Random sum for hypergeometric mixtures distribution

In this paper we deduce the probability mass function for a random variable which follows the hypergeometric—(binomial and right truncated geometric) mixtures distribution. Also, we derive the probability mass function for a random sum of the hypergeometric—(binomial and right truncated geometric) mixtures, where the two parameters of the hypergeometric distribution vary randomly. Moreover, we investigate the mean and the variance of this random sum when the number of terms is also a random variable.