Goodness of Fit Tests and Entropy

Abstract

This paper discusses the unifying role of entropy statistics and concepts in developing goodness of fit tests for a parametric model F(x; ) for a continuous distribution function F(x), given an random sample from the distribution F. Statistics discussed are those by Moran (extended by Cheng and Stephens), Vasicek and Dudewicz & van der Meulen (based on gap estimators of quantile density function), Parzen (autoregressive estimators of quantile density functions), and shapiro and Wilk. They are given unified formulations as entropy difference statistics. Their 95% significance levels for sample sizes 20 and 50 are compared and shown to increase as amount of smoothing decreases. Keywords: Goodness of fit; Entropy; Moran's statistic; Information divergence; Gap estimators; Autoregressive estimation; Shapiro Wilk statistic.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
May 01, 1990
Accession Number
ADA224860

Entities

People

  • Emanuel Parzen

Organizations

  • Texas A&M University

Tags

DTIC Thesaurus Topics

  • Analysis Of Variance
  • Data Analysis
  • Data Mining
  • Data Science
  • Distribution Functions
  • Estimators
  • Goodness Of Fit Tests
  • Information Science
  • Maximum Likelihood Estimation
  • Military Research
  • Monte Carlo Method
  • Order Statistics
  • Probability
  • Random Variables
  • Statistical Algorithms
  • Statistical Samples
  • Statistics

Fields of Study

  • Mathematics

Readers

  • Statistical inference.