Generalizing Benford's Law Using Power Laws: Application to Integer Sequences

Table 2

Minimum chi-square estimators.

Name of sequence	Sample size	TSPB	PB
		Parameter	Parameters
		c	alpha	beta	m
Square	100	0.79837	15.55957	1.74552	100
Cube	500	2.46519	5.55849	1.69860	100
Cube	1000	2.26798	20.56506	1.47082	100
Cube	10000	2.27054	20.53577	1.475760	100
Square root	99	1.40176	89491723	1.34334	100
Prime < 100	25	2.68581	23.13952	2.14449	100
Prime < 1000	168	2.95216	22.99754	2.28436	100
Prime < 10000	1229	3.03542	29.76729	2.30760	100
Princeton number	25	2.76170	6.94595	2.36119	100
Mixing sequence	618	2.53958	4.78641	1.83119	100
Pentagonal number	100	2.94847	2.06797	3.31268	100
Keith number	71	2.73338	2.16107	2.63720	1000
Bell number	100	1.08191	10.14820	1.24828	100
Catalan number	100	1.13522	0.67095	1.15377	5000
Lucky number	45	3.15721	7.56962	0.94576	100
Ulam number	44	3.55375	9.99445	0.81215	100
Numeri ideoni	65	1.12410	1297612.16	0.98591	100
Fibonacci number	100	2.05365	257000.42	1.00560	100
Partition number	94	1.23268	0.65651	1.71409	1000