rpstable: Simulating positive stable random variable.

In mixSSG: Clustering Using Mixtures of Sub Gaussian Stable Distributions

Simulating positive stable random variable.

Description

The cumulative distribution function of positive stable distribution is given by

F_{P}(x)=\frac{1}{π}\int_{0}^{π}\exp\Bigl\{-x^{-\frac{α}{2-α}}a(θ)\Bigr\}dθ,

where 0<α ≤q 2 is tail thickness or index of stability and

a(θ)=\frac{\sin\Bigl(\bigl(1-\frac{α}{2}\bigr)θ\Bigr)\Bigl[\sin \bigl(\frac{α θ}{2}\bigr)\Bigr]^{\frac{α}{2-α}}}{[\sin(θ)]^{\frac{2}{2-α}}}.

Kanter (1975) used the above integral transform to simulate positive stable random variable as

P\mathop=\limits^d\Bigl( \frac{a(θ)}{W} \Bigr)^{\frac{2-α}{α}},

in which θ\sim U(0,π) and W independently follows an exponential distribution with mean unity.

Usage

rpstable(n, alpha)

Arguments

n	the number of samples required.
alpha	the tail thickness parameter.

Value

simulated realizations of size n from positive α-stable distribution.

Author(s)

Mahdi Teimouri

References

M. Kanter, 1975. Stable densities under change of scale and total variation inequalities, Annals of Probability, 3(4), 697-707.

Examples

 rpstable(10, alpha = 1.2) 

mixSSG documentation built on Sept. 11, 2022, 5:06 p.m.