urtriang: UNU.RAN Triangular random variate generator
Description
UNU.RAN random variate generator for the Triangular distribution with
shape parameters a, m and b.
It also allows sampling from the truncated distribution.
[Special Generator] -- Sampling Function: Triangular.
Usage
urtriang(n, a, m, b, lb=a, ub=b)
Arguments
n
size of required sample.
a,b
left and right boundary of domain
m
mode of distribution
lb
lower bound of (truncated) distribution.
ub
upper bound of (truncated) distribution.
Details
The Triangular distribution with domain $(a,b)$ and mode $m$
has a density proportional to
$$f(x) \sim (x-a)/(m-a)$$
for $a \le x \le m$, and
$$f(x) \sim (b-x)/(b-m)$$
for $m \le x \le b$.
The generation algorithm uses fast numerical inversion. The parameters
lb and ub can be used to generate variates from
the Triangular 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
See Also
runif and .Random.seed about random number
generation and unuran for the UNU.RAN class.