Mathematical Problems in Engineering

Research Article

Bayesian Estimation of Two-Parameter Weibull Distribution Using Extension of Jeffreys' Prior Information with Three Loss Functions

Table 1

Estimated values for scale parameter .





	0.5	0.4	0.8	0.4481	0.4506	0.7577	0.2982	0.2878	0.5216	0.2927	0.4086	0.6929	0.3945
	0.5	0.4	1.2	0.7224	0.7274	0.5663	0.3964	0.5016	0.3636	0.4649	0.5314	0.5381	0.4828
	0.5	1.4	0.8	0.3179	0.4793	0.5134	0.6203	0.5109	0.6936	0.5456	0.5601	0.6574	0.6406
25	0.5	1.4	1.2	0.4688	0.4876	0.5355	0.6270	0.6468	0.4243	0.5028	0.7379	0.6546	0.5319
25	1.5	0.4	0.8	1.9488	1.9168	1.3999	2.0563	1.4683	1.1745	1.4409	2.1533	1.8531	1.7247
	1.5	0.4	1.2	1.8768	1.8859	1.4652	1.3522	1.9847	1.5382	0.9764	1.2448	1.6580	1.3147
	1.5	1.4	0.8	1.0121	1.0121	2.4225	1.5837	1.2562	1.7038	1.8135	1.3075	1.8037	1.4071
	1.5	1.4	1.2	1.4759	1.4626	1.4955	1.4546	1.2494	1.6919	1.4134	1.4910	1.2567	1.7653

	0.5	0.4	0.8	0.6308	0.6319	0.4218	0.6790	0.4096	0.6027	0.5996	0.5046	0.5296	0.3645
	0.5	0.4	1.2	1.2471	0.4031	1.5041	1.4592	1.4338	1.5799	1.1694	1.8736	1.6057	1.4472
	0.5	1.4	0.8	0.6095	0.6364	0.6759	0.3801	0.4645	0.6033	0.4195	0.6020	0.4212	0.4390
50	0.5	1.4	1.2	0.5483	0.5676	0.7103	0.5264	0.6535	0.4715	0.5167	0.5348	0.5112	0.4293
50	1.5	0.4	0.8	2.1209	2.1008	1.5653	1.3988	1.4286	1.6753	1.1195	1.2420	1.3932	1.4784
	1.5	0.4	1.2	1.2471	1.2447	1.5041	1.4592	1.4338	1.5799	1.1694	1.8736	1.6057	1.4472
	1.5	1.4	0.8	1.3866	1.3658	1.3538	1.0390	1.4067	1.1281	1.5264	1.5330	1.3423	1.9056
	1.5	1.4	1.2	1.6538	1.6539	2.0394	1.1159	1.5960	1.8360	1.1559	1.8099	1.4305	1.5092

	0.5	0.4	0.8	0.4156	0.4163	0.4656	0.5054	0.3940	0.5870	0.5498	0.4971	0.5169	0.4530
	0.5	0.4	1.2	0.5032	0.5037	0.5125	0.5192	0.5725	0.4626	0.4840	0.4821	0.5422	0.5204
	0.5	1.4	0.8	0.4974	0.5147	0.4776	0.5799	0.4369	0.4692	0.5693	0.4846	0.4067	0.4844
100	0.5	1.4	1.2	0.4633	0.4699	0.4664	0.5334	0.4638	0.5310	0.4300	0.4883	0.4595	0.4384
100	1.5	0.4	0.8	1.6509	1.6475	1.5147	1.4651	1.5878	1.3966	1.5910	1.5514	1.3278	1.4129
	1.5	0.4	1.2	1.6169	1.6186	1.3703	1.3680	1.5696	1.4485	1.4048	1.3890	1.5579	1.5339
	1.5	1.4	0.8	1.1622	1.1578	1.2926	1.6746	1.5554	1.3959	1.4872	1.6832	1.1781	1.5639
	1.5	1.4	1.2	1.4098	1.4038	1.3709	1.4442	1.5666	1.6591	1.5686	1.5005	1.7630	1.2944

ML: maximum likelihood, BG: general entropy loss function, BL: LINEX loss function, BS: squared error loss function.