Estimating the Parameters of the Negative-Lindley Distribution using Broyden-Fletcher-Goldfarb-Shanno
Naushad Mamode Khan
DOI : 10.3844/jmssp.2011.1.4
Journal of Mathematics and Statistics
Volume 7, Issue 1
Problem statement: The Maximum Likelihood Estimation (MLE) technique is the most efficient statistical approach to estimate parameters in a cross-sectional model. Often, MLE gives rise to a set of non-linear systems of equations that need to be solved iteratively using the Newton-Raphson technique. However, in some situations such as in the Negative-Lindley distribution where it involves more than one unknown parameter, it becomes difficult to apply the Newton-Raphson approach to estimate the parameters jointly as the second derivatives of the score functions in the Hessian matrix are complicated. Approach: In this study, we propose an alternate iterative algorithm based on the Broyden-Fletcher-Goldfarb-Shanno (BFGS) approach that does not require the computation of the higher derivatives. Conclusion: To assess the performance of BFGS, we generate samples of overdispersed count with various dispersion parameters and estimate the mean and dispersion parameters. Results: BFGS estimates the parameters of the Negative-Lindley model efficiently.
© 2011 Naushad Mamode Khan. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.