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Some characterizations of distributions of the exponential-type
Authors:M. L. Targhetta
Affiliation:1. Department of Mathematics, University of Cagliari, Via Ospedale 72, 09124, Cagliari, Italy
Abstract:
We consider a particular subclass of the two-parameter exponential family with natural parameters γ1, γ2 and characterize those distributions of the family having a ratio of the mean value and the variance that is a linear function of γ1 by the form of the moment generating function. As special cases we find the normal and the gamma distributions.
Keywords:exponential family  natural parameter space  moment generating function
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