The Poisson distribution plays important role in count data analysis. However, the Poisson distribution cannot model some data with over-dispersion because of its property, equi-dispersion. Here we propose a new distribution for overdispersed count data, namely the Poisson-generalised Lindley distribution. Basic properties of the distribution and special cases are also derived. In addition, the new distribution is applied to some real data sets using the method of maximum likelihood for parameter estimation. The results based on p-value of the discrete Anderson-Daring test show that the new distribution can be used as an alternative model for count data analysis.
