Maximum-Likelihood Parameter Estimation of a Generalized Gumbel Distribution

Abstract

A microcomputer-based algorithm for estimation of the three parameters of a generalized Gumbel (extreme value type I) distribution class is presented. The parameters are shift, scale, and shape. The classical Gumbel distribution results if the shape parameter is equal to unity. Three-parameter as well as two-parameter (shape equal to unity) estimation can be performed for given histogram data. Parameter estimation is accomplished by means of the maximum-likelihood principle. The derivative equations which result from the associated logarithmic likelihood function are used. A more comprehensive presentation of generalized Gumbel distribution estimation which also allows treatment of population data and which includes moment estimates and maximum- likelihood estimates by direct optimization of the logarithmic likelihood function will be presented elsewhere.

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Document Details

Document Type
Technical Report
Publication Date
Mar 24, 1989
Accession Number
ADA207994

Entities

People

  • Charles E. Hall Jr.
  • Guttalu R. Viswanath
  • Siegfried H. Lehnigk

Organizations

  • United States Army Aviation and Missile Command

Tags

Communities of Interest

  • Biomedical
  • Weapons Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Classification
  • Computer Science
  • Computers
  • Data Science
  • Data Sets
  • Equations
  • Histograms
  • Information Science
  • Intervals
  • Mathematics
  • Maximum Likelihood Estimation
  • Personality
  • Probability
  • Probability Density Functions
  • Rainfall
  • Test And Evaluation

Fields of Study

  • Mathematics

Readers

  • Computational Modeling and Simulation
  • Fluid Dynamics.
  • Spectroscopy.