The generalized method of moments as applied to the generalized gamma distribution
type: Item
instance of: scholarly article
title: The generalized method of moments as applied to the generalized gamma distribution
zbMATH Open document ID: 0658.76007
DOI: 10.1007/BF01550839
author: F. Ashkar
author: D. Leroux
author: D. Morisette
author: Bernard Bobée
published in: Stochastic Hydrology and Hydraulics
publication date: 1988-01-01T00:00:00Z
review text: The generalized gamma (GG) distribution has a density function that can take on many possible forms commonly encountered in hydrologic applications. This fact has led many authors to study the properties of the distribution and to propose various estimation techniques (method of moments, mixed moments, maximum likelihood etc.). We discuss some of the most important properties of this flexible distribution and present a flexible method of parameter estimation, called the ``generalized method of moments'' (GMM) which combines any three moments of GG distribution. The main advantage of this general method is that it has many of the previously proposed methods of estimation as special cases. We also give a general formula for the variance of the T-year event \(X_ T\) obtained by the GMM along with a general formula for the variance of the parameter estimates and also for the covariances and correlation coefficients between any pair of such estimates. By applying the GMM and carefully choosing the order of the moments that are used in the estimation one can significantly reduce the variance of T-year events for the range of return periods that are of interest.
Mathematics Subject Classification ID: 76A99
Mathematics Subject Classification ID: 76M99
Mathematics Subject Classification ID: 86A05
zbMATH DE Number: 4076795
zbMATH Keywords: floods
zbMATH Keywords: estimation
zbMATH Keywords: quantiles
zbMATH Keywords: generalized gamma
zbMATH Keywords: generalized moments
zbMATH Keywords: standard error
zbMATH Keywords: hydrologic applications
zbMATH Keywords: generalized method of moments
MaRDI profile type: Publication
cites work: Inferential Procedures for the Generalized Gamma Distribution
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cites work: Q3757131
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full work available at URL: https://doi.org/10.1007/bf01550839
OpenAlex ID: W2088691027
description: scientific article; zbMATH DE number 4076795