InverseSurvivalFunction

InverseSurvivalFunction[dist,q]

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)^(th) 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

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Basic Examples  (2)

Inverse survival function for a continuous univariate distribution:

Inverse survival function for a discrete univariate distribution:

Scope  (11)

Parametric Distributions  (4)

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:

Derived Distributions  (3)

Quadratic transformation of an exponential distribution:

Truncated distribution:

InverseSurvivalFunction for distributions with quantities:

For a data distribution:

Nonparametric Distributions  (2)

Inverse survival function for nonparametric distributions:

Compare with the value for the underlying parametric distribution:

Plot the survival function for a histogram distribution:

Random Processes  (2)

InverseSurvivalFunction for the SliceDistribution of a random process:

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

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

Generalizations & Extensions  (1)

InverseSurvivalFunction threads element-wise over lists:

Applications  (3)

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:

Properties & Relations  (3)

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:

Possible Issues  (2)

Symbolic closed forms do not exist for some distributions:

Numerical evaluation works:

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

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.

CMS

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

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: 30-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: 30-June-2025 ]}