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

Table 8

Monte Carlo power comparisons from long-tailed symmetric alternative distributions at .

Distribution		Symmetric long-tailed alternative distributions: set 2 (2 of 2)
		Selected EDF-based tests				Selected moment-based tests						SW tests		Proposed tests
		AD	LL	CVM		JB	RJB			DP	SEELR	SW	SF	CSELR	SRELR
Double-exp (0, 1)	20	0.2705	0.2190	0.2697	0.2361	0.3080	0.3852	0.2914	0.2511	0.2974	0.1566	0.2593	0.3092	0.2373	0.2272
	30	0.3701	0.2932	0.3705	0.3363	0.3968	0.5071	0.4127	0.3017	0.3740	0.1741	0.3610	0.4280	0.3439	0.3360
	50	0.5510	0.4327	0.5327	0.5291	0.5481	0.6798	0.5905	0.3554	0.5071	0.1759	0.5147	0.5956	0.5320	0.5238
	80	0.7392	0.6121	0.7385	0.7197	0.7212	0.8350	0.7549	0.3964	0.6509	0.1854	0.7112	0.7665	0.7265	0.7343
	100	0.8207	0.7026	0.8256	0.8103	0.8056	0.8956	0.8362	0.4097	0.7353	0.1889	0.8024	0.8517	0.8194	0.8208
Double-exp (0, 4)	20	0.2715	0.2153	0.2709	0.2468	0.2983	0.3826	0.2874	0.2576	0.2979	0.1581	0.2577	0.3166	0.2296	0.2221
	30	0.3685	0.2934	0.3627	0.3426	0.3993	0.5058	0.4050	0.3056	0.3743	0.1779	0.3531	0.4230	0.3428	0.3388
	50	0.5529	0.4303	0.5409	0.5316	0.5540	0.6775	0.5807	0.3476	0.5089	0.1677	0.5213	0.6004	0.5223	0.5260
	80	0.7390	0.6142	0.7280	0.7196	0.7220	0.8278	0.7606	0.3930	0.6624	0.1817	0.7050	0.7784	0.7415	0.7339
	100	0.8216	0.7000	0.8165	0.8088	0.8020	0.8946	0.8330	0.4078	0.7321	0.1777	0.7950	0.8448	0.8124	0.8160
Tukey (0, 1, −0.10, −0.10)	20	0.1961	0.1481	0.1822	0.1620	0.2401	0.2964	0.2352	0.2235	0.2460	0.1437	0.2041	0.2510	0.1865	0.1837
	30	0.2481	0.1760	0.2281	0.2222	0.3410	0.3959	0.3433	0.2777	0.3223	0.1748	0.2781	0.3248	0.2600	0.2576
	50	0.3552	0.2513	0.3273	0.3143	0.4744	0.5397	0.4891	0.3337	0.4347	0.1936	0.3894	0.4614	0.3897	0.3873
	80	0.4954	0.3475	0.4564	0.4403	0.6216	0.6864	0.6492	0.3889	0.5735	0.2148	0.5445	0.6105	0.5580	0.5481
	100	0.5774	0.4237	0.5196	0.5190	0.7041	0.7545	0.7216	0.4105	0.6452	0.2160	0.6218	0.7029	0.6476	0.6464
Tukey (0, 1, −0.15, −0.15)	20	0.2498	0.1870	0.2383	0.2242	0.3104	0.3640	0.2911	0.2804	0.3066	0.1778	0.2596	0.3033	0.2279	0.2304
	30	0.3363	0.2388	0.3084	0.2936	0.4120	0.4755	0.4167	0.3278	0.3977	0.2163	0.3562	0.4186	0.3408	0.3341
	50	0.4643	0.3452	0.4325	0.4149	0.5798	0.6354	0.6004	0.4063	0.5356	0.2375	0.5022	0.5766	0.4995	0.4921
	80	0.6391	0.4881	0.6017	0.5807	0.7335	0.8018	0.7645	0.4779	0.6899	0.2555	0.6828	0.7342	0.6873	0.6867
	100	0.7253	0.5667	0.6843	0.6747	0.8088	0.8629	0.8342	0.5127	0.7638	0.2645	0.7557	0.8149	0.7735	0.7837
Tukey (0, 1, −0.25, −0.25)	20	0.3752	0.2936	0.3461	0.3285	0.4250	0.4838	0.3993	0.3649	0.4198	0.2567	0.3731	0.4273	0.3396	0.3333
	30	0.4841	0.3878	0.4661	0.4234	0.5574	0.6235	0.5710	0.4542	0.5344	0.3127	0.4988	0.5686	0.4892	0.4772
	50	0.6723	0.5478	0.6456	0.6375	0.7379	0.7970	0.7512	0.5281	0.7003	0.3260	0.6903	0.7482	0.6903	0.6907
	80	0.8450	0.7406	0.8169	0.8089	0.8797	0.9197	0.8988	0.6075	0.8503	0.3610	0.8614	0.8934	0.8696	0.8649
	100	0.9069	0.8113	0.8863	0.8953	0.9326	0.9585	0.9447	0.6434	0.9044	0.9252	0.9128	0.9390	0.9252	0.9279