InverseSurvivalFunction
✖
InverseSurvivalFunction
gives the inverse of the survival function for the distribution dist as a function of the variable q.
Details

- The inverse survival function at q is equivalent to the (1-q)
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.
- The value q can be symbolic or any number between 0 and 1.
Examples
open allclose allBasic Examples (2)Summary of the most common use cases
Inverse survival function for a continuous univariate distribution:

https://wolfram.com/xid/0g34lojlkd0q1g85e-hoi9z


https://wolfram.com/xid/0g34lojlkd0q1g85e-cvgzky

Inverse survival function for a discrete univariate distribution:

https://wolfram.com/xid/0g34lojlkd0q1g85e-b5ngre

https://wolfram.com/xid/0g34lojlkd0q1g85e-hhcnr

Scope (11)Survey of the scope of standard use cases
Parametric Distributions (4)

https://wolfram.com/xid/0g34lojlkd0q1g85e-47vk1


https://wolfram.com/xid/0g34lojlkd0q1g85e-dvkmub

Obtain a machine-precision result:

https://wolfram.com/xid/0g34lojlkd0q1g85e-bcclkz

Obtain a result at any precision for a continuous distribution:

https://wolfram.com/xid/0g34lojlkd0q1g85e-bvzj50

Obtain a symbolic expression for the inverse survival function:

https://wolfram.com/xid/0g34lojlkd0q1g85e-bwuue7

Derived Distributions (3)
Quadratic transformation of an exponential distribution:

https://wolfram.com/xid/0g34lojlkd0q1g85e-qx2dx


https://wolfram.com/xid/0g34lojlkd0q1g85e-k0a3dq


https://wolfram.com/xid/0g34lojlkd0q1g85e-b8ebyy


https://wolfram.com/xid/0g34lojlkd0q1g85e-bnm6za

InverseSurvivalFunction for distributions with quantities:

https://wolfram.com/xid/0g34lojlkd0q1g85e-fib5xt


https://wolfram.com/xid/0g34lojlkd0q1g85e-xn0y4a


https://wolfram.com/xid/0g34lojlkd0q1g85e-38ajq

Nonparametric Distributions (2)
Inverse survival function for nonparametric distributions:

https://wolfram.com/xid/0g34lojlkd0q1g85e-cy09q2

https://wolfram.com/xid/0g34lojlkd0q1g85e-decfbs


https://wolfram.com/xid/0g34lojlkd0q1g85e-c44dgq


https://wolfram.com/xid/0g34lojlkd0q1g85e-b7gkfh


https://wolfram.com/xid/0g34lojlkd0q1g85e-mtb0mp


https://wolfram.com/xid/0g34lojlkd0q1g85e-cinns0

Compare with the value for the underlying parametric distribution:

https://wolfram.com/xid/0g34lojlkd0q1g85e-laemrs

Plot the survival function for a histogram distribution:

https://wolfram.com/xid/0g34lojlkd0q1g85e-bezwuv

Random Processes (2)
InverseSurvivalFunction for the SliceDistribution of a random process:

https://wolfram.com/xid/0g34lojlkd0q1g85e-ce9dln


https://wolfram.com/xid/0g34lojlkd0q1g85e-dbfsuo

Find the InverseSurvivalFunction of TemporalData at some time t=0.5:

https://wolfram.com/xid/0g34lojlkd0q1g85e-jfiydh


https://wolfram.com/xid/0g34lojlkd0q1g85e-cnazd

Find the InverseSurvivalFunction for a range of times together with all the simulations:

https://wolfram.com/xid/0g34lojlkd0q1g85e-bdty7n

Generalizations & Extensions (1)Generalized and extended use cases
InverseSurvivalFunction threads element-wise over lists:

https://wolfram.com/xid/0g34lojlkd0q1g85e-uxh42


https://wolfram.com/xid/0g34lojlkd0q1g85e-8hdoz

Applications (3)Sample problems that can be solved with this function
Plot the inverse survival function for a standard normal distribution:

https://wolfram.com/xid/0g34lojlkd0q1g85e-f0ov1z

Plot the inverse survival function for a binomial distribution:

https://wolfram.com/xid/0g34lojlkd0q1g85e-dz8ev2

Generate a random number from a distribution:

https://wolfram.com/xid/0g34lojlkd0q1g85e-f4x15h

Properties & Relations (3)Properties of the function, and connections to other functions
InverseSurvivalFunction and SurvivalFunction are inverses for continuous distributions:

https://wolfram.com/xid/0g34lojlkd0q1g85e-g2gh3l

https://wolfram.com/xid/0g34lojlkd0q1g85e-cnefrj


https://wolfram.com/xid/0g34lojlkd0q1g85e-bdlj9l

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

https://wolfram.com/xid/0g34lojlkd0q1g85e-e0tr3p

https://wolfram.com/xid/0g34lojlkd0q1g85e-itz2


https://wolfram.com/xid/0g34lojlkd0q1g85e-gpjnzr

InverseSurvivalFunction is equivalent to InverseCDF for distributions:

https://wolfram.com/xid/0g34lojlkd0q1g85e-6g7ow


https://wolfram.com/xid/0g34lojlkd0q1g85e-puok2


https://wolfram.com/xid/0g34lojlkd0q1g85e-hjdob4

Possible Issues (2)Common pitfalls and unexpected behavior
Symbolic closed forms do not exist for some distributions:

https://wolfram.com/xid/0g34lojlkd0q1g85e-gtite


https://wolfram.com/xid/0g34lojlkd0q1g85e-ouxi8x

When giving the input as an argument, complete checking is done and invalid input will not evaluate:

https://wolfram.com/xid/0g34lojlkd0q1g85e-jtmg4

Wolfram Research (2010), InverseSurvivalFunction, Wolfram Language function, https://reference.wolfram.com/language/ref/InverseSurvivalFunction.html.
Text
Wolfram Research (2010), InverseSurvivalFunction, Wolfram Language function, https://reference.wolfram.com/language/ref/InverseSurvivalFunction.html.
Wolfram Research (2010), InverseSurvivalFunction, Wolfram Language function, https://reference.wolfram.com/language/ref/InverseSurvivalFunction.html.
CMS
Wolfram Language. 2010. "InverseSurvivalFunction." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/InverseSurvivalFunction.html.
Wolfram Language. 2010. "InverseSurvivalFunction." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/InverseSurvivalFunction.html.
APA
Wolfram Language. (2010). InverseSurvivalFunction. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/InverseSurvivalFunction.html
Wolfram Language. (2010). InverseSurvivalFunction. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/InverseSurvivalFunction.html
BibTeX
@misc{reference.wolfram_2025_inversesurvivalfunction, author="Wolfram Research", title="{InverseSurvivalFunction}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/InverseSurvivalFunction.html}", note=[Accessed: 05-June-2025
]}
BibLaTeX
@online{reference.wolfram_2025_inversesurvivalfunction, organization={Wolfram Research}, title={InverseSurvivalFunction}, year={2010}, url={https://reference.wolfram.com/language/ref/InverseSurvivalFunction.html}, note=[Accessed: 05-June-2025
]}