A note on overdispersed exponential families
| Autor: | Alan E. Gelfand, S. R. Dalal |
|---|---|
| Rok vydání: | 1990 |
| Předmět: |
Statistics and Probability
Discrete mathematics Class (set theory) Applied Mathematics General Mathematics Poison control Context (language use) Agricultural and Biological Sciences (miscellaneous) Exponential function Exponential family Overdispersion Statistics Statistics::Methodology Statistics Probability and Uncertainty Special case General Agricultural and Biological Sciences Mathematics Statistical hypothesis testing |
| Zdroj: | Biometrika. 77:55-64 |
| ISSN: | 1464-3510 0006-3444 |
| DOI: | 10.1093/biomet/77.1.55 |
| Popis: | 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) |
| Databáze: | OpenAIRE |
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