ON POINTWISE BINOMIAL APPROXIMATION
BY -FUNCTIONS

K. Teerapabolarn, P. Wongkasem
Department of Mathematics
Faculty of Science
Burapha University
Chonburi, 20131, THAILAND

Abstract. This paper, we use Stein's method and -functions to give a result in the binomial approximation to the distribution of a non-negative integer-valued random variable, in terms of the point metric between two such distributions together with its non uniform bound. Furthermore, for applications, we use the obtained result to approximate some distributions such as hypergeometric, negative hypergeometric and Pólya distributions.

Received: May 4, 2011

AMS Subject Classification: 62E17, 60F05

Key Words and Phrases: binomial approximation, non-uniform bound, point metric, Stein's method, -functions

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