BUILT-IN MATHEMATICA SYMBOL

CDF

gives the cumulative distribution function for the symbolic distribution dist evaluated at x.

CDF

gives the multivariate cumulative distribution function for the symbolic distribution dist evaluated at

.

CDF[dist]
gives the CDF as a pure function.

MORE INFORMATION

CDF gives the probability that an observed value will be less than or equal to x.

CDF is equivalent to Probability.

CDF is equivalent to Probability.

CDF is equivalent to 1-SurvivalFunction[dist, x].

EXAMPLES

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Basic Examples (4)

The CDF of a univariate continuous distribution:

The CDF of a univariate discrete distribution:

The CDF of a bivariate continuous distribution:

The CDF for a multivariate Poisson distribution:

The CDF of a univariate continuous distribution:

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The CDF of a univariate discrete distribution:

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Out[1]=

In[2]:=

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The CDF of a bivariate continuous distribution:

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Out[1]=

The CDF for a multivariate Poisson distribution:

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Out[1]=

Scope (17)

Obtain exact numeric results:

Obtain a machine-precision result:

Obtain a result at any precision for a continuous distribution:

Obtain a result at any precision for a discrete distribution with inexact parameters:

CDF for nonparametric distributions:

Plot the CDF for a histogram distribution:

Closed-form expression for the CDF of a kernel mixture distribution:

Plot of the CDF of a bivariate smooth kernel distribution:

Product of independent distributions:

Component mixture distribution:

Quadratic transformation of a discrete distribution:

Censored distribution:

Truncated distribution:

Parameter mixture distribution:

Copula distribution:

Formula distribution defined by its PDF:

Defined by its CDF:

Defined by its SurvivalFunction:

Marginal distribution:

Generalizations & Extensions (1)

CDF threads element-wise over lists:

Multivariate distributions:

Applications (3)

Plot the CDF for a standard normal distribution:

Plot the CDF for a binomial distribution:

Compute the probability of

for a

distribution with 20 degrees of freedom:

Compute the probability of

for the same distribution:

Compute the probability of

:

Properties & Relations (10)

The probability of

for a univariate distribution is given by its CDF:

The probability of

for a multivariate distribution is given by its CDF:

A univariate CDF is 0 at

and 1 at

:

A multivariate CDF has value 0 at

and 1 at

:

The CDF is the integral of the PDF for continuous distributions

:

The CDF is the sum of the PDF for discrete distributions

:

CDF and InverseCDF are inverses for continuous distributions:

Compositions of CDF and InverseCDF give step functions for a discrete distribution:

CDF and Quantile are inverses for continuous distributions:

The sum of the CDF and the survival function is 1:

Possible Issues (2)

Symbolic closed forms do not exist for some distributions:

Numerical evaluation works:

Substitution of invalid values into symbolic formulas can give results that are not meaningful:

When CDF is given an explicit value as an argument, it does complete checking and does not produce invalid results: