Abstract:
Abstract: In this paper, a new count distribution for overdispersed data is introduced. The distribution is a mixture of the negative binomial and generalized Lindley distributions. This new distribution contains the negative binomial-Lindley distribution as a special case. Some statistical properties are studied. The parameters estimation procedure is obtained by the method of maximum likelihood. Simulation studies are performed to assess the performance of the maximum likelihood estimators. Finally, real overdispersed data sets are analyzed to show the usefulness of the distribution. © 2022, Pleiades Publishing, Ltd.