Use of the heuristic optimization in the parameter estimation of generalized gamma distribution: comparison of GA, DE, P
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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 Volkan Soner Özsoy1
· Mehmet Güray Ünsal2 · H. Hasan Örkcü3
Received: 3 January 2018 / Accepted: 4 February 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
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. Keywords Generalized gamma distribution · Maximum likelihood function · Heuristic techniques · Real dataset
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00180020-00966-4) contains supplementary material, which is available to authorized users.
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Volkan Soner Özsoy [email protected]; [email protected]
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Department of Finance, Banking and Insurance, Aksaray University, Aksaray, Turkey
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Department of Statistics, Faculty of Art and Sciences, U¸sak University, U¸sak, Turkey
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Department of Statistics, Faculty of Sciences, Gazi University, Ankara, Turkey
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V. S. Özsoy et al.
1 Introduction The Generalized Gamma Distribution (GGD) is one of the most common distributions that occur in various real-world data applications. It is adaptable to different shape distributions, such as Levy distribution, Rayleigh distribution, Chi Square distribution, Weibull distribution, exponential distribution, half-normal distribution, and 2-p gamma distribution. Thus, it has been used in many different fields of science. Estimating the parameters of the GGD family is a very difficult problem. In order to estimate the parameters of the GGD, some approaches have been used in the literature. Two estimation techniques, maximum likelihood (ML) and method of moments (MM), are generally employed for the parameter estimation of distributions in statistical th
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