The mean of the reciprocal in a Cauchy–Stieltjes family

Raouf Fakhfakh

Statistics & Probability Letters, 2017, vol. 129, issue C, 1-11

Abstract: If the distribution of X belongs to a Cauchy–Stieltjes Kernel (CSK) family concentrated on the positive real line, we determine the expectation of the reciprocal of X as a function of the expectation m of X. This function characterizes the CSK family. Some examples and characterizations of quadratic and cubic CSK families are given.

Keywords: Cauchy–Stieltjes Kernel; Variance function; Semicircle distribution (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.spl.2017.04.021

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