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Use of the heuristic optimization in the parameter estimation of generalized gamma distribution: comparison of GA, DE, PSO and SA methods

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Abstract

The generalized gamma distribution (GGD) is a popular distribution because it is extremely flexible. Due to the density function structure of GGD, estimating the parameters of the GGD family by statistical point estimation techniques is a complicated task. In other words, for the parameter estimation, the maximizing likelihood function of GGD is a problematic case. Hence, alternative approaches can be used to obtain estimators of GGD parameters. This paper proposes an alternative parameter estimation method for GGD by using the heuristic optimization approaches such as Genetic Algorithms (GA), Differential Evolution (DE), Particle Swarm Optimization (PSO), and Simulated Annealing (SA). A comparison between different modern heuristic optimization methods applied to maximize the likelihood function for parameter estimation is presented in this paper. The paper also investigates both the performance of heuristic methods and estimation of GGD parameters. Simulations show that heuristic approaches provide quite accurate estimates. In most of the cases, DE has better performance than other heuristics in terms of bias values of parameter estimations. Besides, the usefulness of an alternative parameter estimation method for GGD using the heuristic optimization approach is illustrated with a real data set.

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Authors and Affiliations

  1. Department of Finance, Banking and Insurance, Aksaray University, Aksaray, Turkey

    Volkan Soner Özsoy

  2. Department of Statistics, Faculty of Art and Sciences, Uşak University, Uşak, Turkey

    Mehmet Güray Ünsal

  3. Department of Statistics, Faculty of Sciences, Gazi University, Ankara, Turkey

    H. Hasan Örkcü

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  1. Volkan Soner Özsoy
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  2. Mehmet Güray Ünsal
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  3. H. Hasan Örkcü
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Correspondence to Volkan Soner Özsoy.

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Özsoy, V.S., Ünsal, M.G. & Örkcü, H.H. Use of the heuristic optimization in the parameter estimation of generalized gamma distribution: comparison of GA, DE, PSO and SA methods. Comput Stat 35, 1895–1925 (2020). https://doi.org/10.1007/s00180-020-00966-4

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