A Family of Waiting time Distributions Arising from a Bivariate Bernoulli Scheme

A new univariate five-parameter generalized negative binomial distribution based on the bivariate Bernoulli scheme is introduced. This distribution produces a new three-parameter generalized geometric distribution in a natural manner using probabilistic properties of the four-outcome model. Some basic statistical properties of the new distribution are studied. In addition, estimation of the unknown parameters is illustrated. Moreover, a new univariate three-parameter generalized exponential distribution is derived as a limit of the proposed three-parameter generalized geometric distribution. Finally, a generalization of the proposed distributions based on trivariate Bernoulli scheme is introduced.