Runuran (version 0.40)

udpareto: UNU.RAN object for Pareto distribution

Description

Create UNU.RAN object for a Pareto distribution (of first kind) with shape parameters k and a.

[Distribution] -- Pareto (of first kind).

Usage

udpareto(k, a, lb=k, ub=Inf)

Value

An object of class "unuran.cont".

Arguments

k

(strictly positive) shape and location parameter.

a

(strictly positive) shape parameter.

lb

lower bound of (truncated) distribution.

ub

upper bound of (truncated) distribution.

Author

Josef Leydold and Wolfgang H\"ormann .

Details

The Pareto distribution with parameters k and a has density $$ f(x) = a k^a x^{-(a+1)} $$ for \(x \ge k\), \(k> 0\) and \(a>0\).

The domain of the distribution can be truncated to the interval (lb,ub).

References

N.L. Johnson, S. Kotz, and N. Balakrishnan (1994): Continuous Univariate Distributions, Volume 1. 2nd edition, John Wiley & Sons, Inc., New York. Chap. 20, p. 574.

See Also

unuran.cont.

Examples

## Create distribution object for Pareto distribution
distr <- udpareto(k=3,a=2)
## Generate generator object; use method PINV (inversion)
gen <- pinvd.new(distr)
## Draw a sample of size 100
x <- ur(gen,100)