \\ 
\multicolumn{11}{l}{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ is known $(\lambda =3)$%
} \\ 
&  &  &  &  &  &  &  &  &  &  \\ \hline
\multicolumn{3}{c}{Parameters} &  & \multicolumn{3}{c}{Without adjusting the
size} &  & \multicolumn{3}{c}{After adjusting the size} \\ 
\cline{1-3}\cline{5-7}\cline{9-11}
$n$ & $\mathbf{\beta }$ & $R_{2,4}$ &  & Generalized & Bayesian & Classical
&  & Generalized & Bayesian & Classical \\ \cline{1-3}\cline{5-11}
$10$ & $(4,2)$ & $0.5429$ &  & $0.1180$ & $0.1180$ & $0.0660$ &  & $0.0500$
& $0.0553$ & $0.0553$ \\ 
$15$ &  &  &  & $0.1010$ & $0.1180$ & $0.0712$ &  & $0.0998$ & $0.0553$ & $%
0.0621$ \\ 
$25$ &  &  &  & $0.1021$ & $0.1180$ & $0.0722$ &  & $0.1000$ & $0.0553$ & $%
0.0702$ \\ 
$35$ &  &  &  & $0.1225$ & $0.0712$ & $0.0741$ &  & $0.1198$ & $0.0553$ & $%
0.0715$ \\ \hline
$10$ & $(4,4)$ & $0.7500$ &  & $0.2222$ & $0.0712$ & $0.1215$ &  & $0.1998$
& $0.2000$ & $0.1125$ \\ 
$15$ &  &  &  & $0.2112$ & $0.0712$ & $0.1015$ &  & $0.2000$ & $0.0715$ & $%
0.1001$ \\ 
$25$ &  &  &  & $0.3125$ & $0.0712$ & $0.2451$ &  & $0.2145$ & $0.2000$ & $%
0.1198$ \\ 
$35$ &  &  &  & $0.3546$ & $0.2451$ & $0.2415$ &  & $0.3212$ & $0.0715$ & $%
0.2356$ \\ \hline
$10$ & $(4,6)$ & $0.8476$ &  & $0.4115$ & $0.3999$ & $0.3874$ &  & $0.3998$
& $0.2000$ & $0.3789$ \\ 
$15$ &  &  &  & $0.4899$ & $0.2451$ & $0.3899$ &  & $0.3454$ & $0.0715$ & $%
0.3877$ \\ 
$25$ &  &  &  & $0.5551$ & $0.3999$ & $0.3999$ &  & $0.4597$ & $0.2000$ & $%
0.3845$ \\ 
$35$ &  &  &  & $0.5789$ & $0.3999$ & $0.4521$ &  & $0.5412$ & $0.4852$ & $%
0.4511$ \\ \hline
$10$ & $(4,8)$ & $0.9000$ &  & $0.6889$ & $0.3999$ & $0.4887$ &  & $0.5778$
& $0.4852$ & $0.4852$ \\ 
$15$ &  &  &  & $0.7888$ & $0.8888$ & $0.6552$ &  & $0.6589$ & $0.4852$ & $%
0.5879$ \\ 
$25$ &  &  &  & $0.8888$ & $0.8888$ & $0.7858$ &  & $0.7777$ & $0.6666$ & $%
0.6666$ \\ 
$35$ &  &  &  & $0.8994$ & $0.8888$ & $0.7889$ &  & $0.8412$ & $0.6666$ & $%
0.6894$ \\ \hline
\end{tabular}

\begin{tabular}{lcccccccccc}
\hline
\multicolumn{11}{l}{Table 5.8(c)$\ $omparison of powers for testing $\
H_{0}:R_{1,3}\leq 0.5429\ $vs $H_{a}:R_{1,3}>0.5429$} \\ 
\multicolumn{11}{l}{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ without and after\
adjusting the size at $\gamma =0.05$ when the common scale parameter} \\ 
\multicolumn{11}{l}{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ is known $(\lambda
=10)$} \\ 
&  &  &  &  &  &  &  &  &  &  \\ \hline
\multicolumn{3}{c}{Parameters} &  & \multicolumn{3}{c}{Without adjusting the
size} &  & \multicolumn{3}{c}{After adjusting the size} \\ 
\cline{1-3}\cline{5-7}\cline{9-11}
$n$ & $\mathbf{\beta }$ & $R_{1,3}$ &  & Generalized & Bayesian & Classical
&  & Generalized & Bayesian & Classical \\ \cline{1-3}\cline{5-7}\cline{9-11}
$10$ & $(4,2)$ & $0.5429$ &  & $0.1001$ & $0.1001$ & $0.0125$ &  & $0.0500$
& $0.0500$ & $0.0500$ \\ 
$15$ &  &  &  & $0.1254$ & $0.1001$ & $0.0245$ &  & $0.1356$ & $0.0500$ & $%
0.0235$ \\ 
$25$ &  &  &  & $0.1540$ & $0.1001$ & $0.325$ &  & $0.1389$ & $0.0500$ & $%
0.0245$ \\ 
$35$ &  &  &  & $0.1656$ & $0.0245$ & $0.0458$ &  & $0.1478$ & $0.0500$ & $%
0.0889$ \\ \hline
$10$ & $(4,4)$ & $0.7500$ &  & $0.2789$ & $0.0245$ & $0.1225$ &  & $0.1899$
& $0.0500$ & $0.0999$ \\ 
$15$ &  &  &  & $0.2889$ & $0.0245$ & $0.1458$ &  & $0.2458$ & $0.0500$ & $%
0.1225$ \\ 
$25$ &  &  &  & $0.3211$ & $0.0245$ & $0.2451$ &  & $0.2589$ & $0.1899$ & $%
0.1889$ \\ 
$35$ &  &  &  & $0.3489$ & $0.3211$ & $0.2898$ &  & $0.3458$ & $0.1899$ & $%
0.1997$ \\ \hline
$10$ & $(4,6)$ & $0.8476$ &  & $0.4569$ & $0.3211$ & $0.3254$ &  & $0.3888$
& $0.1899$ & $0.2458$ \\ 
$15$ &  &  &  & $0.4689$ & $0.3211$ & $0.3589$ &  & $0.4125$ & $0.1899$ & $%
0.2789$ \\ 
$25$ &  &  &  & $0.4889$ & $0.3211$ & $0.3789$ &  & $0.5478$ & $0.2589$ & $%
0.3458$ \\ 
$35$ &  &  &  & $0.5879$ & $0.3211$ & $0.4558$ &  & $0.6521$ & $0.2589$ & $%
0.3333$ \\ \hline
$10$ & $(4,8)$ & $0.9000$ &  & $0.6655$ & $0.3254$ & $0.4789$ &  & $0.7415$
& $0.2589$ & $0.3889$ \\ 
$15$ &  &  &  & $0.7889$ & $0.3254$ & $0.5511$ &  & $0.8888$ & $0.4215$ & $%
0.4215$ \\ 
$25$ &  &  &  & $0.8994$ & $0.6789$ & $0.6654$ &  & $0.8995$ & $0.4215$ & $%
0.4887$ \\ 
$35$ &  &  &  & $0.9994$ & $0.6789$ & $0.6789$ &  & $0.9885$ & $0.4215$ & $%
0.6987$ \\ \hline
\end{tabular}

