There are increasingly many attempts made in expanding the classes of mixed and compound distributions, especially using Lindley distribution which gives the better fit for count data. Further, many researchers have shown a keen interest in generalizing the Lindley distribution. In this paper, we introduce a new distribution called zero-inflated negative binomial-Lindley (ZINB-L) distribution with the aim of obtaining models that are more flexible towards the count data with the high density at zero. The vital statistical properties of the ZINB-L distribution are derived. Maximum likelihood estimation is used for the estimation of distribution parameters.

Lindley distribution, negative binomial distribution, negative binomial-Lindley distribution, zero-inflation.