Runuran (version 0.40)

urpareto: UNU.RAN Pareto random variate generator

Description

UNU.RAN random variate generator for the Pareto distribution (of first kind) with shape parameters k and a. It also allows sampling from the truncated distribution.

[Special Generator] -- Sampling Function: Pareto (of first kind).

Usage

urpareto(n, k, a, lb=k, ub=Inf)

Arguments

n

size of required sample.

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 generation algorithm uses fast numerical inversion. The parameters lb and ub can be used to generate variates from the Pareto distribution truncated to the interval (lb,ub).

References

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

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

runif and .Random.seed about random number generation and unuran for the UNU.RAN class.

Examples

## Create a sample of size 1000
x <- urpareto(n=1000,k=2,a=3)