A Recursive Algorithm for the Single and Product Moments of Order Statistics from the Exponential-geometric Distribution and Some Estimation Methods

The exponential-geometric distribution has been proposed as a simple and useful reliability model for analyzing lifetime data. For this distribution, some recurrence relations are established for the single moments and product moments of order statistics. Using these recurrence relations, the means, variances and covariances of all order statistics can be computed for all sample sizes in a simple and efficient recursive manner. Next, we discuss the maximum likelihood estimation of the model parameters as well as some simple modified methods of estimation. Then, a Monte Carlo simulation study is carried out to evaluate the performance of all these methods of estimation in terms of their bias and mean square error as well as the percentage of times the estimates converged. Two illustrative examples are finally presented to illustrate all the inferential results developed here.