A note on invariance of the Cauchy and related distributions

Wooyoung Chin; Paul Jung; Greg Markowsky

doi:10.1016/j.spl.2019.108668

A note on invariance of the Cauchy and related distributions

Wooyoung Chin, Paul Jung, Greg Markowsky

School of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

4 Citations (Scopus)

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.

Original language	English
Article number	108668
Pages (from-to)	1-6
Number of pages	6
Journal	Statistics and Probability Letters
Volume	158
DOIs	https://doi.org/10.1016/j.spl.2019.108668
Publication status	Published - 1 Mar 2020

Keywords

Boole transformation
Cauchy distribution
Hyperbolic secant distribution
Newton's method

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10.1016/j.spl.2019.108668

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title = "A note on invariance of the Cauchy and related distributions",

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 = "Boole transformation, Cauchy distribution, Hyperbolic secant distribution, Newton's method",

author = "Wooyoung Chin and Paul Jung and Greg Markowsky",

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AU - Jung, Paul

AU - Markowsky, Greg

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AB - 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.

KW - Boole transformation

KW - Cauchy distribution

KW - Hyperbolic secant distribution

KW - Newton's method

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JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

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A note on invariance of the Cauchy and related distributions

Abstract

Keywords

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