# 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 # Examples

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## Basic Examples(4)

A survival function for a continuous univariate distribution:

A survival function for a discrete univariate distribution:

A survival function for a continuous multivariate distribution:

A survival function for a discrete multivariate distribution:

## Scope(23)

### Parametric Distributions(6)

Obtain exact numeric results:

Obtain a machine-precision result:

Obtain a result at any precision for a continuous distribution:

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

Survival function for a multivariate distribution:

Obtain a symbolic expression for the survival function:

### 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:

Censored distribution:

Compare survival function of the censored distribution with the original:

Truncated distribution:

Compare survival function of the truncated distribution with the original:

Parameter mixture distribution:

Copula distribution:

Formula distributions defined by its PDF:

Defined by its CDF:

Defined by its survival function:

Marginal distribution:

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

This allows for direct quantity substitution:

Compare with the direct use of the quantity argument:

### 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:

Multivariate distributions:

## 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 sixsided 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:

## Possible Issues(2)

Symbolic closed forms do not exist for some distributions:

Numerical evaluation works:

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

Passing it as an argument, it stays unevaluated: