### 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 |
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Article number | 108668 |

Pages (from-to) | 1-6 |

Number of pages | 6 |

Journal | Statistics and Probability Letters |

Volume | 158 |

DOIs | |

Publication status | Published - 1 Mar 2020 |

### Keywords

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

## Cite this

Chin, W., Jung, P., & Markowsky, G. (2020). A note on invariance of the Cauchy and related distributions.

*Statistics and Probability Letters*,*158*, 1-6. [108668]. https://doi.org/10.1016/j.spl.2019.108668