Statistical Properties and Estimation of Parameters of Two-Parameter Poisson-Sujatha
Distribution with Applications
Riki Tabassum, Rama Shanker
Abstract
The two-parameter Poisson-Sujatha distribution, which includes Poisson-Sujatha distribution as a particular
case, has been shown to be unimodal, over-dispersed and having increasing hazard rate. It is also a three-
component mixture of negative binomial distributions. The reliability properties of the distribution including
hazard function, reverse hazard function, cumulative hazard function, Mill’s ratio and mean residual life
function has been discussed. Both maximum likelihood estimation and Bayesian estimation has been discussed
for estimating the parameters of the distribution. Simulation study has been conducted to test the consistency of
maximum likelihood estimators. The goodness of fit of the distribution has been tested for two real datasets and
the fit has been compared with other two-parameter over-dispersed discrete distributions including another two-
parameter Poisson-Sujatha distribution, the new two-parameter Poisson-Sujatha distribution and the generalized
Poisson-Sujatha distribution.
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