A New Sequential Goodness of Fit Test for the Three-Parameter Gamma Distribution with Known Shape Based on Skewness and Kurtosis

Abstract

This research presents a new sequential goodness of fit test for the three-parameter gamma distribution with a known shape. The test is accomplished by employing two new tests, sample skewness and sample kurtosis, sequentially as test statistics. Unlike the typical goodness of fit test, using parameter estimation methods such as maximum likelihood estimation and minimum distance estimation, this test using the two test statistics above does not involve a substantial degree of computational complexity. Large Monte Carlo simulation has been used to determine critical values and overall significance levels for all combinations of the two tests, and to conduct extensive power studies against a broad range of alternatives. The results have been compared with those of popular EDF tests such as the Anderson-Darling, Cramer-von Mises, and Komogrov-Smirov tests. The comparative study demonstrated the sequential tests superiority over a broad range of alternatives. Hence, with computational efficiency and good power properties, the new sequential test is powerful enough to be utilized in the goodness of fit test field.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1999
Accession Number
ADA361662

Entities

People

  • Chil H. Park

Organizations

  • Air Force Institute of Technology

Tags

DTIC Thesaurus Topics

  • Computational Complexity
  • Computational Science
  • Computer Programming
  • Data Science
  • Goodness Of Fit Tests
  • Information Science
  • Maximum Likelihood Estimation
  • Metal Matrix Composites
  • Monte Carlo Method
  • Operations Research
  • Plastic Explosives
  • Probability Distributions
  • Random Variables
  • Simulations
  • Statistical Algorithms
  • Statistics
  • Surveys

Fields of Study

  • Mathematics

Readers

  • Statistical inference.