The expectation of \(X^{-1}\) as a function of \({\mathbb{E}}(X)\) for an exponential family on the positive line

DOI10.1214/AOS/1176347391zbMath0694.62006OpenAlexW2027777474MaRDI QIDQ909373

Vanamamalai Seshadri, Gérard Letac

Publication date: 1989

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aos/1176347391

zbMATH Keywords

expectationaffine functiongamma distributionsAbel familiesinverse-Gaussian distributionsnatural exponential family on the positive real linereciprocal of a random variableRessel families

Mathematics Subject Classification ID

Characteristic functions; other transforms (60E10) Characterization and structure theory of statistical distributions (62E10)

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