Order Statistics for Negative Binomial Distribution

Abstract

In this paper, we considers the order statistics from negative binomial distribution .which have moment of all positive orders.We take as example for x_3to find the mean and variance. We define aformula for B . The incomplete beta function of Negative binomial distribution is I_(1-B(x) ) (i,M), But The incomplete beta function of binomial distribution is I_B(x) (i,M-i+1). The purpose of this paper is to study the distribution of x_i and R=x_j-x_i (x_j,x_i ,i>j) . The results are obtained here can be compared to those for a continuous variate.