Permissible noninformative priors for the accelerated life test model with censored data

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Table 1 Frequentist coverage probabilities for \({\alpha }=0.95,0.05\) with true parameters \({\theta }=1,{\beta }=1\), and without considering the hybrid censoring time \(\eta\)

Censoring scheme					\(Q_{\pi _{1}}({\theta })\)		\(Q_{\pi _{1}}({\beta })\)
n	m	\(\left( \begin{array}{cccc} R_{1}&{} R_{2} &{}\cdots \, R_{n_{u}-1}\\ R_{n_{u}} &{}\cdots &{}R_{m} \\ \end{array} \right)\)			\({\alpha }=0.95\)	\({\alpha }=0.05\)	\({\alpha }=0.95\)	\({\alpha }=0.05\)
10	6	\(\left( \begin{array}{ccc} 0&{} 1 &{} 1 \\ 1 &{} 0 &{} 1 \\ \end{array} \right)\)	k = 1		0.9756	0.0763	0.9233	0.0752
			k = 2	\(\tau =4\)	0.9137	0.0869	0.9149	0.0865
16	8	\(\left( \begin{array}{cccc} 1&{} 0 &{} 1 &{} 0 \\ 2 &{} 1 &{} 2 &{}1 \\ \end{array} \right)\)	k = 1		0.9314	0.0321	0.9318	0.0686
			k = 2	\(\tau =5\)	0.9221	0.0764	0.9768	0.0786
24	10	\(\left( \begin{array}{ccccc} 1&{} 0 &{} 1&{} 1&{} 1 \\ 2 &{} 1 &{} 2&{} 2&{} 3 \\ \end{array} \right)\)	k = 1		0.9378	0.0621	0.9629	0.0384
			k = 2	\(\tau =6\)	0.9705	0.0692	0.9304	0.0302
30	12	\(\left( \begin{array}{cccccc} 0&{} 1 &{} 1&{} 2 &{}1&{}1 \\ 2 &{} 3 &{} 1 &{}2 &{}2&{}2 \\ \end{array} \right)\)	k = 1		0.9562	0.0552	0.9441	0.0445
			k = 2	\(\tau =7\)	0.9348	0.0343	0.9659	0.0649
30	10	\(\left( \begin{array}{ccccc} 1&{} 2 &{} 1&{} 2&{} 1 \\ 3 &{} 2 &{} 2&{} 2&{} 4 \\ \end{array} \right)\)	k = 1		0.9628	0.0626	0.9630	0.0372
			k = 2	\(\tau =6\)	0.9712	0.0723	0.9272	0.0727
30	8	\(\left( \begin{array}{cccc} 1&{} 2 &{} 1 &{} 2 \\ 4 &{} 3 &{} 4 &{}5 \\ \end{array} \right)\)	k = 1		0.9290	0.0708	0.9714	0.0274
			k = 2	\(\tau =5\)	0.9801	0.0791	0.9207	0.0796
30	6	\(\left( \begin{array}{ccc} 2&{} 2 &{} 3 \\ 6 &{} 5 &{} 6 \\ \end{array} \right)\)	k = 1		0.9209	0.0203	0.9191	0.0797
			k = 2	\(\tau =4\)	0.9889	0.0896	0.9892	0.0112