Confidence Intervals for the Coefficient of Variation in a Normal Distribution with a Known Population Mean

Table 2

The estimated coverage probabilities and expected lengths of 90% confidence intervals for the coefficient of variation in a normal distribution with a known population mean.

𝑛	𝜅0	Coverage probabilities						Expected lengths
		Miller	McKay	Vangel	Approx.	Shortest	Equal-tailed	Miller	McKay	Vangel	Approx.	Shortest	Equal-tailed
5	0.05	0.8499	0.9066	0.8858	0.9016	0.9023	0.8979	0.0555	0.0607	0.0582	0.0741	0.0587	0.0675
	0.10	0.8518	0.9069	0.8866	0.9024	0.9008	0.8988	0.1120	0.1237	0.1177	0.1482	0.1174	0.1349
	0.20	0.8524	0.9130	0.8960	0.9036	0.8990	0.9006	0.2315	0.2689	0.2457	0.2963	0.2347	0.2696
	0.33	0.8572	0.9258	0.9136	0.9038	0.8999	0.9001	0.4099	0.5872	0.4528	0.4895	0.3878	0.4453
	0.50	0.8664	0.9430	0.9321	0.9036	0.8994	0.9001	0.6959	1.2123	0.9360	0.7409	0.5869	0.6741
	0.67	0.8773	0.9578	0.9428	0.9031	0.9000	0.8992	1.0603	1.5764	1.6394	0.9947	0.7880	0.9050
10	0.05	0.8747	0.9031	0.8870	0.9020	0.8996	0.9006	0.0379	0.0396	0.0382	0.0431	0.0388	0.0416
	0.10	0.8792	0.9052	0.8899	0.9024	0.9001	0.9014	0.0765	0.0804	0.0773	0.0864	0.0778	0.0833
	0.20	0.8802	0.9135	0.9002	0.9013	0.8993	0.9001	0.1576	0.1686	0.1603	0.1726	0.1553	0.1664
	0.33	0.8899	0.9304	0.9202	0.9017	0.9021	0.9015	0.2778	0.3140	0.2893	0.2853	0.2566	0.2750
	0.50	0.8999	0.9527	0.9451	0.9007	0.9004	0.8995	0.4709	0.6575	0.5323	0.4329	0.3895	0.4174
	0.67	0.9129	0.9694	0.9600	0.9018	0.8999	0.8992	0.7128	1.4205	1.0257	0.5801	0.5218	0.5593
15	0.05	0.8846	0.9010	0.8870	0.9000	0.8989	0.8988	0.0307	0.0316	0.0306	0.0333	0.0311	0.0326
	0.10	0.8866	0.9065	0.8925	0.9011	0.9013	0.9001	0.0618	0.0638	0.0617	0.0666	0.0622	0.0652
	0.20	0.8913	0.9127	0.9007	0.9006	0.8993	0.8987	0.1271	0.1328	0.1275	0.1330	0.1242	0.1301
	0.33	0.9046	0.9308	0.9218	0.9012	0.9022	0.9013	0.2239	0.2418	0.2286	0.2200	0.2054	0.2151
	0.50	0.9150	0.9544	0.9477	0.9000	0.9004	0.8991	0.3787	0.4522	0.4087	0.3338	0.3116	0.3264
	0.67	0.9280	0.9725	0.9661	0.9010	0.9002	0.8999	0.5713	0.8900	0.7010	0.4466	0.4170	0.4367
25	0.05	0.8933	0.9056	0.8932	0.9029	0.9035	0.9021	0.0236	0.0240	0.0233	0.0247	0.0238	0.0244
	0.10	0.8948	0.9054	0.8939	0.9010	0.9014	0.9004	0.0475	0.0485	0.0471	0.0495	0.0475	0.0489
	0.20	0.9022	0.9146	0.9042	0.9028	0.9008	0.9021	0.0977	0.1003	0.0971	0.0988	0.0949	0.0976
	0.33	0.9144	0.9318	0.9238	0.9005	0.9016	0.9004	0.1716	0.1796	0.1727	0.1630	0.1566	0.1610
	0.50	0.9285	0.9548	0.9491	0.8976	0.8977	0.8978	0.2893	0.3207	0.3027	0.2471	0.2374	0.2440
	0.67	0.9430	0.9768	0.9722	0.9018	0.8999	0.9008	0.4363	0.5418	0.4930	0.3310	0.3179	0.3268
50	0.05	0.8941	0.8992	0.8905	0.8993	0.8977	0.8989	0.0166	0.0167	0.0164	0.0170	0.0166	0.0168
	0.10	0.8996	0.9043	0.8949	0.9004	0.9007	0.8997	0.0334	0.0337	0.0330	0.0339	0.0333	0.0337
	0.20	0.9061	0.9118	0.9041	0.8994	0.8989	0.8996	0.0688	0.0697	0.0680	0.0678	0.0665	0.0674
	0.33	0.9220	0.9314	0.9253	0.8997	0.8996	0.8994	0.1206	0.1236	0.1204	0.1118	0.1096	0.1112
	0.50	0.9436	0.9583	0.9539	0.9009	0.9022	0.9010	0.2031	0.2153	0.2084	0.1695	0.1662	0.1685
	0.67	0.9588	0.9801	0.9770	0.9010	0.9009	0.9008	0.3062	0.3460	0.3309	0.2271	0.2226	0.2257
100	0.05	0.8998	0.9026	0.8961	0.9019	0.8902	0.9017	0.0117	0.0117	0.0115	0.0118	0.0113	0.0118
	0.10	0.9000	0.9031	0.8959	0.8995	0.8878	0.8992	0.0236	0.0237	0.0233	0.0236	0.0227	0.0236
	0.20	0.9110	0.9131	0.9072	0.9011	0.8901	0.9008	0.0485	0.0488	0.0480	0.0472	0.0453	0.0471
	0.33	0.9277	0.9329	0.9282	0.9015	0.8900	0.9012	0.0850	0.0863	0.0847	0.0779	0.0748	0.0777
	0.50	0.9485	0.9589	0.9561	0.9001	0.8885	0.8998	0.1429	0.1486	0.1455	0.1180	0.1133	0.1177
	0.67	0.9678	0.9810	0.9790	0.9020	0.8910	0.9021	0.2157	0.2347	0.2289	0.1582	0.1519	0.1578