Runuran (version 0.40)

udlomax: UNU.RAN object for Lomax distribution

Description

Create UNU.RAN object for a Lomax distribution (Pareto distribution of second kind) with shape parameter shape and scale parameter scale.

[Distribution] -- Lomax (Pareto of second kind).

Usage

udlomax(shape, scale=1, lb=0, ub=Inf)

Value

An object of class "unuran.cont".

Arguments

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

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 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. 575.

See Also

unuran.cont.

Examples

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