On the generalization of negative binomial distribution

In this paper we study the distribution of the number of trials required to obtain r successes in a sequence of Bernoulli trials. We consider the conditions under which the above distribution is a negative binomial distribution. In fact, we show that the negative binomial distribution can be derived from dependent Bernoulli random variables. Finally, we consider a certain model in a generalized negative binomial distribution and obtain the expected value of the number of trials required.