A note on invariance of the Cauchy and related distributions

Wooyoung Chin, Paul Jung and Greg Markowsky

Statistics & Probability Letters, 2020, vol. 158, issue C

Abstract: It is known that if f is an analytic self map of the complex upper half-plane which also maps R∪{∞} to itself, and f(i)=i, then f preserves the Cauchy distribution. This note concerns three results related to the above fact.

Keywords: Cauchy distribution; Hyperbolic secant distribution; Boole transformation; Newton’s method (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spl.2019.108668

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