Multivariate Inverted Kumaraswamy Distribution: Derivation and Estimation

Table 1

The results of MLEs and Bayesian estimates.

			MLE				Bayesian
			,	n = 30	ABias	0.020	0.015	0.015	0.010	0.016	0.012	0.008	0.012
MSE	0.003	0.004			0.004	0.004	0.003	0.004	0.004	0.003
CW (CL)	0.214	0.248			0.248	0.248	0.213	0.243	0.239	0.230
CP	0.950	0.938			0.957	0.948	0.943	0.932	0.949	0.951
n = 50	ABias	0.011		0.009	0.008	0.007	0.010	0.009	0.004	0.009
	MSE	0.002		0.002	0.002	0.002	0.002	0.002	0.002	0.002
	CW (CL)	0.176		0.176	0.176	0.176	0.162	0.188	0.185	0.179
	CP	0.954		0.940	0.938	0.951	0.956	0.943	0.949	0.942
n = 70	ABias	0.010		0.006	0.006	0.006	0.008	0.006	0.004	0.007
	MSE	0.001		0.002	0.002	0.001	0.001	0.002	0.002	0.001
	CW (CL)	0.124		0.176	0.176	0.124	0.136	0.157	0.156	0.143
	CP	0.952		0.957	0.946	0.951	0.958	0.945	0.949	0.948
,	n = 30	ABias	0.032	0.048	0.046	0.032	0.028	0.041	0.027	0.038
		MSE	0.011	0.034	0.034	0.026	0.011	0.031	0.030	0.025
		CW (CL)	0.392	0.702	0.702	0.620	0.394	0.664	0.659	0.587
		CP	0.947	0.945	0.956	0.951	0.942	0.930	0.945	0.951
	n = 50	ABias	0.018	0.028	0.026	0.022	0.020	0.027	0.026	0.025
		MSE	0.006	0.018	0.018	0.014	0.006	0.017	0.018	0.014
		CW (CL)	0.304	0.512	0.512	0.464	0.299	0.501	0.504	0.448
		CP	0.948	0.944	0.945	0.957	0.954	0.949	0.946	0.937
	n = 70	ABias	0.017	0.019	0.021	0.019	0.013	0.021	0.017	0.019
		MSE	0.004	0.012	0.012	0.010	0.004	0.012	0.012	0.010
		CW (CL)	0.248	0.430	0.430	0.392	0.250	0.417	0.418	0.375
		CP	0.945	0.958	0.948	0.950	0.951	0.929	0.951	0.946
,	n = 30	ABias	0.045	0.088	0.086	0.066	0.037	0.072	0.073	0.060
		MSE	0.022	0.101	0.099	0.076	0.022	0.090	0.091	0.068
		CW (CL)	0.554	1.196	1.188	1.052	0.557	1.129	1.133	0.979
		CP	0.941	0.951	0.954	0.946	0.940	0.939	0.950	0.951
	n = 50	ABias	0.026	0.051	0.049	0.040	0.026	0.059	0.049	0.040
		MSE	0.013	0.052	0.051	0.040	0.013	0.052	0.050	0.038
		CW (CL)	0.430	0.868	0.868	0.764	0.425	0.854	0.850	0.744
		CP	0.950	0.944	0.941	0.956	0.956	0.948	0.948	0.940
	n = 70	ABias	0.024	0.036	0.039	0.035	0.019	0.037	0.030	0.030
		MSE	0.009	0.034	0.036	0.028	0.009	0.034	0.033	0.026
		CW (CL)	0.350	0.712	0.722	0.644	0.358	0.703	0.703	0.619
		CP	0.944	0.956	0.949	0.949	0.958	0.940	0.952	0.946
,	n = 30	ABias	0.068	0.142	0.158	0.307	0.023	0.120	0.162	0.137
		MSE	0.062	0.391	0.442	0.913	0.059	0.355	0.447	0.664
		CW (CL)	0.936	2.388	2.532	3.548	0.924	2.207	2.417	3.063
		CP	0.950	0.940	0.950	0.950	0.940	0.950	0.930	0.960
	n = 50	ABias	0.046	0.099	0.111	0.191	0.018	0.076	0.103	0.091
		MSE	0.035	0.203	0.231	0.444	0.034	0.189	0.219	0.369
		CW (CL)	0.712	1.722	1.834	2.504	0.703	1.633	1.738	2.043
		CP	0.960	0.950	0.950	0.960	0.960	0.920	0.950	0.970
	n = 70	ABias	0.039	0.068	0.082	0.157	0.013	0.068	0.051	0.090
		MSE	0.026	0.134	0.153	0.301	0.023	0.131	0.139	0.258
		CW (CL)	0.608	1.408	1.498	1.627	0.586	1.364	1.416	1.941
