Bounds on Approximating Generalized Waring Distribution In A Generalized Waring Process

Kanint Teerapabolarn

doi:https://doi.org/10.14445/22315373/IJMTT-V66I12P518

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 66 | Issue 12 | Year 2020 | Article Id. IJMTT-V66I12P518 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I12P518

Bounds on Approximating Generalized Waring Distribution In A Generalized Waring Process

Kanint Teerapabolarn

Citation :

Kanint Teerapabolarn, "Bounds on Approximating Generalized Waring Distribution In A Generalized Waring Process," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 12, pp. 128-133, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I12P518

Abstract

This paper uses Stein's method for Poisson and negative binomial distributions to gether with the covariance associated with the generalized Warning random variable to determine error bounds for measuring the accuracy of approximations of generalized Waring distribution with parameters (a,kt,ρ) in a generalized Waring process, where a>0, k>0, ρ>0 and t≥0. The bounds in the present study are pointed out that(i) for c=ρ-1/k >0, the generalized Waring distribution can be approximated by the negative binomial distribution with parameters (a,c/c+t) when c and/or k are large and (ii) for λ=a/c>0, the generalized Waring distribution with parameters(a,kt,c) can be approximated by the Poisson distribution with mean λt when c is large or λt is small.

Keywords

Generalized Waring process, Poisson approximation, Negative binomial approximation, Stein’s method.

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