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CDF

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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.
  • CDF gives the probability that an observed value will be less than or equal to x.
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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The CDF of a bivariate continuous distribution:
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The CDF for a multivariate Poisson distribution:
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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:
CDF threads element-wise over lists:
Multivariate distributions:
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 :
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:
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:
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