ON A WIDE CLASS OF GENERALIZED GEOMETRIC DISTRIBUTION FOR OVER AND UNDER DISPERSED DATA SETS

In this paper, a wide class of generalized geometric distribution is introduced and we name this class of distributions as “the alpha generalized geometric distribution (AGGD)". Several important distributions are obtained as a special cases of this proposed model. Important distributional properties such as generating functions, moments, recursive relations of the proposed distribution are examined. Parameter estimation using maximum likelihood is discussed. Three well-known data sets, having long tails, are analyzed and the results of fitting by various models are provided. Further, the generalized likelihood ratio test procedure is considered for testing the significance of the parameters of the GGD. Finally, performance of the different estimation methods are compared by means of a Monte Carlo simulation.