Generalized logistic distribution and its regression model

Aljarrah, Mohammad A.; Famoye, Felix; Lee, Carl

doi:10.1186/s40488-020-00107-8

Journal of Statistical Distributions and Applications

Table 2 Bias and SD of the parameter estimates using MLE method

From: Generalized logistic distribution and its regression model

Parameters			Sample size	Bias			SD
ξ	μ	σ	Sample size	\( \hat{\xi}-\xi \)	\( \hat{\mu}-\mu \)	\( \hat{\sigma}-\sigma \)	\( SD\left(\hat{\xi}\right) \)	\( SD\left(\hat{\mu}\right) \)	\( SD\left(\hat{\sigma}\right) \)
0.5	−1	− 1	50	0.2585	−0.1125	−0.0425	0.5947	0.3552	0.2162
			100	0.0979	−0.0386	− 0.0160	0.3570	0.2413	0.1550
			200	0.0654	−0.0278	−0.0142	0.2278	0.1587	0.1187
			500	0.0265	−0.0070	− 0.0050	0.1357	0.0999	0.0687
			1000	0.0102	0.0003	−0.0010	0.0928	0.0662	0.0474
2	0	−2	50	1.0074	−0.4525	−0.1085	2.5277	1.3595	0.6366
			100	0.3699	−0.1655	− 0.0345	1.4639	0.8721	0.4376
			200	0.3072	−0.1583	−0.0494	1.1224	0.6916	0.3598
			500	0.1615	−0.0767	− 0.0279	0.8690	0.5048	0.2375
			1000	0.0439	−0.0156	−0.0061	0.4078	0.2709	0.1442
6	2	−3	50	−1.3031	0.9211	0.4806	2.9698	1.5575	0.7229
			100	−0.8896	0.6087	0.2896	2.6342	1.3797	0.6079
			200	−0.4115	0.3154	0.1566	2.2743	1.1780	0.5040
			500	−0.4251	0.2871	0.1219	1.8211	0.9216	0.3595
			1000	−0.4952	0.2921	0.1137	1.3108	0.6636	0.2506
0.5	−1	1	50	0.2017	0.0813	0.0291	0.5106	0.3185	0.2133
			100	0.0981	0.0387	0.0161	0.3569	0.2412	0.1550
			200	0.0659	0.0283	0.0141	0.2289	0.1591	0.1189
			500	0.0271	0.0074	0.0054	0.1364	0.1004	0.0688
			1000	0.0116	0.0004	0.0018	0.0920	0.0662	0.0475
2	0	2	50	0.9262	0.4091	0.0931	2.3871	1.2927	0.6084
			100	0.3652	0.1627	0.0334	1.4761	0.8769	0.4393
			200	0.3072	0.1585	0.0513	1.1224	0.6939	0.3609
			500	0.1562	0.0713	0.0251	0.9162	0.5125	0.2358
			1000	0.0365	0.0106	0.0034	0.4089	0.2720	0.1444
6	4	3	50	1.0664	0.0219	−0.1725	6.0035	2.5586	0.9517
			100	0.8875	0.1094	−0.0699	5.0824	2.2413	0.8278
			200	0.6818	0.1183	−0.0310	3.9748	1.7626	0.6446
			500	0.4806	0.0767	−0.0105	3.7760	1.6030	0.5314
			1000	0.1190	−0.0384	− 0.0374	2.7782	1.2040	0.3957

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