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A global simulated annealing heuristic for the three-parameter lognormal maximum likelihood estimation

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  • Vera, J. Fernando
  • Di­az-Garci­a, Jose A.

Abstract

It is well known that the inclusion of the threshold parameter in a lognormal distribution creates serious complications for parameter estimation; several parameterized schemes and global optimization procedures have been proposed to solve the problem in the maximum likelihood framework. A global Simulated Annealing optimization heuristic is proposed to solve the problem of maximum likelihood estimation in any parameterization scheme for the three-parameter lognormal distribution, as well as for the extended lognormal distribution. Positively and negatively skewed lognormal distributions are considered by introducing a one-parameter conditional estimation procedure in the classical parameterization for the three-parameter lognormal distribution, and a dual reparameterization is introduced for parameters estimation in the extended lognormal distribution. Simulated and real data are analyzed to test the efficiency of the proposed algorithm.

Suggested Citation

  • Vera, J. Fernando & Di­az-Garci­a, Jose A., 2008. "A global simulated annealing heuristic for the three-parameter lognormal maximum likelihood estimation," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5055-5065, August.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:12:p:5055-5065
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    References listed on IDEAS

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    1. Richard L. Smith & J. C. Naylor, 1987. "A Comparison of Maximum Likelihood and Bayesian Estimators for the Three‐Parameter Weibull Distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(3), pages 358-369, November.
    2. J. Fernando Vera & Willem J. Heiser & Alex Murillo, 2007. "Global Optimization in Any Minkowski Metric: A Permutation-Translation Simulated Annealing Algorithm for Multidimensional Scaling," Journal of Classification, Springer;The Classification Society, vol. 24(2), pages 277-301, September.
    3. Hirose, Hideo, 1997. "Maximum likelihood parameter estimation in the three-parameter log-normal distribution using the continuation method," Computational Statistics & Data Analysis, Elsevier, vol. 24(2), pages 139-152, April.
    4. David A. Griffiths, 1980. "Interval Estimation for the Three‐Parameter Lognormal Distribution Via the Likelihood Function," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 29(1), pages 58-68, March.
    5. Gilli, Manfred & Winker, Peter, 2007. "2nd Special Issue on Applications of Optimization Heuristics to Estimation and Modelling Problems," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 2-3, September.
    6. Wingo, Dallas R., 1984. "Fitting three-parameter lognormal models by numerical global optimization -- an improved algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 2(1), pages 13-25, June.
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    Cited by:

    1. Vera, J. Fernando & Macas, Rodrigo & Heiser, Willem J., 2009. "A dual latent class unfolding model for two-way two-mode preference rating data," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 3231-3244, June.
    2. Ajinkya Shirurkar & Yogesh Patil & D. Davidson Jebaseelan, 2019. "Reliability improvement of fork biasing spring in MCCB mechanism," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 10(4), pages 491-498, August.
    3. Santosh B. Rane & Yahya A.M. Narvel & Niloy Khatua, 2017. "Development of mechanism for mounting secondary isolating contacts (SICs) in air circuit breakers (ACBs) with high operational reliability," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 8(2), pages 1816-1831, November.
    4. Gutiérrez-Sánchez, R. & Nafidi, A. & Pascual, A. & Ramos-Ábalos, E., 2011. "Three parameter gamma-type growth curve, using a stochastic gamma diffusion model: Computational statistical aspects and simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(2), pages 234-243.
    5. J. Vera & Rodrigo Macías & Willem Heiser, 2013. "Cluster Differences Unfolding for Two-Way Two-Mode Preference Rating Data," Journal of Classification, Springer;The Classification Society, vol. 30(3), pages 370-396, October.
    6. Román-Román, P. & Torres-Ruiz, F., 2015. "A stochastic model related to the Richards-type growth curve. Estimation by means of simulated annealing and variable neighborhood search," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 579-598.
    7. Nafidi, Ahmed & El Azri, Abdenbi, 2021. "A stochastic diffusion process based on the Lundqvist–Korf growth: Computational aspects and simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 25-38.
    8. Santosh B. Rane & Yahya A. M. Narvel, 2016. "Reliability assessment and improvement of air circuit breaker (ACB) mechanism by identifying and eliminating the root causes," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 7(1), pages 305-321, December.
    9. Kim, Jin Seon & Yum, Bong-Jin, 2008. "Selection between Weibull and lognormal distributions: A comparative simulation study," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 477-485, December.

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