Cumulative Density Function (CDF)

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A Cumulative Density Function (CDF) is a non-decreasing right-continuous unit function that returns the probability that a real-valued random variable X (with a given probability distribution) will be found at a value less than or equal to x



  • (Wikipedia, 2022) ⇒ Retrieved:2022-8-15.
    • In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable [math]\displaystyle{ X }[/math] , or just distribution function of [math]\displaystyle{ X }[/math] , evaluated at [math]\displaystyle{ x }[/math] , is the probability that [math]\displaystyle{ X }[/math] will take a value less than or equal to [math]\displaystyle{ x }[/math] . Every probability distribution supported on the real numbers, discrete or "mixed" as well as continuous, is uniquely identified by an upwards continuous monotonic increasing cumulative distribution function [math]\displaystyle{ F : \mathbb R \rightarrow [0,1] }[/math] satisfying [math]\displaystyle{ \lim_{x\rightarrow-\infty}F(x)=0 }[/math] and [math]\displaystyle{ \lim_{x\rightarrow\infty}F(x)=1 }[/math] .

      In the case of a scalar continuous distribution, it gives the area under the probability density function from minus infinity to [math]\displaystyle{ x }[/math] . Cumulative distribution functions are also used to specify the distribution of multivariate random variables.