Improved Small Sample Inference on the Ratio of Two Coefficients of Variation of Two Independent Lognormal Distributions

Table 3

(a) Empirical coverage rate for the simulation studies 1 to 8

Study	Method	le	cc	ue
1	Wald type	0.08	87.78	12.14
	Fieller type	3.48	95.50	1.02
	Log method	6.28	88.51	5.21
	Likelihood ratio	3.12	93.39	3.49
	Bartlett correction	2.40	94.90	2.70
2	Wald type	0.20	89.31	10.49
	Fieller type	0.82	94.01	5.17
	Log method	1.94	92.71	5.35
	Likelihood ratio	2.22	94.78	3.00
	Bartlett correction	1.92	95.29	2.79
3	Wald type	0.68	92.92	6.40
	Fieller type	3.48	95.50	1.02
	Log method	3.93	93.25	2.82
	Likelihood ratio	2.77	94.57	2.66
	Bartlett correction	2.53	94.85	2.27
4	Wald type	1.44	94.14	4.42
	Fieller type	7.81	91.99	0.20
	Log method	7.04	91.46	1.50
	Likelihood ratio	3.15	94.23	2.62
	Bartlett correction	2.88	94.85	2.27
5	Wald type	0.05	87.47	12.48
	Fieller type	2.99	95.28	1.73
	Log method	5.88	88.45	5.67
	Likelihood ratio	3.13	93.39	3.48
	Bartlett correction	2.42	94.90	2.68
6	Wald type	0.13	89.18	10.69
	Fieller type	0.67	93.59	5.74
	Log method	1.84	92.58	5.58
	Likelihood ratio	2.25	94.75	3.01
	Bartlett correction	2.00	95.23	2.77
7	Wald type	0.57	92.73	6.70
	Fieller type	2.87	95.26	1.87
	Log method	3.68	93.20	3.12
	Likelihood ratio	2.70	94.66	2.64
	Bartlett correction	2.52	94.90	2.58
8	Wald type	1.34	94.14	4.52
	Fieller type	7.36	92.28	0.36
	Log method	6.68	91.63	1.69
	Likelihood ratio	3.15	94.34	2.49
	Bartlett correction	2.88	94.83	2.29

(b) Empirical coverage rate for the simulation studies 9 to 16

Study	Method	le	cc	ue
9	Wald type	0.00	82.10	17.90
	Fieller type	0.01	98.88	1.11
	Log method	1.27	90.26	8.47
	Likelihood ratio	2.99	93.61	3.40
	Bartlett correction	2.40	94.94	2.66
10	Wald type	0.00	83.91	16.09
	Fieller type	0.00	90.18	9.82
	Log method	0.07	90.86	9.07
	Likelihood ratio	2.04	94.82	3.14
	Bartlett correction	1.92	95.24	2.84
11	Wald type	0.00	89.36	10.64
	Fieller type	0.00	96.70	3.30
	Log method	0.96	93.93	5.11
	Likelihood ratio	2.75	94.59	2.66
	Bartlett correction	2.48	94.97	2.55
12	Wald type	0.02	92.69	7.29
	Fieller type	0.47	99.16	0.37
	Log method	3.62	93.86	2.52
	Likelihood ratio	3.17	94.34	2.49
	Bartlett correction	2.96	94.71	2.33
13	Wald type	0.00	79.33	20.67
	Fieller type	2.01	97.99	0.00
	Log method	10.56	88.87	0.57
	Likelihood ratio	3.52	94.54	2.94
	Bartlett correction	2.68	95.03	2.29
14	Wald type	0.01	91.26	8.73
	Fieller type	0.64	99.32	0.04
	Log method	3.15	94.73	2.12
	Likelihood ratio	2.44	94.69	2.87
	Bartlett correction	2.10	95.19	2.71
15	Wald type	0.59	93.88	5.53
	Fieller type	5.44	94.56	0.00
	Log method	6.29	93.43	0.28
	Likelihood ratio	3.01	94.48	2.51
	Bartlett correction	2.84	94.83	2.33
16	Wald type	1.60	94.18	4.22
	Fieller type	12.16	87.84	0.00
	Log method	10.64	89.36	0.00
	Likelihood ratio	3.01	94.48	2.51
	Bartlett correction	2.95	94.71	2.34