Discrete Burr-Hatke distribution with properties, estimation methods and regression model

A new one-parameter discrete distribution, namely discrete Burr-Hatke distribution is introduced and its mathematical properties are studied comprehensively. The main properties of the discrete Burr-Hatke distribution such as mean, variance, skewness and kurtosis measures are obtained in explicit forms. Several parameter estimation methods are used to obtain unknown model parameters and these estimation methods are compared via simulation study. The discrete Burr-Hatke distribution is over-dispersed since its variance is greater than its mean. This property of the proposed distribution opens a new opportunity to model over-dispersed data sets. To show the importance of the proposed distribution against the existing discrete probability distributions, three data sets in different fields are analyzed. Additionally, count regression model based on the discrete Burr-Hatke distribution is introduced with its residual analysis.