A size - biased version of the two parameter Poisson- Lindley distribution introduced by Shanker and Mishra (2014) has been proposed of which the Ghitany and Al Mutairi’s (2008) size - biased one parameter Poisson-Lindley distribution is a particular case. A general expression for its r th factorial moment about origin has been derived and hence its raw moments and central moments are obtained. The expressions for its coefficient of variation, skewness, kurtosis and index of dispersion have also been given. The method of maximum likelihood and the method of moments for the estimation of its parameters have been discussed. The applications and the goodness of fit of the proposed distribution have been discussed with three data sets excluding zero counts and the fit has been compared with that of size-biased Poisson and size-biased Poisson-Lindley distributions.
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