Some recursive formulas related to inverse moments of the random variables with binomial-type distributions

This paper considers the inverse moments of the random variables with binomial-type distributions. We first derive some recursive formulas related to the inverse moments of the random variables with binomial and negative binomial distributions. Then we investigate the inverse moments of the random variables with maximum negative binomial distributions by using the recursive formula related to the negative binomial distribution. We further obtain some similar results for the generalized binomial and negative binomial distributions.