Bounds on Approximating Generalized Waring Distribution In A Generalized Waring Process

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2020 by IJMTT Journal
Volume-66 Issue-12
Year of Publication : 2020
Authors : Kanint Teerapabolarn
  10.14445/22315373/IJMTT-V66I12P518

MLA

MLA Style: Kanint Teerapabolarn  "Bounds on Approximating Generalized Waring Distribution In A Generalized Waring Process" International Journal of Mathematics Trends and Technology 66.12 (2020):128-133. 

APA Style: Kanint Teerapabolarn(2020). Bounds on Approximating Generalized Waring Distribution In A Generalized Waring Process  International Journal of Mathematics Trends and Technology, 128-133.

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.

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