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Cumulative Distribution Function

The cumulative distribution function (CDF) is the probability that the variate takes on a value less than or equal to x:

For discrete distributions, this is expressed as

In this case, the empirical CDF is displayed as vertical lines at each integer x, and the theoretical PDF is displayed as a polygonal line:

For continuous distributions, the CDF is expressed as


so the theoretical CDF is displayed as a continuous curve. The empirical CDF is denoted by


and is displayed as a stepped discontinuous line depending on the number of bins:

See also:

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