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.TH "sim_stable" 2 " 1 April 1997" "Fractales Group" "Scilab Function"
.so ../sci.an
.SH NAME
sim_stable - Generation of stable random processes
.sp
Author: Lotfi Belkacem
.sp
This routine generates a \fIstable random process\fP and its \fIincrements\fP using the Chambers, Mallows and Stuck (1976) algorithm.
.sp
.sp
.SH Usage
\f(CR[\fPproc,inc\f(CR]\fP=sim_stable(alpha,beta,mu,gamma,size)
.SH Input parameters
.RS
.TP
o
\fBalpha\fP : real positive scalar between 0 and 2.
This parameter is often referred to as the characteristic exponent.
.TP
o
\fBbeta\fP : real scalar between -1 and +1.
This parameter is often referred to as the skewness parameter.
.TP
o
\fBmu\fP : real scalar
This parameter is often referred to as the location parameter.
It is equal to the expectation when alpha is greater than 1.
.TP
o
\fBgamma\fP : 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.
.TP
o
\fBsize\fP : integer positive scalar.
size of the simulated sample.
.RE
.SH Output parameters
.RS
.TP
o
\fBproc\fP : real vector \f(CR[\fPsize,1\f(CR]\fP
corresponding to the stable random process.
.TP
o
\fBinc\fP : real vector \f(CR[\fPsize,1\f(CR]\fP
corresponding to the increments of the simulated process.
.RE
.SH Examples
.SH Example 1
\f(CR[\fPproc,inc\f(CR]\fP=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 visualize the process or the increments use plot(proc) or plot(inc).
.SH Example 2
\f(CR[\fPproc,inc\f(CR]\fP=sim_stable(1.5,0,0,1,5000);
generates a standard 1.5-stable motion
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