Some characterizations of distributions of the exponential-type
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.
Key wordsexponential family natural parameter space moment generating function
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- Widder D.V. (1961).Advanced Calculus. Prentice-Hall, Englewood Cliffs, N.J.Google Scholar