The Annals of statistics, 1982-03, Vol.10 (1), p.65-80
1982
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Details
- Autor(en) / Beteiligte
- Titel
- Natural Exponential Families with Quadratic Variance Functions
- Ist Teil von
- The Annals of statistics, 1982-03, Vol.10 (1), p.65-80
- Ort / Verlag
- Institute of Mathematical Statistics
- Erscheinungsjahr
- 1982
- Quelle
- Alma/SFX Local Collection
- Beschreibungen/Notizen
- The normal, Poisson, gamma, binomial, and negative binomial distributions are univariate natural exponential families with quadratic variance functions (the variance is at most a quadratic function of the mean). Only one other such family exists. Much theory is unified for these six natural exponential families by appeal to their quadratic variance property, including infinite divisibility, cumulants, orthogonal polynomials, large deviations, and limits in distribution.
- Sprache
- Englisch
- Identifikatoren
- ISSN: 0090-5364eISSN: 2168-8966DOI: 10.1214/aos/1176345690Titel-ID: cdi_projecteuclid_primary_oai_CULeuclid_euclid_aos_1176345690
- Format
- –
- Schlagworte
- 60E05, 60E07, 60F10, 62E10, 62E15, 62E30, binomial distribution, Binomials, cumulants, Cumulative distribution functions, Degrees of polynomials, Discriminants, exponential distribution, Exponential families, gamma distribution, geometric distribution, hyperbolic secant distribution, infinite divisibility, large deviations, limits in distribution, Linear transformations, Mathematical functions, moments, natural exponential families, negative binomial distribution, normal distribution, orthogonal polynomials, Poisson distribution, Polynomials, quadratic variance function, Secant function, Skewed distribution, Statistical variance, variance function