The discrete weighted Lindley distribution

We have introduced the discrete analogue of the weighted Lindley distribution, namely the discrete weighted Lindley distribution. We present some of its mathematical properties; the probability mass function, distribution function, survival function, hazard rate function, probability generating function and moment generating function. In addition, the estimation of parameters for this distribution is discussed based on maximum likelihood method. The application to biological data which is the number of borers per hill of the European corn is presented. Moreover, the Anderson and Darling (AD) statistic for discrete distribution is used to compare among the proposed, Poisson, and negative binomial distributions.