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The mean of the reciprocal in a Cauchy–Stieltjes family
Journal article   Peer reviewed

The mean of the reciprocal in a Cauchy–Stieltjes family

Raouf Fakhfakh
Statistics & probability letters, Vol.129, pp.1-11
10/2017
DOI: https://doi.org/10.1016/j.spl.2017.04.021

Abstract

Cauchy–Stieltjes Kernel Semicircle distribution Variance function
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.

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