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

Table 3

The estimated coverage probabilities and expected lengths of 95% 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	0.8829	0.9533	0.9440	0.9538	0.9504	0.9511	0.0661	0.0785	0.0762	0.1058	0.0758	0.0870
	0.10	0.8827	0.9537	0.9457	0.9549	0.9501	0.9506	0.1333	0.1608	0.1544	0.2113	0.1513	0.1737
	0.20	0.8847	0.9578	0.9508	0.9548	0.9500	0.9507	0.2756	0.3630	0.3282	0.4226	0.3026	0.3475
	0.33	0.8904	0.9647	0.9599	0.9542	0.9501	0.9501	0.4880	0.8954	0.6498	0.6986	0.5001	0.5743
	0.50	0.8934	0.9711	0.9656	0.9537	0.9487	0.9491	0.8276	1.3796	1.4333	1.0561	0.7561	0.8683
	0.67	0.9042	0.9795	0.9721	0.9548	0.9495	0.9502	1.2550	1.5758	1.9791	1.4140	1.0124	1.1625
10	0.05	0.9115	0.9522	0.9440	0.9511	0.9502	0.9495	0.0451	0.0490	0.0478	0.0551	0.0480	0.0515
	0.10	0.9125	0.9539	0.9460	0.9529	0.9510	0.9505	0.0912	0.0997	0.0968	0.1105	0.0962	0.1031
	0.20	0.9156	0.9588	0.9522	0.9521	0.9506	0.9498	0.1881	0.2113	0.2023	0.2209	0.1924	0.2062
	0.33	0.9201	0.9663	0.9620	0.9507	0.9499	0.9489	0.3311	0.4052	0.3718	0.3645	0.3174	0.3401
	0.50	0.9281	0.9788	0.9751	0.9510	0.9492	0.9500	0.5606	0.9797	0.7415	0.5528	0.4814	0.5159
	0.67	0.9372	0.9856	0.9812	0.9504	0.9500	0.9492	0.8470	1.7544	1.5776	0.7398	0.6442	0.6904
15	0.05	0.9244	0.9517	0.9443	0.9507	0.9506	0.9499	0.0366	0.0386	0.0377	0.0415	0.0380	0.0398
	0.10	0.9250	0.9523	0.9446	0.9494	0.9501	0.9475	0.0737	0.0781	0.0761	0.0830	0.0760	0.0796
	0.20	0.9294	0.9592	0.9537	0.9516	0.9509	0.9507	0.1520	0.1637	0.1584	0.1660	0.1521	0.1593
	0.33	0.9324	0.9681	0.9634	0.9502	0.9493	0.9489	0.2669	0.3016	0.2861	0.2737	0.2508	0.2626
	0.50	0.9418	0.9811	0.9783	0.9501	0.9490	0.9497	0.4495	0.5917	0.5267	0.4141	0.3794	0.3973
	0.67	0.9528	0.9894	0.9862	0.9496	0.9510	0.9493	0.6819	1.3361	1.0306	0.5564	0.5097	0.5338
25	0.05	0.9356	0.9513	0.9458	0.9504	0.9500	0.9505	0.0281	0.0290	0.0284	0.0302	0.0287	0.0295
	0.10	0.9338	0.9509	0.9452	0.9491	0.9481	0.9484	0.0566	0.0586	0.0573	0.0604	0.0574	0.0590
	0.20	0.9383	0.9580	0.9527	0.9497	0.9495	0.9491	0.1167	0.1219	0.1188	0.1209	0.1149	0.1181
	0.33	0.9453	0.9701	0.9664	0.9510	0.9497	0.9505	0.2043	0.2192	0.2118	0.1990	0.1892	0.1945
	0.50	0.9575	0.9839	0.9816	0.9520	0.9516	0.9512	0.3456	0.4004	0.3783	0.3024	0.2875	0.2956
	0.67	0.9651	0.9920	0.9899	0.9512	0.9503	0.9505	0.5205	0.7126	0.6382	0.4045	0.3845	0.3953
50	0.05	0.9400	0.9504	0.9458	0.9504	0.9488	0.9499	0.0198	0.0201	0.0197	0.0204	0.0199	0.0202
	0.10	0.9431	0.9520	0.9473	0.9493	0.9491	0.9492	0.0398	0.0405	0.0398	0.0409	0.0399	0.0405
	0.20	0.9479	0.9581	0.9534	0.9496	0.9491	0.9491	0.0819	0.0837	0.0821	0.0817	0.0797	0.0808
	0.33	0.9581	0.9695	0.9669	0.9506	0.9510	0.9502	0.1437	0.1490	0.1457	0.1349	0.1316	0.1334
	0.50	0.9686	0.9853	0.9834	0.9518	0.9512	0.9514	0.2420	0.2615	0.2538	0.2044	0.1994	0.2022
	0.67	0.9776	0.9940	0.9927	0.9507	0.9506	0.9510	0.3652	0.4272	0.4089	0.2740	0.2673	0.2710
100	0.05	0.9454	0.9502	0.9463	0.9496	0.9496	0.9492	0.0139	0.0140	0.0138	0.0141	0.0140	0.0141
	0.10	0.9479	0.9528	0.9494	0.9511	0.9502	0.9507	0.0281	0.0283	0.0279	0.0283	0.0280	0.0282
	0.20	0.9545	0.9590	0.9554	0.9500	0.9501	0.9501	0.0578	0.0584	0.0576	0.0566	0.0559	0.0563
	0.33	0.9621	0.9697	0.9675	0.9493	0.9489	0.9491	0.1013	0.1034	0.1018	0.0934	0.0923	0.0929
	0.50	0.9758	0.9844	0.9834	0.9489	0.9486	0.9488	0.1705	0.1789	0.1757	0.1416	0.1399	0.1408
	0.67	0.9849	0.9946	0.9939	0.9495	0.9489	0.9492	0.2570	0.2840	0.2775	0.1896	0.1873	0.1886