Kanint Teerapabolarn

DOI: 10.14456/sjst-psu.2017.39

pp. 355 - 358

Abstract

This paper uses the Stein–Chen method to determine a non-uniform bound on the point metric between the distribution
of a sum of independent negative binomial random variables and a Poisson distribution with mean λ = ∑ⁿ _i=1r_iq_i , where r_i
 and p_{i = 1 -} q_i are parameters of each negative binomial distribution. The result gives a good Poisson approximation when all q_i
are small or λ is small.

Keywords

• negative binomial distribution
• non-uniform bound
• point metric
• Poisson approximation
• Stein–Chen method