A weighted negative binomial Lindley distribution with applications to dispersed data

Abstract

A new discrete distribution is introduced. The distribution involves the negative binomial and size biased negative binomial distributions as sub-models among others and it is a weighted version of the two parameter discrete Lindley distribution. The distribution has various interesting properties, such as bathtub shape hazard function along with increasing/decreasing hazard rate, positive skewness, symmetric behavior, and over-and under-dispersion. Moreover, it is self decomposable and infinitely divisible, w…