In this paper, a new discrete distribution called Binomial-Discrete Lindley (BDL) distribution is proposed by compounding the binomial and dis- crete Lindley distributions. Some properties of the distribution are discussed including the moment generating function, moments and hazard rate function. The estimation of distribution parameter is studied by methods of moments, proportions and maximum likelihood. A simulation study is performed to compare the performance of the different estimates in terms of bias and mean square errors. Automobile claim data applications are also presented to see that the new distribution is useful in modelling data.
