Comparison of Estimation Techniques for the Four Parameter Beta Distribution.

Abstract

This thesis compares three estimation techniques in application to the beta distribution: method of moments, maximum likelihood, and minimum distance. The four parameter version of the beta distribution is used; it has two shape parameters, and upper and lower limit parameters. Linear interpolation on order statistics is used to find initial estimates of the limits. The classical estimation procedures, method of moments and maximum likelihood, are applied through procedures found in the literature. A newer technique, minimum distance, is applied for the first time to the beta distribution. Comparison of estimation techniques is accomplished using Monte Carlo analysis. Five sample sizes are considered -- 4, 8, 12, 16, and 20 -- and three pairs of shape parameters -- (3,3), (9,4), and (1,2) -- for a total of fifteen cases. One thousand samples are generated for each case, and each estimation technique is then applied to all samples.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1981
Accession Number
ADA115562

Entities

People

  • David E. Bertrand

Organizations

  • Air Force Institute of Technology

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Air Force
  • Computational Science
  • Computer Programs
  • Computers
  • Data Science
  • Distribution Functions
  • Estimators
  • Information Science
  • Maximum Likelihood Estimation
  • Method Of Moments
  • Order Statistics
  • Probability
  • Probability Distributions
  • Random Variables
  • Statistical Algorithms
  • Statistical Analysis
  • Statistics

Fields of Study

  • Mathematics

Readers

  • Computational Modeling and Simulation
  • Regression Analysis.