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)Summary of the most common use cases
Scope (23)Survey of the scope of standard use cases
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)Generalized and extended use cases
SurvivalFunction threads element-wise over lists:
Applications (2)Sample problems that can be solved with this function
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)Properties of the function, and connections to other functions
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