Table 1.

Mean and Variance of D₂ Calculated from Theoretical Formulas

		Order
		0	1	2	3
Mean	Lower 95%	18.84	24.70	27.66	28.84
	Theoretical	18.92	24.73	27.79	28.97
	Empirical	18.95	24.83	27.80	29.00
	Upper 95%	19.07	24.96	27.95	29.15
Variance	Lower 95%	32.89	43.23	53.06	59.01
	Theoretical	33.24	44.69	55.56	60.53
	Empirical	33.81	44.44	54.54	60.65
	Upper 95%	34.77	45.70	56.09	62.37

Mean and variance of D₂ were calculated from the theoretical formulas derived in Section 3, and estimated from synthetically generated data (10,000 sequence pairs) for Markov models of order θ = 0, 1, 2, and 3 using Markov matrices estimated from human chromosome 1. Word length k = 8, alphabet size d = 4, sequence lengths m = n = 1,000.