The Distribution Function of a Probability Measure on a Linearly Ordered Topological Space
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2019-09-18Abstract
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.
Palabra/s clave
probability
measure
σ-algebra
Borel σ-algebra
distribution function
cumulative distribution function
sample
linearly ordered topological space