Table 4 MLE and Bayesian for TCPE parameters based on Type-II UPHCS: \(\lambda =0.7, \zeta =1.4, \eta =0.5\).

From: Utilizing unified progressive hybrid censored data in parametric inference under accelerated life tests

\(\lambda =0.7, \zeta =1.4, \eta =0.5\)				MLE		SELF		LLF \(\nu =-0.5\)		LLF \(\nu =0.5\)		ACI		Bootstrap		HPD
\(\tau _1, \tau _2\)	Scheme	r		Bias	MSE	Bias	MSE	Bias	MSE	Bias	MSE	LACI	CP	LBPCI	LBTCI	SELF	LLF \(\nu ={-}0.5\)	LLF \(\nu =0.5\)
0.7,0.95	1	0.6	\(\lambda\)	\(-\)0.1474	0.1980	\(-\)0.0284	0.0153	\(-\)0.0262	0.0152	\(-\)0.0306	0.0154	1.6468	94.86%	0.0631	0.0634	0.4518	0.4566	0.4521
			\(\zeta\)	0.5007	0.7795	\(-\)0.0066	0.0217	\(-\)0.0037	0.0216	\(-\)0.0095	0.0218	2.8525	96.57%	0.1102	0.1112	0.5550	0.5545	0.5558
			\(\eta\)	\(-\)0.0331	0.0351	0.0259	0.0039	0.0266	0.0040	0.0252	0.0039	0.7233	93.71%	0.0281	0.0278	0.2167	0.2168	0.2162
		0.8	\(\lambda\)	\(-\)0.3933	0.1735	\(-\)0.0341	0.0088	\(-\)0.0328	0.0087	\(-\)0.0353	0.0089	0.5380	94.43%	0.0204	0.0201	0.3413	0.3410	0.3414
			\(\zeta\)	0.4916	0.7001	0.0080	0.0120	0.0098	0.0121	0.0063	0.0119	1.5767	94.29%	0.0602	0.0610	0.4321	0.4324	0.4310
			\(\eta\)	\(-\)0.1234	0.0188	0.0422	0.0038	0.0428	0.0038	0.0417	0.0037	0.2351	94.14%	0.0084	0.0084	0.1684	0.1693	0.1682
	2	0.6	\(\lambda\)	\(-\)0.0364	0.1137	\(-\)0.0022	0.0132	0.0000	0.0133	\(-\)0.0044	0.0131	1.3153	94.86%	0.0530	0.0532	0.4384	0.4424	0.4374
			\(\zeta\)	0.2361	0.3822	0.0000	0.0204	0.0027	0.0204	\(-\)0.0027	0.0204	2.2412	96.00%	0.0837	0.0857	0.5613	0.5612	0.5605
			\(\eta\)	\(-\)0.0043	0.0232	0.0119	0.0030	0.0127	0.0030	0.0111	0.0030	0.5970	94.43%	0.0219	0.0220	0.2073	0.2077	0.2059
		0.8	\(\lambda\)	\(-\)0.0249	0.1027	\(-\)0.0232	0.0090	\(-\)0.0219	0.0089	\(-\)0.0245	0.0090	1.0036	95.57%	0.0384	0.0374	0.3395	0.3415	0.3373
			\(\zeta\)	0.0549	0.3556	0.0017	0.0125	0.0034	0.0125	0.0000	0.0125	1.9788	95.14%	0.0788	0.0787	0.4198	0.4218	0.4178
			\(\eta\)	\(-\)0.0714	0.0183	0.0247	0.0024	0.0253	0.0024	0.0242	0.0023	0.4506	95.29%	0.0166	0.0166	0.1578	0.1575	0.1572
	3	0.6	\(\lambda\)	\(-\)0.1722	0.1401	\(-\)0.0264	0.0157	\(-\)0.0242	0.0156	\(-\)0.0287	0.0158	1.3038	95.29%	0.0504	0.0511	0.4624	0.4646	0.4618
			\(\zeta\)	0.5284	0.7386	0.0064	0.0222	0.0093	0.0223	0.0035	0.0221	2.6589	96.57%	0.0961	0.0961	0.5635	0.5618	0.5649
			\(\eta\)	\(-\)0.0532	0.0244	0.0178	0.0033	0.0185	0.0034	0.0171	0.0033	0.5758	95.29%	0.0219	0.0219	0.2120	0.2125	0.2115
		0.8	\(\lambda\)	\(-\)0.2357	0.1397	\(-\)0.0299	0.0130	\(-\)0.0281	0.0129	\(-\)0.0318	0.0131	1.1380	93.57%	0.0426	0.0419	0.4137	0.4142	0.4134
			\(\zeta\)	0.6047	0.7331	0.0076	0.0198	0.0101	0.0199	0.0051	0.0197	2.3780	95.00%	0.0889	0.0880	0.5371	0.5418	0.5360
