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sim_stable(2) Scilab Function sim_stable(2)
NAME
sim_stable - Generation of stable random processes
Author: Lotfi Belkacem
This routine generates a stable random process and its increments using the
Chambers, Mallows and Stuck (1976) algorithm.
Usage
[proc,inc]=sim_stable(alpha,beta,mu,gamma,size)
Input parameters
o alpha : real positive scalar between 0 and 2. This parameter is
often referred to as the characteristic exponent.
o beta : real scalar between -1 and +1. This parameter is often
referred to as the skewness parameter.
o mu : real scalar This parameter is often referred to as the location
parameter. It is equal to the expectation when alpha is greater
than 1.
o gamma : real positive scalar. This parameter is often referred to as
the scale parameter. It is equal to the standard deviation over two
squared when alpha equal 2.
o size : integer positive scalar. size of the simulated sample.
Output parameters
o proc : real vector [size,1] corresponding to the stable random pro-
cess.
o inc : real vector [size,1] corresponding to the increments of the
simulated process.
Examples
Example 1
[proc,inc]=sim_stable(2,0,0,1.4142136,5000); generates a standard stable
random process with alpha=2, beta=0 (symmetric), mu=0 and gamma=1.4142
which coinside with a standard gaussian process (Brownian motion). To visu-
alize the process or the increments use plot(proc) or plot(inc).
Example 2
[proc,inc]=sim_stable(1.5,0,0,1,5000); generates a standard 1.5-stable
motion
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