A Fast Algorithm for Computing Maximum Likelihood Estimates of the Negative-Binomial Lindley Distribution

Negative-binomial Lindley distribution is a two-parameter discrete model that has been recently introduced in statistical literature. It has been used mostly in the analysis of insurance data and has shown to provide suitable fits as compared with the Poisson and Negative -binomial distributions. The parameters of the Negativebinomial Lindley model were estimated using separate maximum likelihood equations via the Newton-Raphson iterative technique. However, this method of estimation does not require the construction of a joint Hessian matrix. Further to this, it becomes difficult to estimate the joint covariance matrix. To overcome this shortcoming, we propose a joint maximum likelihood estimation approach that is based on a diagonal Jacobian approximation of the joint Hessian matrix. We further compare this estimation methodology with the separate maximum likelihood approach and show that the joint maximum likelihood approach is computationally faster.