BUILT-IN MATHEMATICA SYMBOL

InverseSurvivalFunction

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

The inverse survival function at q is equivalent to the quantile of a distribution.

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

For a discrete distribution dist, the inverse survival function at q is the smallest integer x such that SurvivalFunction[dist, x]≤q.

Inverse survival function for a continuous univariate distribution:

Inverse survival function for a discrete univariate distribution:

Inverse survival function for a continuous univariate distribution:

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Inverse survival function 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 a continuous distribution:

Obtain a symbolic expression for the inverse survival function:

Quadratic transformation of an exponential distribution:

Truncated distribution:

Inverse survival function for nonparametric distributions:

Compare with the value for the underlying parametric distribution:

Plot the survival function for a histogram distribution:

InverseSurvivalFunction threads element-wise over lists:

Plot the inverse survival function for a standard normal distribution:

Plot the inverse survival function for a binomial distribution:

Generate a random number from a distribution:

InverseSurvivalFunction and SurvivalFunction are inverses for continuous distributions:

Compositions of InverseSurvivalFunction and SurvivalFunction give step functions for a discrete distribution:

InverseSurvivalFunction is equivalent to InverseCDF 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 an argument, complete checking is done: