The discrete Poisson-Ishita Distribution
In this paper, a study on Poisson-Ishita distribution (PID), a Poisson mixture of Ishita distribution introduced, has been carried out. The expression for th factorial moment about origin has been derived. The expressions for coefficient of variation, skewness, kurtosis and index of dispersion have been obtained and their behaviors have been studied graphically. Its hazard rate, over-dispersion and generating functions have been discussed. The method of moments and the method of maximum likelihood estimation for estimating parameter have been discussed. The simulation study has been presented in order to illustrate the performance of developed methodology. The goodness of fit of the proposed distribution has been explained with three count datasets and the fit has been found quite satisfactory over Poisson distribution (PD), Poisson-Lindley distribution (PLD) and Poisson-Akash distribution (PAD).
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