On Size Biased Poisson - Lindley Distribution and Its Applications to Model Thunderstorms

摘要

In this paper firstly a general expression for the r th factorial moment of size biased Poisson-Lindley distribution (SBPLD) has been obtained and hence its first four moments about origin have been given. The expression for moment generating function and the first inverse moment of SBPLD has also been obtained. To test the goodness of fit of SBPLD over size-biased Poisson distribution (SBPD) for modeling thunderstorms, SBPLD has been fitted to a number of data sets related to thunderstorms using maximum likelihood estimate and it has been found that SBPLD gives much closer fit than SBPD, and thus SBPLD can be considered as an important alternative tool for modeling thunderstorms.