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

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