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Estimation of Beta-Pareto Distribution Based on Several Optimization Methods

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  • Badreddine Boumaraf

    (Department of Mathematics and Informatics, University of Souk-Ahras, Souk Ahras 41000, Algeria
    Laboratory of Probability and Statistics LaPS, University of Badji Mokhtar of Annaba, Annaba 23000, Algeria
    Laboratory of Mathematics Raphaël Salem, University of Rouen-Normandy, 76801 Saint Étienne du Rouvray, France
    The authors contributed equally to this work.)

  • Nacira Seddik-Ameur

    (Laboratory of Probability and Statistics LaPS, University of Badji Mokhtar of Annaba, Annaba 23000, Algeria
    The authors contributed equally to this work.)

  • Vlad Stefan Barbu

    (Laboratory of Mathematics Raphaël Salem, University of Rouen-Normandy, 76801 Saint Étienne du Rouvray, France
    The authors contributed equally to this work.)

Abstract

This paper is concerned with the maximum likelihood estimators of the Beta-Pareto distribution introduced in Akinsete et al. (2008), which comes from the mixing of two probability distributions, Beta and Pareto. Since these estimators cannot be obtained explicitly, we use nonlinear optimization methods that numerically provide these estimators. The methods we investigate are the method of Newton-Raphson, the gradient method and the conjugate gradient method. Note that for the conjugate gradient method we use the model of Fletcher-Reeves. The corresponding algorithms are developed and the performances of the methods used are confirmed by an important simulation study. In order to compare between several concurrent models, namely generalized Beta-Pareto, Beta, Pareto, Gamma and Beta-Pareto, model criteria selection are used. We firstly consider completely observed data and, secondly, the observations are assumed to be right censored and we derive the same type of results.

Suggested Citation

  • Badreddine Boumaraf & Nacira Seddik-Ameur & Vlad Stefan Barbu, 2020. "Estimation of Beta-Pareto Distribution Based on Several Optimization Methods," Mathematics, MDPI, vol. 8(7), pages 1-22, July.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:7:p:1055-:d:378849
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    References listed on IDEAS

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    1. Moshe Levy & Haim Levy, 2003. "Investment Talent and the Pareto Wealth Distribution: Theoretical and Experimental Analysis," The Review of Economics and Statistics, MIT Press, vol. 85(3), pages 709-725, August.
    2. Mahmoudi, Eisa, 2011. "The beta generalized Pareto distribution with application to lifetime data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(11), pages 2414-2430.
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