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.
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Targhetta, M.L. Some characterizations of distributions of the exponential-type. Statistical Papers 34, 175–180 (1993). https://doi.org/10.1007/BF02925539
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DOI: https://doi.org/10.1007/BF02925539