Research Article Open Access

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

Naushad Mamode Khan1
  • 1 , Afganistan
Journal of Mathematics and Statistics
Volume 7 No. 1, 2011, 1-4

DOI: https://doi.org/10.3844/jmssp.2011.1.4

Submitted On: 26 December 2010 Published On: 29 January 2011

How to Cite: Khan, N. M. (2011). Estimating the Parameters of the Negative-Lindley Distribution using Broyden-Fletcher-Goldfarb-Shanno. Journal of Mathematics and Statistics, 7(1), 1-4. https://doi.org/10.3844/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.

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Keywords

  • Maximum likelihood
  • Negative-Lindley
  • Hessian matrix
  • Newton-Raphson
  • Broyden-Fletcher-Goldfarb-Shanno (BFGS)
  • Maximum Likelihood Estimation (MLE)
  • dispersion parameters