Lower-Bound Estimates for Poisson-Type Approximations

“…Note that, though condition (5) requires the smallness of p and q, it allows for both parameters to be constants. In [8,Corollary 3] it was shown that, for p 0 = 1, nq 1 and ( p + q) 2 | p −q| the estimate (6) is of the right order. Estimate (6) is uniform over p 0 in a sense, that the right-hand side of (6) does not depend on p 0 .…”

Section: Known Resultsmentioning

confidence: 99%

“…In the remaining part of this section, we assume that condition (5) is satisfied and nq 1. Further, let µ and σ be defined as in (19), a = µ − σ 2 , and let δ be the fractional part of µ − σ 2 , see (8). It is not difficult to check that…”

Section: Auxiliary Resultsmentioning

confidence: 99%

Poisson type approximations for the Markov binomial distribution

Čekanavičius

Roos

2009

Stochastic Processes and their Applications

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The Markov binomial distribution is approximated by the Poisson distribution with the same mean, by a translated Poisson distribution and by two-parametric Poisson type signed measures. Using an adaptation of Le Cam's operator technique, estimates of accuracy are proved for the total variation, local and Wasserstein norms. In a special case, asymptotically sharp constants are obtained. For some auxiliary results, we used Stein's method.

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“…An integer-valued smoothing measure was used in [88]. Sections 10.2, 10.3, 10.4 and 10.5 are based on lemmas from [137], see also [39].…”

Section: Bibliographical Notesmentioning

confidence: 99%