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SurvivalFunction
✖
SurvivalFunction

✖

gives the survival function for the distribution dist evaluated at x.

✖
SurvivalFunction[dist,{x1,x2,…}]

gives the multivariate survival function for the distribution dist evaluated at {x1,x2,…}.

✖

gives the survival function as a pure function.

Details

Examples

open allclose all

Basic Examples  (4)Summary of the most common use cases

A survival function for a continuous univariate distribution:

In[1]:=1
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-yq67n
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-b1cc59
Out[2]=2

A survival function for a discrete univariate distribution:

In[1]:=1
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-caapo2
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-cdcagg
Out[2]=2

A survival function for a continuous multivariate distribution:

In[1]:=1
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-e3k6fw
Out[1]=1

A survival function for a discrete multivariate distribution:

In[1]:=1
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-fpmd7v
Out[1]=1

Scope  (23)Survey of the scope of standard use cases

Parametric Distributions  (6)

Obtain exact numeric results:

In[1]:=1
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-47vk1
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-dvkmub
Out[2]=2

Obtain a machine-precision result:

In[1]:=1
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-bcclkz
Out[1]=1

Obtain a result at any precision for a continuous distribution:

In[1]:=1
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-bvzj50
Out[1]=1

Obtain a result at any precision for a discrete distribution with inexact parameters:

In[1]:=1
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-c30oe4
Out[1]=1

Survival function for a multivariate distribution:

In[1]:=1
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-oe4vdr
Out[1]=1

Obtain a symbolic expression for the survival function:

In[1]:=1
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-bwuue7
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-n7lmp
Out[2]=2

Nonparametric Distributions  (4)

Survival function for nonparametric distributions:

In[1]:=1
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-cy09q2
In[2]:=2
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-decfbs
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-c44dgq
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-b7gkfh
Out[4]=4

Compare with the value for the underlying parametric distribution:

In[5]:=5
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-laemrs
Out[5]=5

Plot the survival function for a histogram distribution:

In[1]:=1
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-bezwuv
Out[1]=1

Closed form expression for the survival function of a kernel mixture distribution:

In[1]:=1
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-dldvgo
Out[1]=1

Plot of the survival function of a bivariate smooth kernel distribution:

In[1]:=1
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-d1pyr5
Out[1]=1

Derived Distributions  (10)

Product of independent distributions:

In[1]:=1
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-wkzb98
In[2]:=2
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-8pyz0
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-i185f
Out[3]=3

Component mixture distribution:

In[1]:=1
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-zst18z
In[2]:=2
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-g8oy2
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-l97u83
Out[3]=3

Quadratic transformation of a discrete distribution:

In[1]:=1
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-nog3b1
In[2]:=2
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-qx2dx
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-k0a3dq
Out[3]=3

Censored distribution:

In[1]:=1
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-wzpdhu
In[2]:=2
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-d2ukan
Out[2]=2

Compare survival function of the censored distribution with the original:

In[3]:=3
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-sc32m
Out[3]=3

Truncated distribution:

In[1]:=1
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-2khkop
In[2]:=2
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-b8ebyy
Out[2]=2

Compare survival function of the truncated distribution with the original:

In[3]:=3
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-bnm6za
Out[3]=3

Parameter mixture distribution:

In[1]:=1
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-8ncjcz
In[2]:=2
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-bct2he
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-ofva0y
Out[3]=3

Copula distribution:

In[1]:=1
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-soi5ca
In[2]:=2
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-o4vib6
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-4j88yk
Out[3]=3

Formula distributions defined by its PDF:

In[1]:=1
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-cqlvum
In[2]:=2
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-few7li
Out[2]=2

Defined by its CDF:

In[3]:=3
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-icgxr8
In[4]:=4
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-ceb6ni
Out[4]=4

Defined by its survival function:

In[5]:=5
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-eq1y4f
In[6]:=6
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-hfkb2
Out[6]=6

Marginal distribution:

In[1]:=1
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-jneah
In[2]:=2
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-gmxz4v
Out[2]=2

The survival function for QuantityDistribution assumes the argument is a Quantity with compatible units:

In[1]:=1
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-z6cqh
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-bjwd0p
Out[2]=2

This allows for direct quantity substitution:

In[3]:=3
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-bs6882
Out[3]=3

Compare with the direct use of the quantity argument:

In[4]:=4
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-kkvt7w
Out[4]=4

Random Processes  (3)

Find the survival function for a SliceDistribution of a discrete-state random process:

In[1]:=1
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-hha5jz
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-ec193c
Out[2]=2

A continuous-state random process:

In[3]:=3
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-cg4akz
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-dzmz38
Out[4]=4

Find the multiple time-slice survival function for a discrete-state process:

In[1]:=1
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-r98gn
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-hlbkqt
Out[2]=2

