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2017•Communications in Statistics - Simulation and ComputationOpen access

A generalized Gumbel distribution and its parameter estimation

Haydar Demirhan

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Abstract

In this article, main characteristics of a generalized Gumbel (GG) distribution are derived. Parameter estimation with method of moments, maximum likelihood, and Bayesian approaches are demonstrated. Due to the ranges of its skewness and kurtosis, it is satisfactory for fitting a wide variety of datasets. Also, it can be used to model block maxima or minima data due to its close connection with the standard Gumbel distribution. It is demonstrated that the GG distribution fits more accurately than both of the standard Gumbel and generalized extreme value distributions to block maxima data under specific conditions.

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What this paper is about

In this article, main characteristics of a generalized Gumbel (GG) distribution are derived. Parameter estimation with method of moments, maximum likelihood, and Bayesian approaches are demonstrated. Due to the ranges of its skewness and kurtosis, it is satisfactory for fitting a wide variety of datasets. Also, it can be used to model block maxima or minima data due to its close connection with the standard Gumbel distribution. It is demonstrated that the GG distribution fits more accurately than both of the standard Gumbel and generalized extreme value distributions to block maxima data under specific conditions.

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Available abstract

In this article, main characteristics of a generalized Gumbel (GG) distribution are derived. Parameter estimation with method of moments, maximum likelihood, and Bayesian approaches are demonstrated. Due to the ranges of its skewness and kurtosis, it is satisfactory for fitting a wide variety of datasets. Also, it can be used to model block maxima or minima data due to its close connection with the standard Gumbel distribution. It is demonstrated that the GG distribution fits more accurately than both of the standard Gumbel and generalized extreme value distributions to block maxima data under specific conditions.

Key concepts: Gumbel distribution, Kurtosis, Maxima, Generalized extreme value distribution, Maxima and minima, Mathematics, Extreme value theory, Skewness

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