Marshall–Olkin Extended Gumbel Type-II Distribution: Properties and Applications

Table 3

MLE and their sample statistics for some simulated samples and true values  = 1,  = 1,  = 1, and  = 1.

		Nelder–Mead				Quasi-Newton				Fletcher–Reeves
N	Parameters	Min	Max	Mean	Std	Min	Max	Mean	Std	Min	Max	Mean	Std
50		0.087	27.866	1.319	1.149	0.090	3.884	1.095	0.387	0.132	4.952	1.017	0.192
		0.245	3.929	1.071	0.386	0.118	2.722	1.041	0.261	0.237	2.869	1.009	0.169
		0.649	1.791	1.016	0.107	0.772	1.783	1.024	0.095	0.784	1.461	1.025	0.087
		15.934	42.289	1.007	1.252	0.026	2.346	1.005	0.127	0.475	3.853	1.015	0.125
	Iteration	69	279	126	24	4	576	88	39	399	899	813	43
100		0.118	8.549	1.141	0.597	0.055	5.072	1.036	0.294	0.058	2.289	1.011	0.119
		0.248	2.652	1.034	0.267	0.099	2.555	1.019	0.191	0.119	1.792	0.009	0.114
		0.768	1.355	1.007	0.074	0.821	1.339	1.012	0.064	0.862	1.334	1.012	0.058
		7.725	16.290	1.062	0.705	0.492	3.687	1.002	0.117	0.481	2.598	1.007	0.087
	Iteration	65	279	119	23	19	603	112	55	411	953	818	46
300		0.366	2.945	1.039	0.285	0.447	2.359	1.017	0.147	0.406	1.558	1.003	0.065
		0.513	1.623	1.008	0.148	0.585	1.492	1.007	0.099	0.566	1.386	1.004	0.067
		0.861	1.139	1.003	0.042	0.894	1.154	1.004	0.036	0.909	1.119	1.005	0.034
		5.753	5.349	1.078	0.421	0.506	1.608	1.002	0.056	0.599	1.428	1.001	0.039
	Iteration	61	233	112	21	18	502	86	37	440	899	828	38
500		0.454	2.129	1.026	0.223	0.502	1.759	1.007	0.116	0.502	1.905	1.003	0.049
		0.649	1.485	1.007	0.117	0.671	1.388	1.005	0.081	0.721	1.401	1.005	0.041
		0.898	1.124	1.002	0.033	0.899	0.117	1.003	0.026	0.912	1.340	1.002	0.019
		3.133	3.761	1.091	0.333	0.652	1.646	1.004	0.051	0.661	1.627	1.003	0.029
	Iteration	64	234	107	22	24	691	120	60	402	910	835	49
1000		0.575	1.747	1.017	0.152	0.513	1.509	1.004	0.081	0.631	1.302	1.002	0.039
		0.759	1.331	1.006	0.082	0.666	1.269	1.002	0.055	0.753	1.215	1.002	0.036
		0.919	1.091	1.001	0.023	0.934	1.082	1.002	0.019	0.936	1.083	1.001	0.018
		1.785	3.743	1.093	0.264	0.424	1.431	1.001	0.035	0.738	1.253	1.001	0.026
	Iteration	63	221	105	20	24	606	108	45	453	901	839	41