Factorial moment -generating function and the Pascal distribution

Abstract

Given a distribution, the cumulants or factorial moments can be used to obtain the skewness and kurtosis which in turn are used to determine the normal approximation of the given distribution. It is shown in this paper that for the Pascal Distribution, the factorial moment generating function provides a simpler technique. It is also shown that the probability that at the xth trial, we will obtain the kth success can be obtain easily from the factorial moment generating function of the Pascal distribution.


[Global Jnl Mathematical Sci Vol.2(1) 2003: 51-56]