udpareto {Runuran} | R Documentation |
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)
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. |
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
).
Value
An object of class "unuran.cont"
.
Author(s)
Josef Leydold and Wolfgang H\"ormann unuran@statmath.wu.ac.at.
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
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)