A comparison of parameter estimations of the Poisson-generalised Lindley distribution

Abstract

In this paper, the Poisson-generalised Lindley distribution is presented. It is obtained by mixing the Poisson distribution with a generalised Lindley distribution. This distribution is an alternative distribution for count data with over-distribution. We apply two methods of parameter estimation, maximum likelihood estimation and method of moment, to estimate the parameters. The Monte Carlo simulation study is conducted for efficiency comparison between two methods of estimation based on root of mean squared error. The study exposes that method of moment is highly efficient with maximum likelihood estimation when the model is decreasing or bimodal model. Finally, the proposed distribution is applied to real data sets,but the result based on p-value of the discrete Anderson-Daring test show that maximum likelihood estimation can be hight efficiency for fitting data set.In this paper, the Poisson-generalised Lindley distribution is presented. It is obtained by mixing the Poisson distribution with a generalised Lindley distribution. This distribution is an alternative distribution for count data with over-distribution. We apply two methods of parameter estimation, maximum likelihood estimation and method of moment, to estimate the parameters. The Monte Carlo simulation study is conducted for efficiency comparison between two methods of estimation based on root of mean squared error. The study exposes that method of moment is highly efficient with maximum likelihood estimation when the model is decreasing or bimodal model. Finally, the proposed distribution is applied to real data sets,but the result based on p-value of the discrete Anderson-Daring test show that maximum likelihood estimation can be hight efficiency for fitting data set.