udgamma {Runuran} | R Documentation |
UNU.RAN object for Gamma distribution
Description
Create UNU.RAN object for a Gamma distribution
with parameters shape
and scale
.
[Distribution] – Gamma.
Usage
udgamma(shape, scale=1, lb=0, ub=Inf)
Arguments
shape |
(strictly positive) shape parameter. |
scale |
(strictly positive) scale parameter. |
lb |
lower bound of (truncated) distribution |
ub |
upper bound of (truncated) distribution |
Details
The Gamma distribution with parameters shape
=\alpha
and scale
=\sigma
has density
f(x) = \frac{1}{{\sigma}^{\alpha}\Gamma(\alpha)} {x}^{\alpha-1} e^{-x/\sigma}
for x \ge 0
, \alpha > 0
and \sigma > 0
.
(Here \Gamma(\alpha)
is the function implemented by R's
gamma()
and defined in its help.)
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. 17, p. 337.
See Also
Examples
## Create distribution object for gamma distribution
distr <- udgamma(shape=4)
## Generate generator object; use method PINV (inversion)
gen <- pinvd.new(distr)
## Draw a sample of size 100
x <- ur(gen,100)