A Generalized Size-Biased Poisson-Lindley Distribution and Its Applications to Model Size Distribution of Freely-Forming Small Group

In this paper, generalized size-biased Poisson-Lindley distribution (GSBPLD) which includes size-biased Poisson-Lindley distribution (SBPLD) as particular case, has been proposed and studied. Its moments based measures including coefficients of variation, skewness, kurtosis, and index of dispersion have been derived and their nature and behavior have been discussed with varying values of the parameters. The estimation of its parameter has been discussed using maximum likelihood estimation. Some applications of the proposed distribution have been explained through datasets relating to size distribution of freely-forming and the goodness of fit has been found satisfactory over SBPLD and size-biased Poisson distribution (SBPD).