Statistical inference for geometric process with the Two-Parameter Lindley Distribution

Abstract

The geometric process is a popular method for the modeling of arrival times with trend. In this study, the statistical inference problem for geometric process is considered when the distribution of first arrival time is two-parameter Lindley. The parameters a, lambda and beta are estimated using the maximum likelihood, modified least-squares, modified moments and modified L-moments methods. The estimation performances of the obtained estimators are compared by comprehensive simulations. The simulation results show that maximum likelihood estimators outperform the other estimators. Finally, on three real-life datasets, we present data analyses showing the modeling performance of geometric process against renewal process.