منابع مشابه
The central limit theorem and Poisson approximation
2 Poisson approximation 6 2.1 A coupling approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Stein’s method for Poisson approximation . . . . . . . . . . . . . . . . . . . . . 8 2.2.1 Independent summands . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2.2 Dependent summands: the local approach . . . . . . . . . . . . . . . . . 10 2.2.3 Size biasing and coup...
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In this paper we refine a Poisson limit theorem of Gnedenko and Kolmogorov (1954): we determine the error order of a Poisson approximation for sums of asymptotically negligible integer-valued random variables that converge in distribution to the Poisson law. As an application of our results, we investigate the case of the coupon collector’s problem when the distribution of the collector’s waiti...
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In this paper, we prove the Hyers-Ulam stability of the symmetric functionalequation $f(ph_1(x,y))=ph_2(f(x), f(y))$ in random normed spaces. As a consequence, weobtain some random stability results in the sense of Hyers-Ulam-Rassias.
متن کاملA hooray for Poisson approximation
We give several examples for Poisson approximation of quantities of interest in the analysis of algorithms: the distribution of node depth in a binary search tree, the distribution of the number of losers in an election algorithm and the discounted profile of a binary search tree. A simple and well-known upper bound for the total variation distance between the distribution of a sum of independe...
متن کاملA Compound Poisson Approximation Inequality
We give conditions under which the number of events which occur in a sequence of m-dependent events is stochastically smaller than a suitably defined compound Poisson random variable. The results are applied to counts of sequence pattern appearances and to system reliability. We also provide a numerical example.
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1975
ISSN: 0091-1798
DOI: 10.1214/aop/1176996313