IJPAM: Volume 78, No. 7 (2012)

A NON-UNIFORM BOUND ON
POISSON APPROXIMATION BY $w$-FUNCTIONS

K. Teerapabolarn
Department of Mathematics
Faculty of Science
Burapha University
Chonburi, 20131, THAILAND
and
Centre of Excellence in Mathematics, CHE
Sri Ayutthaya Road, Bangkok 10400, THAILAND


Abstract. The Stein-Chen method and $w$-functions are used to give a result in the Poisson approximation to the distribution of a non-negative integer-valued random variable $X$, in terms of the difference of cumulative distribution function of $X$ 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; $w$-functions

Download paper from here.



Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 78
Issue: 7