A note on overdispersed exponential families

Journal Article (Journal Article)

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 (1987) exponential dispersion models. Uniformly most powerful 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 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 illustrations are given.

Full Text

Duke Authors

Cited Authors

  • Gelfand, AE; Dalal, SR

Published Date

  • December 1, 1990

Published In

Volume / Issue

  • 77 / 1

Start / End Page

  • 55 - 64

Electronic International Standard Serial Number (EISSN)

  • 1464-3510

International Standard Serial Number (ISSN)

  • 0006-3444

Digital Object Identifier (DOI)

  • 10.2307/2336049

Citation Source

  • Scopus