Mixed distribution of negative binomial and two-parameter Lindley distributions

In this work, we propose a new mixed distribution, the negative binomial two-parameter Lindley distribution. Some properties such as but not limited to, factorial moment, mean, and variance, including a random variate generation are studied. Parameters of the proposed distribution are estimated by maximum likelihood estimation, which illustrated high-efficiency when a sample size is large. Moreover, when the negative binomial two-parameter Lindley distribution is used in application of count data modeling-especially for data with large number of zeros and overdispersion-it provides a better fit compared to the negative binomial distribution and negative binomial Lindley distribution.