law0025.Stable {PoweR} | R Documentation |
The Stable Distribution
Description
Random generation for the Stable distribution with parameters stability
, skewness
, scale
and location
.
This generator is called by function gensample
to create random variables based on its parameters.
Details
If stability
, skewness
, scale
and location
are not specified they assume the default values of 2, 0, 1 and 0, respectively.
The Stable distribution with parameters stability =
\alpha
,
skewness =
\beta
, scale =
c
and location =
\mu
doesn't have an analytically expressible probability density function, except for some parameter values.
The parameters have conditions : 0 < \alpha \le 2
, -1 \le \beta \le 1
and c > 0
.
The mean of Stable distribution is defined \mu
when \alpha > 1
, otherwise undefined.
The variance of Stable distribution is defined 2 c^2
when \alpha = 2
, otherwise infinite.
Author(s)
P. Lafaye de Micheaux, V. A. Tran
References
Pierre Lafaye de Micheaux, Viet Anh Tran (2016). PoweR: A Reproducible Research Tool to Ease Monte Carlo Power Simulation Studies for Studies for Goodness-of-fit Tests in R. Journal of Statistical Software, 69(3), 1–42. doi:10.18637/jss.v069.i03
See Also
See Distributions
for other standard distributions.
Examples
res <- gensample(25,10000,law.pars=c(2,1,1,2))
res$law
res$law.pars
mean(res$sample)
sd(res$sample)