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December, 1989 The Expectation of $X^1$ as a Function of $\mathbb{E}(X)$ for an Exponential Family on the Positive Line
Gerard Letac, Vanamamalai Seshadri
Ann. Statist. 17(4): 1735-1741 (December, 1989). DOI: 10.1214/aos/1176347391

Abstract

If the distribution of $X$ belongs to a natural exponential family on the positive real line, this note studies the expectation of the reciprocal of $X$ as a function of the expectation $m$ of $X$ and characterizes the cases where this function is an affine function of $m^{-1}$ as gamma, inverse-Gaussian, Ressel or Abel families.

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Gerard Letac. Vanamamalai Seshadri. "The Expectation of $X^1$ as a Function of $\mathbb{E}(X)$ for an Exponential Family on the Positive Line." Ann. Statist. 17 (4) 1735 - 1741, December, 1989. https://doi.org/10.1214/aos/1176347391

Information

Published: December, 1989
First available in Project Euclid: 12 April 2007

zbMATH: 0694.62006
MathSciNet: MR1026309
Digital Object Identifier: 10.1214/aos/1176347391

Subjects:
Primary: 62E10
Secondary: 60E10

Rights: Copyright © 1989 Institute of Mathematical Statistics

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Vol.17 • No. 4 • December, 1989
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