TY  - JOUR
AU  - Khan, Naushad Mamode 
PY  - 2011
TI  - Estimating the Parameters of the Negative-Lindley Distribution using Broyden-Fletcher-Goldfarb-Shanno
JF  - Journal of Mathematics and Statistics
VL  - 7
IS  - 1
DO  - 10.3844/jmssp.2011.1.4
UR  - https://thescipub.com/abstract/jmssp.2011.1.4
AB  - 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.