SurvivalFunction
SurvivalFunction[dist,x]
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,…}.
SurvivalFunction[dist]
gives the survival function as a pure function.
Details
- SurvivalFunction is also known as a complementary cumulative distribution function or a reliability function.
- SurvivalFunction[dist,x] gives the probability that an observed value is greater than x.
- SurvivalFunction[dist,x] is equivalent to Probability[ξ>x,ξ∈dist].
- SurvivalFunction[dist,{x1,…,xn}] is equivalent to Probability[ξ1>x1∧⋯∧ξn>xn,{ξ1,…,ξn}dist].
- SurvivalFunction[dist,x] is equivalent to 1-CDF[dist,x].
Examples
open allclose allBasic Examples (4)
Scope (23)
Parametric Distributions (6)
Nonparametric Distributions (4)
Survival function for nonparametric distributions:
Compare with the value for the underlying parametric distribution:
Plot the survival function for a histogram distribution:
Closed form expression for the survival function of a kernel mixture distribution:
Plot of the survival function of a bivariate smooth kernel distribution:
Derived Distributions (10)
Product of independent distributions:
Component mixture distribution:
Quadratic transformation of a discrete distribution:
Compare survival function of the censored distribution with the original:
Compare survival function of the truncated distribution with the original:
Parameter mixture distribution:
Formula distributions defined by its PDF:
Defined by its survival function:
The survival function for QuantityDistribution assumes the argument is a Quantity with compatible units:
Random Processes (3)
Find the survival function for a SliceDistribution of a discrete-state random process:
A continuous-state random process:
Find the multiple time-slice survival function for a discrete-state process:
A multi-slice for a continuous-state process:
Survival function for the StationaryDistribution of a discrete-state random process:
Generalizations & Extensions (1)
SurvivalFunction threads element-wise over lists:
Applications (2)
Compute the probability of 
for a 
distribution with 20 degrees of freedom:
Compute the probability of 
for the same distribution:
Probability of getting at least one six in 6 throws of a regular six‐sided die:
Probability of getting at least two sixes in 12 throws:
Probability of getting at least three sixes in 18 throws:
Getting at least one six in 6 throws is the most favorable bet:
Properties & Relations (6)
The probability of 
for a continuous univariate distribution is given by SurvivalFunction:
The survival function has value 1 at 
and is 0 at 
:
The sum of the survival function and the CDF is 1:
SurvivalFunction and InverseSurvivalFunction are inverses for continuous distributions:
Compositions of SurvivalFunction and InverseSurvivalFunction give step functions for a discrete distribution:
Calculate the PDF of a continuous univariate distribution:
Text
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.
APA
Wolfram Language. (2010). SurvivalFunction. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SurvivalFunction.html