Power Series Approximations to the Null Distributions of Some Chi-Bar-Square Statistics.

Abstract

Some power series approximations to the exact null distribution of the Chi-bar-square statistic for several testing situations are developed using the first four cumulants of the null distributions, and their performance is investigated numerically. The series expansions use Laguerre polynomials and the associated gamma densities. Chi-bar-square statistics arise when testing the homogeneity of normal means with the alternative restricted by a partial ordering on the means and when testing the ordering against all alternatives. Approximations are provided for the case of a total order and a simple tree with equal, or nearly equal, sample sizes. The numerical investigations indicate the accuracy and usefulness of these approximations. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1985
Accession Number
ADA159785

Entities

People

  • B. Singh
  • F. T. Wright

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Analysis Of Variance
  • Data Science
  • Distribution Functions
  • Equations
  • Errors
  • Information Science
  • Numerical Integration
  • Polynomials
  • Power Series
  • Probability
  • Probability Density Functions
  • Random Variables
  • Sampling
  • Statistical Distributions
  • Statistical Inference
  • Statistics
  • Three Dimensional

Fields of Study

  • Mathematics

Readers

  • Statistical inference.