urlomax {Runuran} | R Documentation |
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. |
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
).
Note
This function is a wrapper for the UNU.RAN class in R.
Author(s)
Josef Leydold and Wolfgang H\"ormann unuran@statmath.wu.ac.at.
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)