Characterization and Goodness-of-Fit Test of Pareto and Some Related Distributions Based on Near-Order Statistics

Table 1

Monte Carlo power estimates of the tests at 5 percent significant level with null distribution function Power (1,2).

Sample size	Test	LG (2,8)	LN (0,1)	G (3,1)	W (0.5,2)	U
5		0.9999 (0.0494)	0.892 (0.0475)	0.7619 (0.05)	0.8969 (0.048)	0.8698 (0.0498)
		b = 2.1	b = 1.66	b = 1.69	b = 1.68	b = 1.67
		0.9999 (0.05)	0.892 (0.0495)	0.7619 (0.05)	0.8969 (0.05)	0.8698 (0.05)
		b = 2.22	b = 1.42	b = 1.39	b = 1.65	b = 1.39
		0.757 (0.05)	0.752 (0.05)	0.3217 (0.05)	0.618 (0.05)	0.121 (0.05)
		0.428 (0.05)	0.588 (0.05)	0.3217 (0.05)	0.367 (0.05)	0.08 (0.05)
7		1 (0.05)	0.9626 (0.499)	0.8711 (0.05)	0.963 (0.05)	0.9528 (0.05)
		b = 2.3	b = 1.67	b = 1.61	b = 1.71	b = 1.62
		1 (0.05)	0.9626 (0.05)	0.8711 (0.05)	0.963 (0.05)	0.9528 (0.05)
		b = 2.42	b = 1.37	b = 1.88	b = 1.381	b = 1.89
		0.826 (0.05)	0.810 (0.05)	0.392 (0.05)	0.81 (0.05)	0.11 (0.05)
		0.833 (0.05)	0.766 (0.05)	0.496 (0.05)	0.764 (0.05)	0.094 (0.05)
10		1 (0.05)	1 (0.05)	1 (0.05)	1 (0.05)	0.8813 (0.05)
		b = 2.38	b = 1.15	b = 1.15	b = 1.11	b = 2
		1 (0.05)	1 (0.05)	1 (0.05)	1 (0.05)	0.8813 (0.05)
		b = 2.57	b = 1.38	b = 1.88	b = 1.38	b = 2.01
		0.945 (0.05)	0.9066 (0.05)	0.559 (0.05)	0.9118 (0.05)	0.129 (0.05)
		0.975 (0.05)	0899 (0.05)	0.706 (0.05	0.9071 (0.05)	0.121 (0.05)