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RESEARCH PRODUCT
Some Remarks on Exponential Families
Joachim SehrWolfgang J. Bühlersubject
Statistics and ProbabilityPure mathematicsLocation parameterLebesgue measureGeneral MathematicsLocation-scale familyShape parameterExponential familyCalculusDifferentiable functionStatistics Probability and UncertaintyNatural exponential familyScale parameterMathematicsdescription
Abstract The following facts may serve to provide a feeling about how restrictive the assumption of an exponential family is. (a) A one-parameter exponential family in standard form with respect to Lebesgue measure is a location parameter family iff it is normal with fixed variance. (b) It is a scale parameter family iff it is gamma with fixed shape parameter. Both facts are known (see Borges and Pfanzagl 1965; Ferguson 1962; Lindley 1958) but may not have received as much attention as they deserve. Under the assumption of differentiable densities, short and elementary proofs are given.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1987-11-01 | The American Statistician |