		CP	0.930	0.940	0.940	0.960	0.910	0.940	0.950	0.960
,	n = 30	ABias	0.094	0.296	0.295	0.237	0.060	0.264	0.247	0.147
		MSE	0.099	0.890	0.892	0.680	0.094	0.811	0.790	0.519
		CW (CL)	1.176	3.510	3.518	3.096	1.166	3.312	3.237	2.723
		CP	0.943	0.949	0.950	0.952	0.949	0.931	0.948	0.952
	n = 50	ABias	0.055	0.169	0.166	0.136	0.040	0.185	0.169	0.101
		MSE	0.055	0.427	0.428	0.326	0.055	0.432	0.418	0.290
		CW (CL)	1.176	3.510	3.518	3.096	0.898	2.443	2.388	2.050
		CP	0.953	0.946	0.941	0.961	0.952	0.946	0.945	0.952
	n = 70	ABias	0.051	0.123	0.119	0.051	0.031	0.129	0.101	0.063
		MSE	0.040	0.281	0.285	0.226	0.038	0.277	0.263	0.195
		CW (CL)	0.754	2.022	2.030	1.804	0.753	1.979	1.948	1.695
		CP	0.942	0.953	0.945	0.942	0.961	0.942	0.949	0.942
.5,	n = 30	ABias	0.086	0.383	0.493	0.507	0.037	0.268	0.426	0.178
		MSE	0.089	1.832	2.583	2.476	0.219	1.497	2.411	0.908
		CW (CL)	1.122	5.088	5.996	5.840	0.843	4.543	5.563	3.387
		CP	0.950	0.950	0.950	0.950	0.942	0.950	0.880	0.938
	n = 50	ABias	0.053	0.226	0.279	0.297	0.019	0.197	0.304	0.095
		MSE	0.051	0.870	1.194	1.132	0.049	0.815	1.197	0.865
		CW (CL)	0.858	3.548	4.141	4.006	0.842	3.376	3.996	3.541
		CP	0.950	0.940	0.940	0.970	0.930	0.910	0.930	0.950
	n = 70	ABias	0.049	0.173	0.236	0.244	0.014	0.166	0.149	0.091
		MSE	0.036	0.574	0.800	0.766	0.033	0.543	0.688	0.607
		CW (CL)	0.712	2.894	3.382	3.294	0.697	2.770	3.116	2.997
		CP	0.940	0.940	0.950	0.960	0.950	0.930	0.930	0.960
,	n = 30	ABias	0.111	0.390	0.489	0.326	0.067	0.374	0.418	0.168
		MSE	0.140	1.535	2.191	1.234	0.134	1.435	1.938	0.891
		CW (CL)	1.402	4.610	5.476	4.164	1.395	4.375	5.016	3.545
		CP	0.943	0.950	0.954	0.947	0.946	0.903	0.915	0.955
	n = 50	ABias	0.068	0.232	0.279	0.183	0.041	0.236	0.262	0.108
		MSE	0.079	0.737	1.017	0.577	0.078	0.725	0.977	0.496
		CW (CL)	1.066	3.240	3.798	2.892	1.074	3.167	3.657	2.697
		CP	0.950	0.940	0.949	0.961	0.949	0.917	0.886	0.952
	n = 70	ABias	0.060	0.164	0.214	0.160	0.028	0.166	0.166	0.069
		MSE	0.057	0.479	0.669	0.399	0.037	0.472	0.622	0.333
		CW (CL)	0.902	2.636	3.094	2.394	0.903	2.581	2.972	2.217
		CP	0.948	0.950	0.950	0.943	0.966	0.887	0.883	0.950
,	n = 30	ABias	0.152	0.717	0.607	0.533	0.068	0.663	0.536	0.115
		MSE	0.257	4.574	3.552	2.888	0.237	4.168	3.127	1.682
		CW (CL)	1.896	7.898	6.994	6.322	1.873	7.403	6.356	4.974
		CP	0.938	0.949	0.949	0.954	0.836	0.928	0.955	0.956
	n = 50	ABias	0.091	0.414	0.352	0.289	0.053	0.438	0.357	0.133
		MSE	0.143	2.075	1.637	1.277	0.141	2.080	1.606	1.038
		CW (CL)	1.440	5.410	4.822	4.282	1.448	5.311	4.641	3.905
		CP	0.952	0.947	0.934	0.966	0.761	0.919	0.932	0.963
	n = 70	ABias	0.082	0.309	0.268	0.259	0.031	0.283	0.232	0.060
		MSE	0.103	1.352	1.066	0.883	0.099	1.297	1.012	0.701
		CW (CL)	1.214	4.394	3.908	3.542	1.222	4.275	3.773	3.240
		CP	0.940	0.951	0.945	0.953	0.696	0.928	0.957	0.953