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Abstract: this paper, we shall describe the asymptotic behaviors of several distances of Poisson approximation to a wide class of discrete distributions covering many examples from number theory, combinatorics and arithmetic semigroups. Our aim is to show that whenever (analytic) generating functions of the random variables in question are available, complex-analytic methods can be used to derive precise asymptotic results for the five distances above. Actually, we shall consider the following... (Update)
Context of citations to this paper: More
.... z) 1 z Therefore the distribution of X n is asymptotically Poisson with parameter log n and thus asymptotically normal; see [38]. The mean was discussed by Brinck [10] Quickselect. The number of comparisons and exchanges used by quickselect to nd the smallest (or the largest)...
.... fl denotes Euler s constant: d TV (L(M n ) Poi( 1 fi fi P(M n = j) Gamma e Gamma (j Gamma 1) fi fi 2e log n see Hwang [16]. Returning to our n , we first observe that the mean of n is smaller than that of M n in view of the presence of ties. Prodinger [24] showed...
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BibTeX entry: (Update)
H.-K. Hwang, Asymptotics of Poisson approximation to random discrete distributions: an analytic approach, Advances in Applied Probability, 31, 448-491 (1999). http://citeseer.ist.psu.edu/hwang98asymptotics.html More
@article{ hwang98asymptotics,
author = "Hsien-Kuei Hwang",
title = "Asymptotics of Divide-and-Conquer Recurrences: Batcher's Sorting Algorithm and a Minimum Euclidean Matching Heuristic",
journal = "Algorithmica",
volume = "22",
number = "4",
pages = "529-546",
year = "1998",
url = "citeseer.ist.psu.edu/hwang98asymptotics.html" }
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