The Mixture of the Marshall–Olkin Extended Weibull Distribution under Type-II Censoring and Different Loss Functions

Table 1

The estimate, estimated risk, and length of the interval, Bayes method based on the squared loss function, and Bayes method based on the LINEX function when the prior distribution is gamma at different sample sizes.

n	20			40			80
MLEs
Parameter	Estimate	Estimated risk	Length	Estimate	Estimated risk	Length	Estimate	Estimated risk	Length
	2.2266962	0.45522293	1.7844411	1.9255029	0.26150688	1.0250881	1.7196975	0.17338100	0.679611
	5.4480750	0.74643451	2.9259695	4.8738022	0.4519073	1.7714444	4.6622334	0.29481590	1.1556571
	2.6050691	0.4696128	1.8408485	2.3622973	0.32997054	1.2934608	2.1965263	0.2134274	0.8366198
	4.9593311	0.74254833	2.9107360	4.6106123	0.4359577	1.7089228	4.4158906	0.28053577	1.0996800
	2.1842048	0.78639415	3.2410730	1.8386415	0.3436788	1.3471963	1.7059249	0.18937750	0.7423461
	4.8291733	1.51823446	5.9513697	4.1635412	0.7380715	2.8931873	3.8762212	0.40641529	1.5931187
	2.2241709	0.8904526	3.5851222	1.9410834	0.4002303	1.5688740	1.8120731	0.23350051	0.9153052
	4.5922180	1.32300762	5.1860946	4.1184271	0.7396291	2.8992929	3.8127630	0.39210727	1.5370323
	1.78123132	0.51279547	2.0599757	1.7370224	0.327979	1.2856868	1.7424558	0.22229935	0.8713974
	4.1672100	1.27710513	5.0061601	3.7528999	0.7512598	2.9448842	3.3100211	0.44260320	1.7349727
	1.6369791	0.56717175	2.2361035	1.4859141	0.3043238	1.1929277	1.3966339	0.18769952	0.7357686
	5.0407180	1.56241461	6.1245527	4.3449870	0.8754458	3.4316845	3.8052724	0.51894037	2.0342089
	0.4997187	0.07901453	0.309731	0.4993052	0.0558837	0.2190601	0.994209	0.03951937	0.1549131
	0.4797218	0.07900847	0.3097075	0.5003156	0.0558811	0.2190499	0.5000605	0.03952083	0.1549188
Bayes estimates based on the squared loss function
	2.1729181	0.004552293	0.9784551	1.08645905	0.00227611	0.48922755	0.543229525	0.001138055	0.244613775
	4.980901	0.05829461	1.9342585	2.4904505	0.0291473	0.9671291	1.245225	0.014574	0.483565
	2.056629	0.4696128	1.1297355	1.0283145	0.2348064	0.56486775	0.514157	0.117403	0.282434
	4.5283112	0.07326548	2.4938260	2.2641556	0.03663274	1.246913	1.132078	0.018316	0.623457
	1.7043984	0.092688415	2.3864156	0.8521992	0.0463442075	1.1932078	0.4261	0.023172	0.596604
	4.1261944	0.0692846326	2.5368135	2.0630972	0.03464231	1.2684065	1.031549	0.017321	0.634203
	2.1368209	0.0845269	2.1851222	1.06841045	0.0422636	1.0925611	0.534205	0.021132	0.546281
	4.3123180	0.032300762	1.9860946	2.1561599	0.01615036	0.9930473	1.07808	0.008075	0.496524
	1.2926875	0.051279547	2.0599757	0.64634375	0.02563897	1.02998785	0.323172	0.012819	0.514994
	3.9683190	0.49710513	3.0061601	0.9841595	1.9841595	1.50308005	0.99208	0.099208	0.75154
	1.4398321	0.06717175	2.2361035	0.71991605	0.71991605	1.1180515	0.359958	0.359958	0.559026
	4.28437120	1.56241461	0.9245527	2.1421856	0.014021856	0.46227635	1.071093	0.007011	0.231138
	0.4991957857	0.07901453	0.6309731	0.24959785	0.03495978	0.31548655	0.124799	0.0124799	0.157743
	0.6389978	0.07900847	0.0309792	0.3194989	0.02194989	0.0154896	0.159749	0.019749	0.007745
Bayes estimates based on the LINEX function
	2.272918	0.104552	1.078455	1.186459	0.102276	0.589228	0.64323	0.101138	0.344614
	5.080901	0.158295	2.034259	2.590451	0.129147	1.067129	1.345225	0.114574	0.583565
	2.156629	0.569613	1.229736	1.128315	0.334806	0.664868	0.614157	0.217403	0.382434
	4.628311	0.173265	2.593826	2.364156	0.136633	1.346913	1.232078	0.118316	0.723457
	1.804398	0.192688	2.486416	0.952199	0.146344	1.293208	0.5261	0.123172	0.696604
	4.226194	0.169285	2.636814	2.163097	0.134642	1.368407	1.131549	0.117321	0.734203
	2.236821	0.184527	2.285122	1.16841	0.142264	1.192561	0.634205	0.121132	0.646281
	4.412318	0.132301	2.086095	2.25616	0.11615	1.093047	1.17808	0.108075	0.596524
	1.392688	0.15128	2.159976	0.746344	0.125639	1.129988	0.423172	0.112819	0.614994
	4.068319	0.597105	3.10616	1.08416	2.08416	1.60308	1.09208	0.199208	0.85154
	1.539832	0.167172	2.336104	0.819916	0.819916	1.218052	0.459958	0.459958	0.659026
	4.384371	1.662415	1.024553	2.242186	0.114022	0.562276	1.171093	0.107011	0.331138
	0.599196	0.179015	0.730973	0.349598	0.13496	0.415487	0.224799	0.11248	0.257743
	0.738998	0.179008	0.130979	0.419499	0.12195	0.11549	0.259749	0.119749	0.107745