			\(\eta\)	\(-\)0.0718	0.0211	0.0247	0.0033	0.0253	0.0033	0.0240	0.0032	0.4948	94.86%	0.0180	0.0180	0.2049	0.2057	0.2040
0.85,1.2	1	0.6	\(\lambda\)	0.0145	0.1213	\(-\)0.0140	0.0154	\(-\)0.0117	0.0154	\(-\)0.0162	0.0154	1.3649	97.00%	0.0512	0.0514	0.4740	0.4767	0.4689
			\(\zeta\)	0.1249	0.3749	\(-\)0.0023	0.0215	0.0008	0.0214	\(-\)0.0054	0.0213	2.3514	96.29%	0.0928	0.0918	0.6023	0.6038	0.6026
			\(\eta\)	0.0238	0.0288	0.0101	0.0028	0.0108	0.0029	0.0094	0.0028	0.6588	94.29%	0.0249	0.0252	0.2031	0.2030	0.2032
		0.8	\(\lambda\)	\(-\)0.0352	0.1157	\(-\)0.0362	0.0096	\(-\)0.0349	0.0095	\(-\)0.0376	0.0097	0.7112	94.71%	0.0257	0.0260	0.3391	0.3388	0.3398
			\(\zeta\)	0.1080	0.3083	0.0053	0.0125	0.0070	0.0134	0.0035	0.0133	1.7493	95.00%	0.0665	0.0666	0.4470	0.4497	0.4465
			\(\eta\)	\(-\)0.1146	0.0190	0.0299	0.0028	0.0304	0.0028	0.0294	0.0027	0.3001	95.29%	0.0115	0.0114	0.1645	0.1645	0.1645
	2	0.6	\(\lambda\)	0.0222	0.1118	0.0006	0.0136	0.0028	0.0138	\(-\)0.0017	0.0135	1.3090	96.29%	0.0504	0.0519	0.4502	0.4507	0.4513
			\(\zeta\)	0.1290	0.2932	\(-\)0.0089	0.0202	\(-\)0.0062	0.0202	\(-\)0.0117	0.0203	2.0630	94.71%	0.0783	0.0786	0.5360	0.5346	0.5352
			\(\eta\)	0.0032	0.0218	0.0099	0.0030	0.0107	0.0030	0.0091	0.0030	0.6494	95.14%	0.0254	0.0253	0.2120	0.2129	0.2107
		0.8	\(\lambda\)	\(-\)0.0201	0.1016	\(-\)0.0169	0.0073	\(-\)0.0156	0.0072	\(-\)0.0182	0.0073	1.0780	95.43%	0.0396	0.0393	0.3315	0.3318	0.3315
			\(\zeta\)	0.1046	0.2049	0.0028	0.0124	0.0045	0.0124	0.0012	0.0124	2.0590	96.86%	0.0767	0.0757	0.4337	0.4330	0.4348
			\(\eta\)	\(-\)0.0644	0.0178	0.0154	0.0020	0.0159	0.0020	0.0149	0.0020	0.4585	95.57%	0.0177	0.0177	0.1605	0.1616	0.1596
	3	0.6	\(\lambda\)	0.0003	0.1131	\(-\)0.0049	0.0150	\(-\)0.0026	0.0152	\(-\)0.0072	0.0149	1.3195	96.71%	0.0482	0.0480	0.4669	0.4718	0.4651
			\(\zeta\)	0.1961	0.4759	\(-\)0.0010	0.0226	0.0017	0.0227	\(-\)0.0038	0.0226	2.5946	96.29%	0.1027	0.1031	0.6062	0.6101	0.6059
			\(\eta\)	0.0127	0.0217	0.0113	0.0032	0.0120	0.0032	0.0106	0.0032	0.6473	94.29%	0.0246	0.0244	0.2095	0.2107	0.2083
		0.8	\(\lambda\)	\(-\)0.0309	0.1047	\(-\)0.0256	0.0083	\(-\)0.0243	0.0082	\(-\)0.0270	0.0083	0.8888	95.57%	0.0349	0.0350	0.3305	0.3298	0.3314
			\(\zeta\)	0.1724	0.3786	0.0036	0.0125	0.0054	0.0125	0.0019	0.0125	2.0063	96.14%	0.0750	0.0781	0.4155	0.4144	0.4169
			\(\eta\)	\(-\)0.1012	0.0209	0.0260	0.0028	0.0265	0.0028	0.0255	0.0027	0.4044	95.57%	0.0151	0.0152	0.1702	0.1711	0.1692

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Table 4 MLE and Bayesian for TCPE parameters based on Type-II UPHCS: \(\lambda =0.7, \zeta =1.4, \eta =0.5\).

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