Expectation identities from integration by parts for univariate continuous random variables with applications to high-order moments,Statistical Papers

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Expectation identities from integration by parts for univariate continuous random variables with applications to high-order moments
Statistical Papers ( IF 1.3 ) Pub Date : 2022-06-08 , DOI: 10.1007/s00362-022-01329-5
Hong-Jiang Wu , Ying-Ying Zhang , Han-Yu Li

Inspired by the Conjugate Variables Theorem in physics, we provide a general expectation identity for univariate continuous random variables by utilizing integration by parts. We then apply the general expectation identity to some common univariate continuous random variables (normal, gamma (including chi-square and exponential), beta, double exponential, F, inverse gamma, logistic, lognormal, Pareto, t, uniform, and Weibul) and obtain their specific expectation identities from the general expectation identity. After that, we use the specific expectation identities to derive high-order moments of the corresponding univariate continuous random variables.

更新日期：2022-06-09

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