Poisson approximation for (k(1), k(2))-events via the Stein-Chen method
DSpace at IIT Bombay
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Title |
Poisson approximation for (k(1), k(2))-events via the Stein-Chen method
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Creator |
VELLAISAMY, P
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Subject |
order-k
random-variables distributions patterns runs (k1, k2)-event binomial distribution of order (k(1) , k(2)) poisson approximation stein-chen method markov-bernoulli variable rate of convergence limit theorem |
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Description |
Consider a sequence of independent Bernoulli trials with success probability p. Let N(n; k(1), k(2)) denote the number of times that k(1) failures are followed by k(2) successes among the first n Bernoulli trials. We employ the Stein-Chen method to obtain a total variation upper bound for the rate of convergence of N(n; k(1), k(2)) to a suitable Poisson random variable. As a special case, the corresponding limit theorem is established. Similar results are obtained for Nk(3) (n; k(1), k(2)), the number of times that k(1) failures followed by k(2) successes occur k(3) times successively in n Bernoulli trials. The bounds obtained are generally sharper than, and improve upon, some of the already known results. Finally, the technique is adapted to obtain Poisson approximation results for the occurrences of the above-mentioned events under Markov-dependent trials.
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Publisher |
APPLIED PROBABILITY TRUST
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Date |
2011-07-18T10:02:42Z
2011-12-26T12:50:32Z 2011-12-27T05:35:51Z 2011-07-18T10:02:42Z 2011-12-26T12:50:32Z 2011-12-27T05:35:51Z 2004 |
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Type |
Article
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Identifier |
JOURNAL OF APPLIED PROBABILITY, 41(4), 1081-1092
0021-9002 http://dx.doi.org/10.1239/jap/1101840553 http://dspace.library.iitb.ac.in/xmlui/handle/10054/4870 http://hdl.handle.net/10054/4870 |
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Language |
en
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