Some properties of two distributions of the exponential family (Q1060792)

This paper is concerned with two classical distributions belonging to the exponential family: the normal distribution and the negative exponential distribution. Under some regularity conditions, the author first shows that the normal is the unique distribution, belonging to a particular subclass of the exponential family, having the variance unrelated to its mean value. In the second part of the paper, the negative exponential has been shown to be the only distribution of the same subclass, having the variance equal to the corresponding mean squared.