Parameter Estimation and Application of Generalized Inflated Geometric Distribution

A count data that have excess number of zeros, ones, twos or threes are commonplace in experimental studies. But these inflated frequencies at particular counts may lead to overdispersion and thus may cause difficulty in data analysis. So to get appropriate results from them and to overcome the possible anomalies in parameter estimation, we may need to consider suitable inflated distribution. Generally, Inflated Poisson or Inflated Negative Binomial distribution are the most commonly used for modeling and analyzing such data. Geometric distribution is a special case of Negative Binomial distribution. This work deals with parameter estimation of a Geometric distribution inflated at certain counts, which we called Generalized Inflated Geometric (GIG) distribution. Parameter estimation is done using method of moments, empirical probability generating function based method and maximum likelihood estimation approach. The three types of estimators are then compared using simulation studies and finally a Swedish fertility dataset was modeled using a GIG distribution.