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

José Fulgencio Gálvez-Rodríguez and Miguel Ángel Sánchez-Granero
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José Fulgencio Gálvez-Rodríguez: Departamento de Matemáticas, Universidad de Almería, 04120 Almería, Spain
Miguel Ángel Sánchez-Granero: Departamento de Matemáticas, Universidad de Almería, 04120 Almería, Spain

Mathematics, 2019, vol. 7, issue 9, 1-21

Abstract: 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.

Keywords: probability; measure; ?-algebra; Borel ?-algebra; distribution function; cumulative distribution function; sample; linearly ordered topological space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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