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Statistics

  

SurvivalFunction

  

compute the survival function

 

Calling Sequence

Parameters

Description

Computation

Options

Examples

References

Calling Sequence

SurvivalFunction(X, t, options)

Parameters

X

-

algebraic; random variable or distribution

t

-

algebraic; point

options

-

(optional) equation of the form numeric=value; specifies options for computing the survival function of a random variable

Description

• 

The SurvivalFunction function computes the survival function of the random variable X at the point t, which is defined as the probability that X takes a value greater than t. In other words, if St denotes the survival function of X and Ft denotes the cumulative distribution function of X, then St=1Ft for all real values of t.

• 

The first parameter can be a distribution (see Statistics[Distribution]), a random variable, or an algebraic expression involving random variables (see Statistics[RandomVariable]).

Computation

• 

By default, all computations involving random variables are performed symbolically (see option numeric below).

• 

For more information about computation in the Statistics package, see the Statistics[Computation] help page.

Options

  

The options argument can contain one or more of the options shown below. More information for some options is available in the Statistics[RandomVariables] help page.

• 

numeric=truefalse -- By default, the survival function is computed using exact arithmetic. To compute the survival function numerically, specify the numeric or numeric = true option.

Examples

withStatistics:

Compute the survival function of the beta distribution with parameters p and q.

SurvivalFunction'Β'p,q,t

1&lcub;0t<0tphypergeomp&comma;1q&comma;1&plus;p&comma;t&Beta;p&comma;qpt<11otherwise

(1)

If p = 3 and q = 5, the plot of the survival function is as follows:

plotSurvivalFunction&apos;&Beta;&apos;3&comma;5&comma;t&comma;t&equals;0..1

The survival function can also be evaluated directly using numeric parameters.

SurvivalFunction&apos;&Beta;&apos;3&comma;5&comma;12

1358hypergeom4&comma;3&comma;4&comma;12

(2)

The numeric option gives a floating point result.

SurvivalFunction&apos;&Beta;&apos;3&comma;5&comma;12&comma;numeric

0.226562500000000

(3)

Define new distribution.

TDistributionPDF&equals;t&rarr;1&pi;t2&plus;1&colon;

XRandomVariableT&colon;

CDFX&comma;t

12&pi;&plus;2arctant&pi;

(4)

SurvivalFunctionX&comma;t

112&pi;&plus;2arctant&pi;

(5)

plot&comma;t&equals;10..10

Another distribution

UDistributionCDF&equals;t&rarr;Ft&comma;PDF&equals;t&rarr;ft&colon;

YRandomVariableU&colon;

CDFY&comma;t

Ft

(6)

SurvivalFunctionY&comma;t

1Ft

(7)

References

  

Stuart, Alan, and Ord, Keith. Kendall's Advanced Theory of Statistics. 6th ed. London: Edward Arnold, 1998. Vol. 1: Distribution Theory.

See Also

Statistics

Statistics[Computation]

Statistics[Distributions]

Statistics[InverseSurvivalFunction]

Statistics[RandomVariables]

 


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