Modified Anderson-Darling and Cramer-Von Mises Goodness-of-Fit Tests for the Normal Distribution

Abstract

New techniques for calculating goodness-of-fit statistics for normal distributions with parameters estimated from the sample are investigated. Samples are generated for a Normal(0,1) distribution. Critical values are calculated for five modifications to the Anderson-Darling statistic and five modifications to the Cramer-Von Mises statistic. An extensive power study is done to test the power of the new statistics versus the power of the unmodified statistics. Powers of six of the new statistics show minimal to no improvement, two of the new statistics show a marked decrease in power, and two of the new statistics show an overall increase in power over the unmodified statistics. One of these two improved statistics was the obvious better of the two, and it was a modification to the Anderson-Darling statistic. Complete tables of critical values for sample sizes n=4 through n=50 are included for all Anderson-Darling and Cramer-Von Mises statistics, both modified and unmodified.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1993
Accession Number
ADA262554

Entities

People

  • David A. Gwinn

Organizations

  • Air Force Institute of Technology

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Air Force
  • Chi Square Test
  • Data Mining
  • Data Science
  • Distribution Functions
  • Goodness Of Fit Tests
  • Information Science
  • Monte Carlo Method
  • Normal Distribution
  • Probability
  • Sampling
  • Simulations
  • Standards
  • Statistical Algorithms
  • Statistical Samples
  • Statistical Tests
  • Statistics

Fields of Study

  • Mathematics

Readers

  • Computational Modeling and Simulation
  • Fluid Mechanics and Fluid Dynamics.
  • Personnel Management and Statistics in the Military and Department of Defense