Properties, Estimation and Applications of Poisson-Amarendra Distribution
Ipshita Sarma, Rama Shanker
Abstract
The present paper deals with structural, statistical and reliability properties of Poisson-Amarendra distribution.
The probability model captures the longer right tail of data while converging to zero at a faster rate. The
distribution is shown to be unimodal, over-dispersed, and characterized by an increasing hazard rate. Stochastic
ordering of distribution has been established and entropy measures have also been derived. Maximum likelihood
estimation method and Bayesian estimation have been derived for the estimation of parameter. Simulation study
has been carried out to examine the consistency of maximum likelihood estimator. The practical usefulness of the
distribution is further assessed through its application to two real datasets. Its goodness of fit is compared with
one parameter equi-dispersed Poisson distribution and over-dispersed Poisson-Lindley distribution, Poisson-
Sujatha distribution, Poisson-Akash distribution and Poisson-Rama distribution. The results indicate that Poisson-
Amarendra distribution provides a superior and more flexible alternative for modeling over-dispersed count data
in practice.
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