Classical Estimation of the Index and Its Confidence Intervals for Power Lindley Distributed Quality Characteristics

Table 1

Classical estimates of the parameters α and β using different methods.

Parameters	n	Estimates	MLEs	LSEs	WLSEs	CMEs	MPSEs	ADEs	RTADEs
	10		1.76734	1.65161	1.63494	1.68981	1.62149	1.69094	1.70079
			0.65521	0.63513	0.65418	0.67247	0.62064	0.66606	0.65932
α = 1.50	20		1.72966	1.63456	1.59965	1.64055	1.56868	1.63674	1.63584
			0.63231	0.57784	0.58071	0.62074	0.58616	0.61944	0.61191
β = 0.50	30		1.64579	1.56177	1.54958	1.57218	1.53307	1.57661	1.59127
			0.57224	0.54852	0.54651	0.56965	0.54727	0.56964	0.56049
	50		1.53862	1.52989	1.51685	1.52746	1.21246	1.53517	1.54239
			0.52083	0.51634	0.52589	0.54450	0.51544	0.53142	0.54413
	10		2.51384	2.48984	2.43719	2.77994	2.42864	2.42864	2.67545
			0.62635	0.68777	0.71527	0.61097	0.72919	0.65469	0.69694
α = 2.00	20		2.44839	2.36855	2.31785	2.57792	2.37323	2.29830	2.55131
			0.56407	0.56846	0.66575	0.53423	0.67279	0.56507	0.60958
β = 0.50	30		2.35788	2.29573	2.26426	2.47782	2.30075	2.23093	2.42243
			0.53185	0.54211	0.55079	0.52473	0.57378	0.53497	0.53931
	50		2.18335	2.22406	2.15245	2.27591	2.17762	2.19035	2.24006
			0.52274	0.51361	0.51088	0.50192	0.52799	0.50251	0.52560
	10		2.71771	2.67307	2.66022	2.79007	2.82722	2.82416	2.83159
			0.92929	0.83002	0.82454	0.87826	0.81764	0.87955	0.84966
α = 2.50	20		2.64297	2.59323	2.64268	2.74312	2.74263	2.74329	2.74326
			0.89968	0.78031	0.79258	0.79511	0.78386	0.81821	0.82088
β = 0.75	30		2.60260	2.56903	2.61764	2.68423	2.68474	2.67252	2.61235
			0.82096	0.76587	0.76992	0.76217	0.77752	0.76915	0.76824
	50		2.53792	2.49415	2.54408	2.54941	2.56324	2.51164	2.55552
			0.78838	0.74181	0.74455	0.73030	0.74173	0.73849	0.73005
	10		7.75678	7.81757	7.86120	7.74842	7.69410	7.77461	7.81194
			0.31787	0.35308	0.38158	0.28888	0.32420	0.32665	0.31735
α = 7.50	20		7.66016	7.73530	7.73144	7.69019	7.64883	7.64127	7.69165
			0.28845	0.30230	0.33050	0.27387	0.27150	0.27394	0.27054
β = 0.25	30		7.53170	7.61765	7.69628	7.65637	7.54035	7.54510	7.66296
			0.27608	0.32751	0.30899	0.26808	0.26692	0.26817	0.26396
	50		7.52985	7.56082	7.51582	7.54020	7.47283	7.53227	7.52185
			0.26037	0.26529	0.27228	0.26341	0.24049	0.25071	0.24701