PoweR (version 1.0.7)

law0025.Stable: 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.

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

# NOT RUN {
res <- gensample(25,10000,law.pars=c(2,1,1,2))
res$law
res$law.pars
mean(res$sample)
sd(res$sample)
# }