Poisson Lindley-Quasi XGamma Distribution For Count Data: Properties And Applications

The literature contains innumerable probability distributions for modeling over-dispersion and under-dispersion count datasets from various fields of study. However, some of these proposed distributions are inadequate due to empirical or theoretical characteristics. Therefore, minimizing information loss during modeling has prompted the demand to modify the classical discrete distributions. A new two-parameter count distribution is proposed by combining Poisson and Lindley-quasi XGamma distributions via a continuous mixture technique. Some statistical properties have been derived and studied, including factorial moments, raw moments, probability generating function, moment generating function, characteristic function, mean, variance, dispersion index, skewness, and kurtosis. The shape of the PMF and dispersion index suggest that the proposed distribution is right-skewed with a heavy tail, over-dispersion, and approximately equi-dispersion. The unknown parameters of the proposed model are estimated using both maximum likelihood and Bayesian techniques. The usefulness and flexibility of the proposed distribution are measured using two distinctive datasets. The application results reveal that the developed distribution provides maximum fit to the given datasets compared to the other eight standard discrete distributions. The Poisson Lindley-quasi XGamma distribution should therefore be considered by researchers when modeling over-dispersed count data from all fields of study.