rstable {CircStats} | R Documentation |
Random Generator for Stable Family of Distributions
Description
Returns random deviates from the stable family of probability distributions.
Usage
rstable(n, scale = 1, index = stop("no index arg"), skewness = 0)
Arguments
n |
sample size |
index |
number from the interval (0, 2]. An index of 2 corresponds to the normal, 1 to the Cauchy. Smaller values mean longer tails. |
skewness |
number giving the modified skewness (see Chambers et al., 1976). Negative values correspond to skewness to the left (the median is smaller than the mean, if it exists), and positive values correspond to skewness to the right (the median is larger than the mean). The absolute value of skewness should not exceed 1. |
scale |
the scale of the distribution. |
Details
This function returns a random variate from the Levy skew stable
distribution with index
=,
scale
= and
skewness
=. The
skewness
parameter must lie in the range [-1,1] while the index
parameter must lie in the range (0,2]. The Levy skew stable probability distribution is defined by a fourier transform,
When the term
is replaced by
. For
the distribution reduces to a Gaussian distribution with
and the skewness parameter has no effect. For
the tails of the distribution become extremely
wide. The symmetric distribution corresponds to
.
The Levy alpha-stable distributions have the property that if alpha-stable variates are drawn from the distribution
then the sum $Y = X_1 + X_2 + ... + X_N$ will also be distributed as an alpha-stable variate,
.
There is no explicit solution for the form of and there are no density, probability or quantile functions supplied for this distribution.
Value
random sample from the specified stable distribution.
References
Chambers, J. M., Mallows, C. L. and Stuck, B. W. (1976). A Method for Simulating Stable Random Variables. Journal of the American Statistical Association 71, 340-344.
Lo\"gae\"ve, M. (1977). Probability Theory I. (fourth edition) Springer-Verlag, New York.
See Also
Examples
hist(rstable(200, 1.5, .5)) #fairly long tails, skewed right