On the Poisson transmuted Ailamujia distribution with applications to dispersed and skewed count data

Abstract

Assuming classical Poisson distribution for skewed and dispersed count observations may be misleading since it assumes equality for mean and variance. A new count distribution suitable for modelling dispersed and skewed count observations is proposed in this paper. This is achieved by assuming transmuted Ailamujia distribution for the parameter of the Poisson distribution and used mixed Poisson distribution process to obtain a new distribution. Mathematical properties of the new distribution are obtained and some measures of dispersion are assessed by assuming different parameter combinations for the distribution. Using the MLE for parameter estimation, the performance of the new proposition is assessed on four referred dispersed count data. Results obtained show that the new proposition provide better fit for all the datasets considered.