Probability that random variable X is less than or equal to x
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Cumulative distribution function for the exponential distributionCumulative distribution function for the normal distribution
In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable , or just distribution function of , evaluated at , is the probability that will take a value less than or equal to .[1]
Every probability distribution supported on the real numbers, discrete or "mixed" as well as continuous, is uniquely identified by a right-continuous monotone increasing function (a càdlàg function) satisfying and .
In the case of a scalar continuous distribution, it gives the area under the probability density function from negative infinity to . Cumulative distribution functions are also used to specify the distribution of multivariate random variables.
^Deisenroth, Marc Peter; Faisal, A. Aldo; Ong, Cheng Soon (2020). Mathematics for Machine Learning. Cambridge University Press. p. 181. ISBN 9781108455145.
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the cumulativedistributionfunction) or inverse distributionfunction. With reference to a continuous and strictly monotonic cumulativedistribution function...
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refer to the cumulativedistributionfunction, or it may be a probability mass function (PMF) rather than the density. "Density function" itself is also...
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\\0&{\text{otherwise}}.\end{cases}}} The cumulativedistributionfunction of the continuous uniform distribution is: F ( x ) = { 0 for x < a , x − a b...
statistics, the logistic distribution is a continuous probability distribution. Its cumulativedistributionfunction is the logistic function, which appears in...
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vector, its probability density function, cumulativedistributionfunction, and inverse cumulativedistributionfunction can be computed with the numerical...
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Finally, the probability density function for X {\displaystyle X} is the derivative of its cumulativedistributionfunction, which by the fundamental theorem...
tractability in posterior distribution computations. The probability density and cumulativedistributionfunctions of the gamma distribution vary based on the...
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![{\displaystyle F\colon \mathbb {R} \rightarrow [0,1]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b4c45b6faf38bb3fb300ab4678d3675afd172f56)
