Modified Kolmogorov-Smirnov, Anderson-Darling and Cramer-Von Mises Tests for the Logistic Distribution with Unknown Location and Scale Parameters.

Abstract

The method of maximum likelihood is used to determine invariant estimates of the unknown location and scale parameters of a sample from the Logistic distribution. The partial derivatives of the likelihood function can not be solved explicitly, therefore the Secant method is used to iteratively determine the roots of the partial derivatives. Using these estimates, modified Kolmogorov-Smirnov, Anderson-Darling and Cramer-von Mises statistics are calculated for a given sample. This procedure is repeated 5000 times for sample sizes of n= 5(5)30. The 80th, 85th, 90th, 95th and 99th percentiles of the distribution of each statistic, for each sample size, is then calculated. These values are then used to generate tables of critical values for the Logistic distribution with unknown location and scale parameters. A power comparison between the three tests is performed using samples from various distributions.

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Document Details

Document Type
Technical Report
Publication Date
Dec 16, 1983
Accession Number
ADA138098

Entities

People

  • J. D. Yoder

Organizations

  • Air Force Institute of Technology

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Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Air Force
  • Computer Programs
  • Computers
  • Data Science
  • Distribution Functions
  • Distribution Theory
  • Goodness Of Fit Tests
  • Information Science
  • Knowledge Management
  • Monte Carlo Method
  • Normal Distribution
  • Order Statistics
  • Probability
  • Random Variables
  • Statistical Algorithms
  • Statistical Analysis
  • Statistics

Fields of Study

  • Mathematics

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  • Statistical inference.