An Empirical Likelihood Ratio-Based Omnibus Test for Normality with an Adjustment for Symmetric Alternatives

Table 9

Monte Carlo power comparisons from asymmetric alternative distributions at .

Distribution		Asymmetric alternative distributions: set 3 (1 of 1)
		Selected EDF-based tests				Selected moment-based tests						SW tests		Proposed tests
		AD	LL	CVM		JB	RJB			DP	SEELR	SW	SF	CSELR	SRELR
Gamma (2, 1)	20	0.4656	0.3111	0.4130	0.5309	0.4105	0.3909	0.2606	0.4653	0.3664	0.5680	0.5250	0.5045	0.2754	0.2401
	30	0.6542	0.4684	0.5967	0.7111	0.5720	0.5478	0.3508	0.6650	0.5136	0.8123	0.7516	0.7103	0.3793	0.3325
	50	0.8905	0.6973	0.8461	0.9068	0.8240	0.7711	0.4895	0.8915	0.6949	0.9693	0.9469	0.9266	0.5671	0.4837
	80	0.9878	0.8958	0.9689	0.9857	0.9739	0.9434	0.6363	0.9859	0.8386	0.9991	0.9980	0.9962	0.7557	0.6737
	100	0.9977	0.9528	0.9897	0.9972	0.9948	0.9845	0.6997	0.9976	0.8796	0.9999	0.9999	0.9995	0.8307	0.7590
Weibull (2 ,1)	20	0.1359	0.0941	0.1147	0.1805	0.1234	0.1201	0.0909	0.1405	0.1225	0.1725	0.1548	0.1452	0.1118	0.1029
	30	0.1929	0.1283	0.1633	0.2343	0.1706	0.1519	0.1144	0.2151	0.1614	0.2818	0.2425	0.2015	0.1262	0.1183
	50	0.3110	0.2062	0.2493	0.3379	0.2656	0.2450	0.1229	0.3670	0.2529	0.5136	0.4111	0.3516	0.1613	0.1237
	80	0.4869	0.3125	0.4116	0.5063	0.4400	0.3808	0.1413	0.5803	0.3914	0.7662	0.6604	0.5883	0.2080	0.1597
	100	0.6080	0.3930	0.5119	0.6295	0.5661	0.4818	0.1529	0.6976	0.4703	0.8703	0.7940	0.7185	0.2216	0.1753
SN (0, 1, 5)	20	0.2443	0.1783	0.2156	0.3008	0.1992	0.2003	0.1300	0.2497	0.2212	0.2915	0.2764	0.2600	0.1576	0.1297
	30	0.3563	0.2464	0.3238	0.4197	0.2956	0.2828	0.1584	0.3710	0.3343	0.4659	0.4157	0.3955	0.1938	0.1612
	50	0.5852	0.4036	0.5246	0.6397	0.4815	0.4390	0.2084	0.6077	0.4672	0.7048	0.6677	0.6331	0.2642	0.2099
	80	0.8152	0.6093	0.7556	0.8268	0.7366	0.6619	0.2529	0.8291	0.7346	0.9028	0.8874	0.8533	0.3769	0.2935
	100	0.8987	0.7235	0.8487	0.9059	0.8484	0.7889	0.2847	0.9204	0.8004	0.9523	0.9517	0.9303	0.4283	0.3323
SC (0, 2, 5)	20	0.9693	0.9353	0.9632	0.9769	0.9477	0.9446	0.8649	0.9526	0.9346	0.9514	0.9705	0.9693	0.8690	0.8444
	30	0.9974	0.9882	0.9958	0.9972	0.9905	0.9910	0.9567	0.9884	0.9708	0.9782	0.9961	0.9974	0.9680	0.9585
	50	1.0000	0.9997	1.0000	1.0000	1.0000	0.9999	0.9958	0.9972	0.9886	0.9857	0.9999	1.0000	0.9981	0.9972
	80	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	0.9998	0.9985	0.9900	0.9934	1.0000	1.0000	1.0000	1.0000
	100	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	0.9999	0.9990	0.9912	0.9982	1.0000	1.0000	1.0000	1.0000
Beta (2, 1)	20	0.2558	0.1745	0.2298	0.1162	0.0767	0.0744	0.0887	0.1157	0.1107	0.3243	0.3062	0.2147	0.1905	0.1822
	30	0.4282	0.2654	0.3672	0.2107	0.0918	0.0815	0.0896	0.1749	0.1678	0.5164	0.5185	0.3676	0.3569	0.3116
	50	0.7142	0.4572	0.6174	0.4376	0.1992	0.1175	0.1094	0.3200	0.3021	0.7994	0.8411	0.7026	0.7051	0.5928
	80	0.9349	0.7011	0.8569	0.7309	0.6129	0.2429	0.1765	0.5645	0.5511	0.9641	0.9871	0.9538	0.9478	0.8971
	100	0.9817	0.8204	0.9362	0.8540	0.8353	0.4430	0.2243	0.6914	0.6699	0.9909	0.9983	0.9935	0.9840	0.9627
Beta (3, 1.5)	20	0.1447	0.1057	0.1348	0.0702	0.0615	0.0623	0.0687	0.0915	0.0871	0.1855	0.1715	0.1272	0.1064	0.1091
	30	0.2313	0.1587	0.2051	0.1181	0.0793	0.0727	0.0659	0.1335	0.1237	0.3157	0.2700	0.1985	0.1844	0.1735
	50	0.4311	0.2718	0.3670	0.2188	0.1277	0.0935	0.0716	0.2395	0.2022	0.5751	0.5390	0.3935	0.4089	0.3435
	80	0.6974	0.4347	0.5793	0.4296	0.3340	0.1670	0.0940	0.4359	0.3654	0.8381	0.8412	0.7221	0.7253	0.6313
	100	0.8207	0.5347	0.7112	0.5502	0.5358	0.2722	0.1220	0.5671	0.4855	0.9270	0.9370	0.8628	0.8347	0.7700