Runuran (version 0.40)

urlomax: UNU.RAN Lomax random variate generator

Description

UNU.RAN random variate generator for the Lomax distribution (Pareto distribution of second kind) with shape parameter shape and scale parameter scale. It also allows sampling from the truncated distribution.

[Special Generator] -- Sampling Function: Lomax.

Usage

urlomax(n, shape, scale=1, lb=0, ub=Inf)

Arguments

n

size of required sample.

shape

(strictly positive) shape parameter.

scale

(strictly positive) scale parameter.

lb

lower bound of (truncated) distribution.

ub

upper bound of (truncated) distribution.

Author

Josef Leydold and Wolfgang H\"ormann .

Details

If scale is omitted, it assumes the default value of 1.

The Lomax distribution with parameters shape \(=\alpha\) and scale \(=\sigma\) has density $$ f(x) = \alpha \sigma^\alpha (x+\sigma)^{-(\alpha+1)} $$ for \(x \ge 0\), \(\alpha > 0\) and \(\sigma > 0\).

The generation algorithm uses fast numerical inversion. The parameters lb and ub can be used to generate variates from the Lomax 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.575.

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 <- urlomax(n=1000,shape=2)