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May 2021 Angle distribution of two random chords in the disc: A sine law
Jesus Igor Heberto Barahona-Torres, Paulo Cesar Manrique-Mirón, Erick Treviño-Aguilar
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Braz. J. Probab. Stat. 35(2): 263-280 (May 2021). DOI: 10.1214/20-BJPS479

Abstract

Motivated by models in engineering and also biology we determine in closed form the probability density function of the angle shaped by two random chords in a fixed disc. Our main result focus on the event in which the intersection locates inside the fixed disc and establishes a sine law.

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Jesus Igor Heberto Barahona-Torres. Paulo Cesar Manrique-Mirón. Erick Treviño-Aguilar. "Angle distribution of two random chords in the disc: A sine law." Braz. J. Probab. Stat. 35 (2) 263 - 280, May 2021. https://doi.org/10.1214/20-BJPS479

Information

Received: 1 November 2019; Accepted: 1 July 2020; Published: May 2021
First available in Project Euclid: 24 March 2021

Digital Object Identifier: 10.1214/20-BJPS479

Rights: Copyright © 2021 Brazilian Statistical Association

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Vol.35 • No. 2 • May 2021
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