A multi-slice for a continuous-state process:

In[3]:=3
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-m37pj
Out[3]=3

Survival function for the StationaryDistribution of a discrete-state random process:

In[1]:=1
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-mpszqf
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-bdqzil
Out[2]=2

Generalizations & Extensions  (1)Generalized and extended use cases

SurvivalFunction threads element-wise over lists:

In[1]:=1
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-uxh42
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-8hdoz
Out[2]=2

Multivariate distributions:

In[3]:=3
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-en7mbd
Out[3]=3

Applications  (2)Sample problems that can be solved with this function

Compute the probability of for a distribution with 20 degrees of freedom:

In[1]:=1
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-hksahd
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-ct08dz
Out[2]=2

Compute the probability of for the same distribution:

In[3]:=3
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-jhlkj6
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-rfauio
Out[4]=4

Probability of getting at least one six in 6 throws of a regular six‐sided die:

In[1]:=1
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-gfbgba
Out[1]=1

Probability of getting at least two sixes in 12 throws:

In[2]:=2
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-po3qmr
Out[2]=2

Probability of getting at least three sixes in 18 throws:

In[3]:=3
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-e6gp00
Out[3]=3

Getting at least one six in 6 throws is the most favorable bet:

In[4]:=4
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-bnj8vq
Out[4]=4
In[5]:=5
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-d5du0z
Out[5]=5

Properties & Relations  (6)Properties of the function, and connections to other functions

The probability of for a continuous univariate distribution is given by SurvivalFunction:

In[1]:=1
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-3se3v
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-d1kk3s
Out[2]=2

The survival function has value 1 at and is 0 at :

In[1]:=1
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-e90ztq
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-h48duv
Out[2]=2

The sum of the survival function and the CDF is 1:

In[1]:=1
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-jqydpp
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-dyrxg5
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-igglac
Out[3]=3

SurvivalFunction and InverseSurvivalFunction are inverses for continuous distributions:

In[1]:=1
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-g2gh3l
In[2]:=2
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-cnefrj
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-bdlj9l
Out[3]=3

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

In[1]:=1
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-e0tr3p
In[2]:=2
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-itz2
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-gpjnzr
Out[3]=3

Calculate the PDF of a continuous univariate distribution:

In[1]:=1
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-k5jnts
In[2]:=2
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-ya9mv
Out[2]=2

Possible Issues  (2)Common pitfalls and unexpected behavior

Symbolic closed forms do not exist for some distributions:

In[1]:=1
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-gtite
Out[1]=1

Numerical evaluation works:

In[2]:=2
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-k4p5g
Out[2]=2

Substitution of invalid values into symbolic outputs gives results that are not meaningful:

In[1]:=1
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-w93
Out[1]=1

Passing it as an argument, it stays unevaluated:

In[2]:=2
✖
https://wolfram.com/xid/0jz5mj4qzw8ar2-jt2z9
Out[2]=2
Wolfram Research (2010), SurvivalFunction, Wolfram Language function, https://reference.wolfram.com/language/ref/SurvivalFunction.html.
✖
Wolfram Research (2010), SurvivalFunction, Wolfram Language function, https://reference.wolfram.com/language/ref/SurvivalFunction.html.

Text

Wolfram Research (2010), SurvivalFunction, Wolfram Language function, https://reference.wolfram.com/language/ref/SurvivalFunction.html.

✖
Wolfram Research (2010), SurvivalFunction, Wolfram Language function, https://reference.wolfram.com/language/ref/SurvivalFunction.html.

CMS

Wolfram Language. 2010. "SurvivalFunction." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SurvivalFunction.html.

✖
Wolfram Language. 2010. "SurvivalFunction." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SurvivalFunction.html.

APA

Wolfram Language. (2010). SurvivalFunction. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SurvivalFunction.html

✖
Wolfram Language. (2010). SurvivalFunction. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SurvivalFunction.html

BibTeX

@misc{reference.wolfram_2025_survivalfunction, author="Wolfram Research", title="{SurvivalFunction}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/SurvivalFunction.html}", note=[Accessed: 06-April-2025 ]}

✖
@misc{reference.wolfram_2025_survivalfunction, author="Wolfram Research", title="{SurvivalFunction}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/SurvivalFunction.html}", note=[Accessed: 06-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_survivalfunction, organization={Wolfram Research}, title={SurvivalFunction}, year={2010}, url={https://reference.wolfram.com/language/ref/SurvivalFunction.html}, note=[Accessed: 06-April-2025 ]}

✖
@online{reference.wolfram_2025_survivalfunction, organization={Wolfram Research}, title={SurvivalFunction}, year={2010}, url={https://reference.wolfram.com/language/ref/SurvivalFunction.html}, note=[Accessed: 06-April-2025 ]}