IJPAM: Volume 69, No. 4 (2011)
APPROXIMATION BY -FUNCTIONS
Department of Mathematics
Faculty of Science
Chonburi 20131, THAILAND
e-mail: [email protected]
Abstract. We use Stein's method and -functions to determine a result in approximating the distribution of a non-negative integer-valued random variable by negative binomial distribution with parameters and in terms of the point metric between two such distributions together with its non uniform upper bound. In addition, when , we also give a non-uniform upper bound on pointwise geometric approximation to the distribution of . For applications, we use these results to approximate some discrete distributions such as Pólya, negative Pólya, hypergeometric and negative hypergeometric distributions.
Received: March 22, 2011
AMS Subject Classification: 60F05, 62E17
Key Words and Phrases: geometric approximation, negative binomial approximation, negative binomial distribution, non-uniform upper bound, point metric, 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