Abstract
Two-runs statistic is approximated by various compound Poisson distributions and second order asymptotic expansions. Estimates of lower bounds are obtained for the uniform Kolmogorov and local metrics.
Highlights
It is obvious, that ηj are 1-dependent random variables
Products and powers of V and M are understood in the convolution sense, i.e, VM {A} =
The exponential of M is given by eM = exp{M } =
Summary
We denote the distribution and characteristic function of S by F and F(t), respectively. Let Ia denote the distribution concentrated at real a and set I = I0. Let V and M be two finite signed measures concentrated on integers Z. The exponential of M is given by eM = exp{M } = Let us define measures used for approximations of F : G1 := exp{γ1U }, G2 := exp γ1U + γ2U 2 , G3 := exp γ1U + γ2U 2 + γ3U 3 .
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