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It is a compound discrete probability distribution which has two parameters and whose particular case is Poisson-New Linear-Exponential Distribution (PNLED) 1. The statistical characteristics required for this distribution such as probability mass function (pmf), statistical moments, estimation of parameters and goodness of fit have been derived and explained nicely. To test theoretical reliability of this distribution, goodness of fit has been applied to some over-dispersed data which were used by other researchers and further, we found that this distribution looks more appropriate for statistical modelling than PNLED, generalised Poisson-Lindley distribution (GPLD) 1, 2 and Poisson-Lindley distribution (PLD) 3.
Sah et al. (Sun,) studied this question.