A note on invariance of the Cauchy and related distributions

Wooyoung Chin, Paul Jung, Greg Markowsky

Research output: Contribution to journalArticleResearchpeer-review

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 languageEnglish
Article number108668
Pages (from-to)1-6
Number of pages6
JournalStatistics and Probability Letters
Volume158
DOIs
Publication statusPublished - 1 Mar 2020

Keywords

  • Boole transformation
  • Cauchy distribution
  • Hyperbolic secant distribution
  • Newton's method

Cite this

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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.",
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A note on invariance of the Cauchy and related distributions. / Chin, Wooyoung; Jung, Paul; Markowsky, Greg.

In: Statistics and Probability Letters, Vol. 158, 108668, 01.03.2020, p. 1-6.

Research output: Contribution to journalArticleResearchpeer-review

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AU - Chin, Wooyoung

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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