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

Hong-Jiang Wu (), Ying-Ying Zhang () and Han-Yu Li ()
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Hong-Jiang Wu: Chongqing University
Ying-Ying Zhang: Chongqing University
Han-Yu Li: Chongqing University

Statistical Papers, 2023, vol. 64, issue 2, No 5, 477-496

Abstract: Abstract 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.

Keywords: Conjugate variables theorem; Expectation identity; High-order moments; Integration by parts; Univariate continuous random variables; 62Exx (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s00362-022-01329-5

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