Natural Exponential Families with Quadratic Variance Functions
Morris, Carl N.
Ann. Statist., Tome 10 (1982) no. 1, p. 65-80 / Harvested from Project Euclid
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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.
Publié le : 1982-03-14
Classification:  Exponential families,  natural exponential families,  quadratic variance function,  normal distribution,  Poisson distribution,  gamma distribution,  exponential distribution,  binomial distribution,  negative binomial distribution,  geometric distribution,  hyperbolic secant distribution,  orthogonal polynomials,  moments,  cumulants,  large deviations,  infinite divisibility,  limits in distribution,  variance function,  60E05,  60E07,  60F10,  62E10,  62E15,  62E30 
@article{1176345690,
     author = {Morris, Carl N.},
     title = {Natural Exponential Families with Quadratic Variance Functions},
     journal = {Ann. Statist.},
     volume = {10},
     number = {1},
     year = {1982},
     pages = { 65-80},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176345690}
}

Morris, Carl N. Natural Exponential Families with Quadratic Variance Functions. Ann. Statist., Tome 10 (1982) no. 1, pp.  65-80. http://gdmltest.u-ga.fr/item/1176345690/