Title: Approximating the negative hypergeometric distribution

Authors: Dongping Hu; Aihua Yin

Addresses: School of Software and Communication Engineering, Jiangxi University of Finance and Economics, Nanchang, China ' School of Software and Communication Engineering, Jiangxi University of Finance and Economics, Nanchang, China

Abstract: An improvement to a suggested negative binomial approximation to the Negative Hypergeometric Distribution (NHGD) is advanced and the accuracy of this approximation is also quantified in terms of variation distance. The method to obtain the improved approximation is to expand the probability function of NHGD. Some numerical examples are presented to compare with the established negative binomial approximation. The result shows our approximation is more accurate almost everywhere than the negative binomial. A gamma approximation to the cumulative distribution of the negative hypergeometric is initiated. Our gamma approximation is attractive in practice because of its arithmetic simplicity and accuracy over a wide range of parameter values. Some numerical examples are presented to illustrate the result obtained.

Keywords: NHGD; negative hypergeometric distribution; negative binomial approximation; gamma approximation; distribution approximation; variation distance.

DOI: 10.1504/IJWMC.2014.065609

International Journal of Wireless and Mobile Computing, 2014 Vol.7 No.6, pp.591 - 598

Available online: 30 Oct 2014 *

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