Estimation methods for the discrete Poisson–Lindley distribution

In this paper, we show that the method of moments and maximum likelihood estimators of the parameter of the discrete Poisson–Lindley distribution are consistent and asymptotically normal. The asymptotic variances of the two estimators are almost equal, indicating that the two estimators are almost equally efficient. Also, a simulation study is presented to compare the two estimators. Finally, the two estimators, their standard errors, and the confidence intervals are compared for two published data sets.