Estimating the Parameters of the Negative-Lindley Distribution using Broyden-Fletcher-Goldfarb-Shanno | Science Publications

Journal of Mathematics and Statistics

Naushad M. Khan¹ 

关键词: Maximum likelihood;    Negative-Lindley;    Hessian matrix;    Newton-Raphson;    Broyden-Fletcher-Goldfarb-Shanno (BFGS);    Maximum Likelihood Estimation (MLE);    dispersion parameter;   

DOI  :  10.3844/jmssp.2011.1.4

学科分类：社会科学、人文和艺术（综合）

来源: Science Publications

【 摘 要 】

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.

【 授权许可】

Unknown