  In this paper, a new mixed Poisson distribution is introduced. This new
distribution is obtained by utilizing mixing process, with Poisson distribution
as mixed distribution and Transmuted Exponential distribution as mixing
distribution. Some distributional properties like unimodality, moments,
over-dispersion, Taylor series expansion of proposed model are studied.
Estimation of the parameters using method of moments, method of moments and
proportion and maximum likelihood estimation along with data fitting experiment
to show its advantage over some existing distribution. Further, an actuarial
applications in context of aggregate claim distribution is discussed. Finally,
we discuss a count regression model based on proposed distribution and its
usefulness over some well established model.
