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Statistics

  

InverseSurvivalFunction

  

compute the inverse survival function

 

Calling Sequence

Parameters

Description

Computation

Options

Examples

References

Calling Sequence

InverseSurvivalFunction(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 inverse survival function of a random variable

Description

• 

The InverseSurvivalFunction function computes the inverse survival function of the specified random variable at the specified point.

• 

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 inverse survival function is computed using exact arithmetic. To compute the inverse survival function numerically, specify the numeric or numeric = true option.

Examples

withStatistics:

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

InverseSurvivalFunctionCauchyp,q,t

p+qtanπ12t

(1)

Use numeric parameters.

InverseSurvivalFunctionCauchy3,5,12

3

(2)

InverseSurvivalFunctionCauchy3,5,12,numeric

3.

(3)

QuantileCauchy3,5,12

3

(4)

Define new distribution.

TDistributionPDF=t→1πt2+1:

XRandomVariableT:

CDFX,t

12π+2arctantπ

(5)

InverseSurvivalFunctionX,t

cot1tπ

(6)

Another distribution

UDistributionCDF=t→Ft,PDF=t→ft:

YRandomVariableU:

CDFY,t

Ft

(7)

InverseSurvivalFunctionY,t

RootOfF_Z1+t

(8)

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[RandomVariables]

Statistics[SurvivalFunction]

 


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