An improved bound for negative binomial approximation with -functions

In this article, we use Stein’s method together with -functions to give an improved bound for the total variation distance between the distribution of a non-negative integer-valued random variable and the negative binomial distribution with parameters and , where is equal to the mean of , . The improved bound is sharper than that mentioned in Teerapabolarn and Boondirek (2010). We give three examples of the negative binomial approximation to the distribution of concerning the negative hypergeometric, Pólya and negative Pólya distributions

P A POINTWISE BINOMIAL APPROXIMATION IN A MODEL OF SOMATIC CELL HYBRID

Abstract: This paper uses Stein's method to give a non-uniform bound for approximating the distribution of the number of pairs of chromosomes for which the Hamming distance is less than some fixed Hamming distance d by the binomial distribution with parameters |Γ| = 253 and p ∈ (0, 1). Two numerical examples have been given to illustrate the obtained result

P A POINTWISE BINOMIAL APPROXIMATION IN A MODEL OF SOMATIC CELL HYBRID

Abstract: This paper uses Stein's method to give a non-uniform bound for approximating the distribution of the number of pairs of chromosomes for which the Hamming distance is less than some fixed Hamming distance d by the binomial distribution with parameters |Γ| = 253 and p ∈ (0, 1). Two numerical examples have been given to illustrate the obtained result

P A AN IMPROVED NEGATIVE BINOMIAL DISTRIBUTION TO APPROXIMATE THE NEGATIVE HYPERGEOMETRIC DISTRIBUTION

Abstract: We give an improved negative binomial distribution with parameters r and p for approximating the negative hypergeometric distribution with parameters R, S and r, where p = 1 − q = R+1 R+S+1 . The improved approximation is more accurate than the negative binomial approximation when R is sufficiently large

New non-uniform bounds on Poisson approximation for dependent Bernoulli trials

Abstract The aim of this article is a use of the Stein-Chen method to obtain new non-uniform bounds on the error of the distribution of sums of dependent Bernoulli random variables and the Poisson distribution. The bounds obtained in this study are improved to be more appropriate for measuring the accuracy of Poisson approximation. Examples are provided to illustrate applications of the obtained results

A Uniform Bound on Negative Binomial Approximation with w-Functions

Abstract This paper uses Stein's method and w-functions to determine a uniform bound for the Kolmogorov distance between the cumulative distribution function of a non-negative integer-valued random variable X and the negative binomial cumulative distribution function with parameter