Runuran (version 0.40)

up: Distribution function for "unuran" object

Description

Evaluates the (approximate) cumulative distribution function (CDF) of a "unuran" object for a continuous or discrete distribution.

Usage

up(obj, x)

Arguments

obj

one of

• a distribution object of class "unuran.cont" that contains the CDF, or

• a distribution object of class "unuran.discr" that contains the CDF, or

• a generator object (class "unuran") that contains a CDF or implements method ‘PINV’.

x

vector of x values. (numeric)

Author

Josef Leydold and Wolfgang H\"ormann .

Details

The routine evaluates the cumulative distribution function of a distribution stored in a UNU.RAN distribution object or UNU.RAN generator object.

For the computation of the CDF the following alternatives are tried (in the given order):

1. The CDF is available in object obj: the function is evaluated and the result is returned.

   Important: In this case routine up just evaluates the CDF but ignores the boundaries of the domain of the distribution, i.e., it does not return 0 and 1, resp., outside the domain unless the implementation of the CDF handles this case correctly. This behavior is in particular important when Runuran built-in distributions are truncated by explicitly setting the domain boundaries.

2. Object obj is a generator object that implements method ‘PINV’: In this case an approximate value for the CDF is returned. The approximation error is about one tenth of the requested uresolution for method ‘PINV’.

3. Neither the CDF nor its approximation is available in object obj: NA is returned and a warning is thrown.

References

W. H\"ormann, J. Leydold, and G. Derflinger (2004): Automatic Nonuniform Random Variate Generation. Springer-Verlag, Berlin Heidelberg.

See Also

unuran.cont, unuran.discr, unuran, pinv.new.

Examples

## Create an UNU.RAN distribution object (for standard Gaussian)
## and evaluate distribution function for some points
distr <- udnorm()
up(distr, 1.5)
up(distr, -3:3)

## Create an UNU.RAN generator object (for standard Gaussian)
## and evaluate distribution function of underyling distribution
unr <- tdrd.new(udnorm())
up(unr, 1.5)
up(unr, -3:3)

## Create an UNU.RAN generator object that does not contain
## the CDF but implements method PINV.
unr <- pinv.new(pdf=function(x){exp(-x)}, lb=0,ub=Inf)
up(unr, 0:5)