A Note on Overdispersed Exponential Families

Abstract

The issue of creating overdispersion in a given one parameter one dimensional exponential family, by extending it to a two parameter exponential family with the same support, is considered. An easily verifiable sufficient condition for this is derived. It is shown that a large class of families satisfy this condition and that this class includes EFron's (1986) and Lindsay's (1986) family as special cases. This class is also closely related to Jorgensen's (1988) Exponential Dispersion Models. UMP unbiased tests for testing overdispersion are exhibited and it is shown that in this context Cox's overdispersion test is a special case. A graphical display is developed to select a family of the general class which should be used with a given set of data to overdisperse a given target one parameter family. Two real data illustrations are given. (KR)

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Document Details

Document Type
Technical Report
Publication Date
Dec 05, 1989
Accession Number
ADA216277

Entities

People

  • A. E. Gelfand
  • S. R. Dalal

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Binomials
  • Data Science
  • Data Sets
  • Discrete Distribution
  • Dispersions
  • Goodness Of Fit Tests
  • Governments
  • Information Science
  • Military Research
  • New York
  • Observation
  • Probability
  • Random Variables
  • Security
  • Statistics
  • United States
  • United States Government

Fields of Study

  • Mathematics

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