1Department of Mathematics, Faculty of Science, Burapha University, Chonburi, 20131, Thailand.
2Applied Statistics Program, Faculty of Science and Technology, Suan Dusit Rajabhat University, Bangkok, 10300, Thailand.
*Corresponding author
2000 Mathematics Subject Classification: Primary 60F05.
The aim of this paper is to approximate a generalized binomial distribution by binomial and Poisson distributions. Using the ω-function and the two Stein identities, the main result of each approximation in terms of the total variation distance between two distributions and its upper bound is obtained. Moreover, some numerical examples have been given to show applications of the results concerning the three special cases of generalized binomial distribution (binomial, hypergeometric and Pólya distributions).
A generalized binomial distribution, binomial approximation, binomial distribution, hypergeometric distribution, Pólya distribution, poisson approximation, Poisson distribution, Stein identity, ω-function
