@article {10.3844/jmssp.2011.1.4,
article_type = {journal},
title = {Estimating the Parameters of the Negative-Lindley Distribution using Broyden-Fletcher-Goldfarb-Shanno},
author = {Khan, Naushad Mamode},
volume = {7},
year = {2011},
month = {Jan},
pages = {1-4},
doi = {10.3844/jmssp.2011.1.4},
url = {https://thescipub.com/abstract/jmssp.2011.1.4},
abstract = {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.},
journal = {Journal of Mathematics and Statistics},
publisher = {Science Publications}
}