Abstract
The normal, Poisson, gamma, binomial, negative binomial, and NEFGHS distributions are the six univariate natural exponential families (NEF) with quadratic variance functions (QVF). This sequel to Morris (1982) treats certain statistical topics that can be handled within this unified NEF-QVF formulation, including unbiased estimation, Bhattacharyya and Cramer-Rao lower bounds, conditional distributions and moments, quadratic regression, conjugate prior distributions, moments of conjugate priors and posterior distributions, empirical Bayes and $G_2$ minimax, marginal distributions and their moments, parametric empirical Bayes, and characterizations.
Keywords
MathematicsNatural exponential familyExponential familyConjugate priorApplied mathematicsStatisticsMinimaxNegative binomial distributionPoisson distributionPrior probabilityBayesian probabilityMathematical optimization
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Publication Info
- Year
- 1983
- Type
- article
- Volume
- 11
- Issue
- 2
- Citations
- 249
- Access
- Closed
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Cite This
Carl N. Morris
(1983).
Natural Exponential Families with Quadratic Variance Functions: Statistical Theory.
The Annals of Statistics
, 11
(2)
.
https://doi.org/10.1214/aos/1176346158
Identifiers
- DOI
- 10.1214/aos/1176346158