A New Skewed Discrete Model: Properties, Inference, and Applications

In this paper, a new probability discrete distribution for analyzing over-dispersed count data encountered in biological sciences was proposed. The new discrete distribution, with one parameter, has a log-concave probability mass functionand an increasing hazard rate function, for all choices of its parameter. Several properties of the proposed distributionincluding the mode, moments and index of dispersion, mean residual life, mean past life, order statistics and L-moment statistics have been established. Two actuarial or risk measures were derived. The numerical computations forthese measures are conducted for several parametric values of the model parameter. The parameter of the introduceddistribution is estimated using eight frequentist estimation methods. Detailed Monte Carlo simulations are conductedto explore the performance of the studied estimators. The performance of the proposed distribution has been examinedby three over-dispersed real data sets from biological sciences.