The Distribution Function of a Probability Measure on a Linearly Ordered Topological Space

In this paper, we describe a theory of a cumulative distribution function on a space with an order from a probability measure defined in this space. This distribution function plays a similar role to that played in the classical case. Moreover, we define its pseudo-inverse and study its properties....

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Main Authors:	José Fulgencio Gálvez-Rodríguez, Miguel Ángel Sánchez-Granero
Format:	Article
Language:	English
Published:	MDPI AG 2019-09-01
Series:	Mathematics
Subjects:	probability measure σ-algebra Borel σ-algebra distribution function cumulative distribution function sample linearly ordered topological space
Online Access:	https://www.mdpi.com/2227-7390/7/9/864

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spelling	doaj-374358b58303404fa7bf12de3e4ca3222020-11-25T01:18:12ZengMDPI AGMathematics2227-73902019-09-017986410.3390/math7090864math7090864The Distribution Function of a Probability Measure on a Linearly Ordered Topological SpaceJosé Fulgencio Gálvez-Rodríguez0Miguel Ángel Sánchez-Granero1Departamento de Matemáticas, Universidad de Almería, 04120 Almería, SpainDepartamento de Matemáticas, Universidad de Almería, 04120 Almería, SpainIn this paper, we describe a theory of a cumulative distribution function on a space with an order from a probability measure defined in this space. This distribution function plays a similar role to that played in the classical case. Moreover, we define its pseudo-inverse and study its properties. Those properties will allow us to generate samples of a distribution and give us the chance to calculate integrals with respect to the related probability measure.https://www.mdpi.com/2227-7390/7/9/864probabilitymeasureσ-algebraBorel σ-algebradistribution functioncumulative distribution functionsamplelinearly ordered topological space
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	José Fulgencio Gálvez-Rodríguez Miguel Ángel Sánchez-Granero
spellingShingle	José Fulgencio Gálvez-Rodríguez Miguel Ángel Sánchez-Granero The Distribution Function of a Probability Measure on a Linearly Ordered Topological Space Mathematics probability measure σ-algebra Borel σ-algebra distribution function cumulative distribution function sample linearly ordered topological space
author_facet	José Fulgencio Gálvez-Rodríguez Miguel Ángel Sánchez-Granero
author_sort	José Fulgencio Gálvez-Rodríguez
title	The Distribution Function of a Probability Measure on a Linearly Ordered Topological Space
title_short	The Distribution Function of a Probability Measure on a Linearly Ordered Topological Space
title_full	The Distribution Function of a Probability Measure on a Linearly Ordered Topological Space
title_fullStr	The Distribution Function of a Probability Measure on a Linearly Ordered Topological Space
title_full_unstemmed	The Distribution Function of a Probability Measure on a Linearly Ordered Topological Space
title_sort	distribution function of a probability measure on a linearly ordered topological space
publisher	MDPI AG
series	Mathematics
issn	2227-7390
publishDate	2019-09-01
description	In this paper, we describe a theory of a cumulative distribution function on a space with an order from a probability measure defined in this space. This distribution function plays a similar role to that played in the classical case. Moreover, we define its pseudo-inverse and study its properties. Those properties will allow us to generate samples of a distribution and give us the chance to calculate integrals with respect to the related probability measure.
topic	probability measure σ-algebra Borel σ-algebra distribution function cumulative distribution function sample linearly ordered topological space
url	https://www.mdpi.com/2227-7390/7/9/864
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The Distribution Function of a Probability Measure on a Linearly Ordered Topological Space

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