IJPAM: Volume 78, No. 7 (2012)
POISSON APPROXIMATION BY -FUNCTIONS
Department of Mathematics
Faculty of Science
Chonburi, 20131, THAILAND
Centre of Excellence in Mathematics, CHE
Sri Ayutthaya Road, Bangkok 10400, THAILAND
Abstract. The Stein-Chen method and -functions are used to give a result in the Poisson approximation to the distribution of a non-negative integer-valued random variable , in terms of the difference of cumulative distribution function of and Poisson cumulative distribution function together with its non-uniform bound. For applications, the result obtained in the present study is applied to approximate binomial, negative binomial, hypergeometric and negative hypergeometric cumulative distribution functions.
Received: June 24, 2012
AMS Subject Classification: 62E17, 60F05
Key Words and Phrases: cumulative distribution function, non-uniform bound, Poisson approximation, Stein's method; -functions
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395