\bigskip 
\begin{tabular}{lcccccccccc}
\hline
\multicolumn{11}{l}{Table 5.8(d)$\ $omparison of powers for testing $\
H_{0}:R_{2,4}\leq 0.5429\ $vs $H_{a}:R_{2,4}>0.5429$} \\ 
\multicolumn{11}{l}{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ without and after\
adjusting the size at $\gamma =0.05$ when the common scale parameter} \\ 
\multicolumn{11}{l}{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ is known $(\lambda
=10)$} \\ 
&  &  &  &  &  &  &  &  &  &  \\ \hline
\multicolumn{3}{c}{Parameters} &  & \multicolumn{3}{c}{Without adjusting the
size} &  & \multicolumn{3}{c}{After adjusting the size} \\ 
\cline{1-3}\cline{5-7}\cline{9-11}
$n$ & $\mathbf{\beta }$ & $R_{1,3}$ &  & Generalized & Bayesian & Classical
&  & Generalized & Bayesian & Classical \\ \cline{1-3}\cline{5-7}\cline{9-11}
$10$ & $(4,2)$ & $0.5429$ &  & $0.1001$ & $0.1001$ & $0.0125$ &  & $0.0500$
& $0.0500$ & $0.0500$ \\ 
$15$ &  &  &  & $0.1254$ & $0.1001$ & $0.0245$ &  & $0.1356$ & $0.0500$ & $%
0.0235$ \\ 
$25$ &  &  &  & $0.1540$ & $0.1001$ & $0.325$ &  & $0.1389$ & $0.0500$ & $%
0.0245$ \\ 
$35$ &  &  &  & $0.1656$ & $0.0245$ & $0.0458$ &  & $0.1478$ & $0.0500$ & $%
0.0889$ \\ \hline
$10$ & $(4,4)$ & $0.7500$ &  & $0.2789$ & $0.0245$ & $0.1225$ &  & $0.1899$
& $0.0500$ & $0.0999$ \\ 
$15$ &  &  &  & $0.2889$ & $0.0245$ & $0.1458$ &  & $0.2458$ & $0.0500$ & $%
0.1225$ \\ 
$25$ &  &  &  & $0.3211$ & $0.0245$ & $0.2451$ &  & $0.2589$ & $0.1899$ & $%
0.1889$ \\ 
$35$ &  &  &  & $0.3489$ & $0.3211$ & $0.2898$ &  & $0.3458$ & $0.1899$ & $%
0.1997$ \\ \hline
$10$ & $(4,6)$ & $0.8476$ &  & $0.4569$ & $0.3211$ & $0.3254$ &  & $0.3888$
& $0.1899$ & $0.2458$ \\ 
$15$ &  &  &  & $0.4689$ & $0.3211$ & $0.3589$ &  & $0.4125$ & $0.1899$ & $%
0.2789$ \\ 
$25$ &  &  &  & $0.4889$ & $0.3211$ & $0.3789$ &  & $0.5478$ & $0.2589$ & $%
0.3458$ \\ 
$35$ &  &  &  & $0.5879$ & $0.3211$ & $0.4558$ &  & $0.6521$ & $0.2589$ & $%
0.3333$ \\ \hline
$10$ & $(4,8)$ & $0.9000$ &  & $0.6655$ & $0.3254$ & $0.4789$ &  & $0.7415$
& $0.2589$ & $0.3889$ \\ 
$15$ &  &  &  & $0.7889$ & $0.3254$ & $0.5511$ &  & $0.8888$ & $0.4215$ & $%
0.4215$ \\ 
$25$ &  &  &  & $0.8994$ & $0.6789$ & $0.6654$ &  & $0.8995$ & $0.4215$ & $%
0.4887$ \\ 
$35$ &  &  &  & $0.9994$ & $0.6789$ & $0.6789$ &  & $0.9885$ & $0.4215$ & $%
0.6987$ \\ \hline
\end{tabular}

\bigskip

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