# 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) 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:

## 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_2024_inversesurvivalfunction, author="Wolfram Research", title="{InverseSurvivalFunction}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/InverseSurvivalFunction.html}", note=[Accessed: 20-July-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_inversesurvivalfunction, organization={Wolfram Research}, title={InverseSurvivalFunction}, year={2010}, url={https://reference.wolfram.com/language/ref/InverseSurvivalFunction.html}, note=[Accessed: 20-July-2024 ]}