Cumulative distribution function (cdf)

See also: The basics of probability theory introduction, Probability density function (pdf), Probability mass function (pmf)

The (cumulative) distribution function, or probability distribution function, F(x) is the mathematical equation that describes the probability that a variable X is less that or equal to x, i.e.

     F(x) = P(Xx)                    for all x

where P(Xx) means the probability of the event Xx.

A cumulative distribution function has the following properties:

1.    F(x) is always non-decreasing, i.e.

2.    F(x) = 0 at x = -∞ or minimum

     F(x) = 1 at x = ∞ or maximum

Read on: Parameters and sample statistics introduction

 

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