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Poisson approximation for (k(1), k(2))-events via the Stein-Chen method

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Title Poisson approximation for (k(1), k(2))-events via the Stein-Chen method
 
Creator VELLAISAMY, P
 
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
 
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.
 
Publisher APPLIED PROBABILITY TRUST
 
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
 
Type Article
 
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
 
Language en