A quasi Poisson-Aradhana distribution

Abstract

In this study, a QPAD (quasi Poisson-Aradhana distribution) by compounding a PD (Poisson distribution) with a QAD (quasi Aradhana distribution) is proposed that includes PAD (Poisson-Aradhana distribution) as a particular case. Expressions for its coefficient of variation, coefficient of skewness, coefficient of kurtosis, and index of dispersion are provided and their behaviours are studied for varying values of the parameters. The QPAD is shown to be unimodal and always over-dispersed. The estimation of its parameters using the method of maximum likelihood is discussed. Finally, the goodness of fit of the QPAD is assessed for two real count datasets from ecology and the fit is compared with that of the PD, PLD (Poisson-Lindley distribution), and PAD.