Runuran.distributions function

UNU.RAN distribution objects

Create objects for particular distributions suitable for using with generation methods from the UNU.RAN library.

Details

Runuran provides an interface to the UNU.RAN library for universal non-uniform random number generators. This is a very flexible and powerful collection of sampling routines, where the user first has to specify the target distribution and then has to choose an appropriate sampling method.

Creating an object for a particular distribution can be a bit tedious especially if the target distribution has a more complex density function. Thus we have compiled a set of functions that provides ready-to-use distribution objects. Moreover, using these object often results in faster setup time than objects created with pure code.

These functions share a similar syntax and naming scheme (only ud is prefixed) with analogous built-in functions that provide density, distribution function and quantile:

ud...(distribution parameters, lb , ub)

Currently generators for the following distributions are implemented.

Continuous Univariate Distributions (26):

Function		Distribution
udbeta		Beta
udcauchy		Cauchy
udchi		Chi
udchisq		Chi-squared
udexp		Exponential
udf		F
udfrechet		Frechet (Extreme value type II)
udgamma		Gamma
udghyp		Generalized Hyperbolic
udgig		Generalized Inverse Gaussian
udgumbel		Gumbel (Extreme value type I)
udhyperbolic		Hyperbolic
udig		Inverse Gaussian (Wald)
udlaplace		Laplace (double exponential)
udlnorm		Log Normal
udlogis		Logistic
udlomax		Lomax (Pareto of second kind)
udmeixner		Meixner
udnorm		Normal (Gaussian)
udpareto		Pareto (of first kind)
udpowerexp		Powerexponential (Subbotin)
udrayleigh		Rayleigh
udslash		Slash
udt		t (Student)
udvg		Variance Gamma
udweibull		Weibull (Extreme value type III)

Discrete Distributions (6):

Function		Distribution
udbinom		Binomial
udgeom		Geometric
udhyper		Hypergeometric
udlogarithmic		Logarithmic
udnbinom		Negative Binomial
udpois		Poisson

Author(s)

Josef Leydold and Wolfgang H"ormann unuran@statmath.wu.ac.at .

See Also

Runuran-package.

Examples

## Create an object for a gamma distribution with shape parameter 5.
distr <- udgamma(shape=5)
## Create the UNU.RAN generator object. use method PINV (inversion).
gen <- pinvd.new(distr)
## Draw a sample of size 100
x <- ur(gen, 100)
## Compute some quantiles for Monte Carlo methods
x <- uq(gen, (1:9)/10)

## Analogous for half normal distribution
distr <- udnorm(lb=0, ub=Inf)
gen <- pinvd.new(distr)
x <- ur(gen, 100)
x <- uq(gen, (1:9)/10)

## Analogous for a generalized hyperbolic distribution
distr <- udghyp(lambda=-1.0024, alpha=39.6, beta=4.14, delta=0.0118, mu=-0.000158)
gen <- pinvd.new(distr)
x <- ur(gen, 100)
x <- uq(gen, (1:9)/10)

## It is also possible to compute density or distribution functions.
## However, this might not work for all generator objects.
##    Density
x <- ud(gen, 1.2)
##    Cumulative distribution function
x <- up(gen, 1.2)