WOLFRAM

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)^(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)Summary of the most common use cases

Inverse survival function for a continuous univariate distribution:

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Inverse survival function for a discrete univariate distribution:

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Scope  (11)Survey of the scope of standard use cases

Parametric Distributions  (4)

Obtain exact numeric results:

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Obtain a machine-precision result:

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Obtain a result at any precision for a continuous distribution:

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Obtain a symbolic expression for the inverse survival function:

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Derived Distributions  (3)

Quadratic transformation of an exponential distribution:

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Truncated distribution:

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InverseSurvivalFunction for distributions with quantities:

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For a data distribution:

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Nonparametric Distributions  (2)

Inverse survival function for nonparametric distributions:

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Compare with the value for the underlying parametric distribution:

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Plot the survival function for a histogram distribution:

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Random Processes  (2)

InverseSurvivalFunction for the SliceDistribution of a random process:

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

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

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Generalizations & Extensions  (1)Generalized and extended use cases

InverseSurvivalFunction threads element-wise over lists:

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Applications  (3)Sample problems that can be solved with this function

Plot the inverse survival function for a standard normal distribution:

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Plot the inverse survival function for a binomial distribution:

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Generate a random number from a distribution:

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Properties & Relations  (3)Properties of the function, and connections to other functions

InverseSurvivalFunction and SurvivalFunction are inverses for continuous distributions:

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

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InverseSurvivalFunction is equivalent to InverseCDF for distributions:

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Possible Issues  (2)Common pitfalls and unexpected behavior

Symbolic closed forms do not exist for some distributions:

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Numerical evaluation works:

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

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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.

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 ]}

@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 ]}

@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 ]}