Interval and Point Estimators for the Location Parameter of the Three-Parameter Lognormal Distribution

Table 1

Critical values of 𝜉(𝛾).

𝑛	𝑖	𝑗	𝑘	𝜉0.025	𝜉0.05	𝜉0.5	𝜉0.95	𝜉0.975
10	1	2	10	0.0065	0.0129	0.1662	0.6988	0.8696
	1	3	10	0.0535	0.0774	0.3677	1.1273	1.3762
	1	4	10	0.1292	0.1709	0.5834	1.6351	1.9893
20	1	4	20	0.0734	0.0970	0.3165	0.7676	0.8935
	1	5	20	0.1190	0.1496	0.4096	0.9242	1.0636
	1	6	20	0.1666	0.2033	0.5027	1.0862	1.2466
	1	7	20	0.2177	0.2590	0.5983	1.2608	1.4448
	1	8	20	0.2695	0.3171	0.6998	1.4511	1.6667
30	1	6	30	0.1266	0.1538	0.3745	0.7761	0.8817
	1	7	30	0.1604	0.1918	0.4339	0.8662	0.9801
	1	8	30	0.1961	0.2299	0.4913	0.9581	1.0794
	1	9	30	0.2328	0.2695	0.5514	1.0541	1.1870
	1	10	30	0.2672	0.3073	0.6131	1.1526	1.2967
	1	11	30	0.3023	0.3462	0.6753	1.2543	1.4072
	1	12	30	0.3409	0.3877	0.7393	1.3651	1.5361
40	1	8	40	0.1629	0.1910	0.4069	0.8739	0.1629
	1	9	40	0.1899	0.2209	0.4493	0.9391	0.1899
	1	10	40	0.2182	0.2513	0.4931	1.0121	0.2182
	1	11	40	0.2728	0.3093	0.5355	1.1488	0.2728
	1	12	40	0.3001	0.3394	0.5792	1.2220	0.3001
	1	13	40	0.3264	0.3683	0.6229	1.3028	0.3264
	1	14	40	0.3556	0.3990	0.6673	1.3812	0.3556
	1	15	40	0.3824	0.4282	0.7140	1.4645	0.3824
	1	16	40	0.1629	0.1910	0.7604	0.8739	0.1629
50	1	10	50	0.1899	0.2186	0.4282	0.7749	0.8613
	1	11	50	0.2135	0.2431	0.4614	0.8244	0.9143
	1	12	50	0.2356	0.2670	0.4953	0.8731	0.9665
	1	13	50	0.2573	0.2901	0.5285	0.9213	1.0203
	1	14	50	0.2796	0.3150	0.5619	0.9724	1.0724
	1	15	50	0.3009	0.3378	0.5964	1.0170	1.1230
	1	16	50	0.3234	0.3624	0.6312	1.0724	1.1840
	1	17	50	0.3447	0.3849	0.6651	1.1276	1.2443
	1	18	50	0.3681	0.4093	0.6995	1.1755	1.2970
	1	19	50	0.3896	0.4326	0.7352	1.2288	1.3516
	1	20	50	0.4140	0.4588	0.7739	1.2938	1.4205
60	1	12	60	0.2121	0.2408	0.4428	0.7749	0.8588
	1	13	60	0.2298	0.2602	0.4711	0.8141	0.8984
	1	14	60	0.2500	0.2803	0.4994	0.8504	0.9369
	1	15	60	0.2668	0.2999	0.5266	0.8941	0.9837
	1	16	60	0.2854	0.3202	0.5542	0.9310	1.0240
	1	17	60	0.3042	0.3388	0.5808	0.9669	1.0628
	1	18	60	0.3232	0.3589	0.6090	1.0129	1.1127
	1	19	60	0.3429	0.3784	0.6372	1.0479	1.1485
	1	20	60	0.3607	0.3985	0.6653	1.0916	1.1964
	1	21	60	0.3791	0.4195	0.6950	1.1342	1.2438
	1	22	60	0.3970	0.4377	0.7236	1.1755	1.2900
	1	23	60	0.4168	0.4589	0.7530	1.2193	1.3407
	1	24	60	0.4349	0.4777	0.7825	1.2638	1.3892