BUILT-IN MATHEMATICA SYMBOL

InverseCDF

gives the inverse of the cumulative distribution function for the symbolic distribution dist as a function of the variable q.

For a continuous distribution dist the inverse CDF at q is the value x such that CDF[dist, x]=q.

For a discrete distribution dist the inverse CDF at q is the smallest integer x such that CDF[dist, x]≥q.

The inverse CDF for a continuous univariate distribution:

The inverse CDF for a discrete univariate distribution:

The inverse CDF for a continuous univariate distribution:

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The inverse CDF for a discrete univariate distribution:

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Obtain exact numeric results:

Obtain a machine-precision result:

Obtain a result at any precision for continuous distributions:

Obtain an exact result at any precision q for discrete distributions:

Plot the inverse CDF for a standard normal distribution:

Plot the inverse CDF for a binomial distribution:

Generate a random number from a distribution:

InverseCDF and CDF are inverses for continuous distributions:

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

InverseCDF is equivalent to Quantile for distributions:

Symbolic closed forms do not exist for some distributions:

Numerical evaluation works:

Substitution of invalid values into symbolic outputs gives results that are not meaningful:

When giving the input as argument complete checking is done: