  In this paper, a new natural discrete version of the one parameter polynomial
exponential family of distributions have been proposed and studied. The
distribution is named as Natural Discrete One Parameter Polynomial Exponential
(NDOPPE) distribution. Structural and reliability properties have been studied.
Estimation procedure of the parameter of the distribution have been mentioned.
Compound NDOPPE distribution in the context of collective risk model have been
obtained in closed form. The new compound distribution has been compared with
the classical compound Poisson, compound Negative binomial, compound discrete
Lindley, compound xgamma-I and compound xgamma-II distributions regarding
suitability of modelling extreme data with the help of some automobile claim.
