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

Author

Listed:
  • José Fulgencio Gálvez-Rodríguez

    (Departamento de Matemáticas, Universidad de Almería, 04120 Almería, Spain
    These authors contributed equally to this work.)

  • Miguel Ángel Sánchez-Granero

    (Departamento de Matemáticas, Universidad de Almería, 04120 Almería, Spain
    These authors contributed equally to this work.)

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.

Suggested Citation

  • José Fulgencio Gálvez-Rodríguez & Miguel Ángel Sánchez-Granero, 2019. "The Distribution Function of a Probability Measure on a Linearly Ordered Topological Space," Mathematics, MDPI, vol. 7(9), pages 1-21, September.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:9:p:864-:d:268398
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