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InverseSurvivalFunction
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InverseSurvivalFunction

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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

open allclose all

Basic Examples  (2)Summary of the most common use cases

Inverse survival function for a continuous univariate distribution:

In[1]:=1
✖
https://wolfram.com/xid/0g34lojlkd0q1g85e-hoi9z
Out[1]=1
In[1]:=1
✖
https://wolfram.com/xid/0g34lojlkd0q1g85e-cvgzky
Out[1]=1

Inverse survival function for a discrete univariate distribution:

In[1]:=1
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https://wolfram.com/xid/0g34lojlkd0q1g85e-b5ngre
In[2]:=2
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https://wolfram.com/xid/0g34lojlkd0q1g85e-hhcnr
Out[2]=2

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

Parametric Distributions  (4)

Obtain exact numeric results:

In[1]:=1
✖
https://wolfram.com/xid/0g34lojlkd0q1g85e-47vk1
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0g34lojlkd0q1g85e-dvkmub
Out[2]=2

Obtain a machine-precision result:

In[1]:=1
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https://wolfram.com/xid/0g34lojlkd0q1g85e-bcclkz
Out[1]=1

Obtain a result at any precision for a continuous distribution:

In[1]:=1
✖
https://wolfram.com/xid/0g34lojlkd0q1g85e-bvzj50
Out[1]=1

Obtain a symbolic expression for the inverse survival function:

In[1]:=1
✖
https://wolfram.com/xid/0g34lojlkd0q1g85e-bwuue7
Out[1]=1

Derived Distributions  (3)

Quadratic transformation of an exponential distribution:

In[1]:=1
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https://wolfram.com/xid/0g34lojlkd0q1g85e-qx2dx
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0g34lojlkd0q1g85e-k0a3dq
Out[2]=2

Truncated distribution:

In[1]:=1
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https://wolfram.com/xid/0g34lojlkd0q1g85e-b8ebyy
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0g34lojlkd0q1g85e-bnm6za
Out[2]=2

InverseSurvivalFunction for distributions with quantities:

In[1]:=1
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https://wolfram.com/xid/0g34lojlkd0q1g85e-fib5xt
Out[1]=1

For a data distribution:

In[2]:=2
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https://wolfram.com/xid/0g34lojlkd0q1g85e-xn0y4a
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0g34lojlkd0q1g85e-38ajq
Out[3]=3

Nonparametric Distributions  (2)

Inverse survival function for nonparametric distributions:

In[1]:=1
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https://wolfram.com/xid/0g34lojlkd0q1g85e-cy09q2
In[2]:=2
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https://wolfram.com/xid/0g34lojlkd0q1g85e-decfbs
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0g34lojlkd0q1g85e-c44dgq
Out[3]=3
In[4]:=4
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https://wolfram.com/xid/0g34lojlkd0q1g85e-b7gkfh
Out[4]=4
In[5]:=5
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https://wolfram.com/xid/0g34lojlkd0q1g85e-mtb0mp
Out[5]=5
In[6]:=6
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https://wolfram.com/xid/0g34lojlkd0q1g85e-cinns0
Out[6]=6

Compare with the value for the underlying parametric distribution:

In[7]:=7
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https://wolfram.com/xid/0g34lojlkd0q1g85e-laemrs
Out[7]=7

Plot the survival function for a histogram distribution:

In[1]:=1
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https://wolfram.com/xid/0g34lojlkd0q1g85e-bezwuv
Out[1]=1

Random Processes  (2)

InverseSurvivalFunction for the SliceDistribution of a random process:

In[1]:=1
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https://wolfram.com/xid/0g34lojlkd0q1g85e-ce9dln
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0g34lojlkd0q1g85e-dbfsuo
Out[2]=2

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

In[1]:=1
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https://wolfram.com/xid/0g34lojlkd0q1g85e-jfiydh
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0g34lojlkd0q1g85e-cnazd
Out[2]=2

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

In[3]:=3
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https://wolfram.com/xid/0g34lojlkd0q1g85e-bdty7n
Out[3]=3

Generalizations & Extensions  (1)Generalized and extended use cases

InverseSurvivalFunction threads element-wise over lists:

In[1]:=1
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https://wolfram.com/xid/0g34lojlkd0q1g85e-uxh42
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0g34lojlkd0q1g85e-8hdoz
Out[2]=2

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

Plot the inverse survival function for a standard normal distribution:

In[1]:=1
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https://wolfram.com/xid/0g34lojlkd0q1g85e-f0ov1z
Out[1]=1

Plot the inverse survival function for a binomial distribution:

In[1]:=1
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https://wolfram.com/xid/0g34lojlkd0q1g85e-dz8ev2
Out[1]=1

Generate a random number from a distribution:

In[1]:=1
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https://wolfram.com/xid/0g34lojlkd0q1g85e-f4x15h
Out[1]=1

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

InverseSurvivalFunction and SurvivalFunction are inverses for continuous distributions:

In[1]:=1
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https://wolfram.com/xid/0g34lojlkd0q1g85e-g2gh3l
In[2]:=2
✖
https://wolfram.com/xid/0g34lojlkd0q1g85e-cnefrj
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0g34lojlkd0q1g85e-bdlj9l
Out[3]=3

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

In[1]:=1
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https://wolfram.com/xid/0g34lojlkd0q1g85e-e0tr3p
In[2]:=2
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https://wolfram.com/xid/0g34lojlkd0q1g85e-itz2
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0g34lojlkd0q1g85e-gpjnzr
Out[3]=3

InverseSurvivalFunction is equivalent to InverseCDF for distributions:

In[1]:=1
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https://wolfram.com/xid/0g34lojlkd0q1g85e-6g7ow
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0g34lojlkd0q1g85e-puok2
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0g34lojlkd0q1g85e-hjdob4
Out[3]=3

Possible Issues  (2)Common pitfalls and unexpected behavior

Symbolic closed forms do not exist for some distributions:

In[1]:=1
✖
https://wolfram.com/xid/0g34lojlkd0q1g85e-gtite
Out[1]=1

Numerical evaluation works:

In[2]:=2
✖
https://wolfram.com/xid/0g34lojlkd0q1g85e-ouxi8x
Out[2]=2

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

In[1]:=1
✖
https://wolfram.com/xid/0g34lojlkd0q1g85e-jtmg4
Out[1]=1
Wolfram Research (2010), InverseSurvivalFunction, Wolfram Language function, https://reference.wolfram.com/language/ref/InverseSurvivalFunction.html.
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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 ]}

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@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 ]}

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@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 ]}