Table 2.

Empirical Estimates of Mean and Variance of D₂ from Human Chromosome 1

	Theoretical values
	θ = 0	1	2	3	4	5	Sample estimate
m = n = 1,000, k = 8
Mean	19.08	24.74	26.90	27.55	28.30	28.74	27.66
Variance	33.58	44.62	50.99	52.19	54.37	56.01	181.1
Std. Dev.	5.795	6.680	7.141	7.224	7.373	7.484	13.46
m = n = 300, k = 5
Mean	101.1	117.4	122.4	123.5	124.3	124.3	120.7
Variance	216.6	254.4	307.5	307.8	315.6	321.9	1,258.
Std. Dev.	14.71	15.95	17.53	17.55	17.77	17.94	35.47

Empirical estimates of the mean and variance of D₂ from human chromosome 1 sample data from Ensembl (right-hand column) were compared with the theoretical mean and variance based on Markov models of various orders using estimated Markov matrices for human chromosome 1. The variance for k = θ = 5 was calculated by implementing Equation (37).