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.TH "Koutrouvelis" 2 " 1 April 1997" "Fractales Group" "Scilab Function"
.so ../sci.an
.SH NAME
Koutrouvelis - Stable Law parameters estimation (Koutrouvelis method)
.sp
Author: Lotfi Belkacem
.sp
This routine estimates parameters of a \fIstable law\fP using the \fIKoutrouvelis\fP (1985) method.
.sp
.sp
.SH Usage
\f(CR[\fPalpha,beta,mu,gamma\f(CR]\fP=Koutrouvelis(data)
.SH Input parameters
.RS
.TP
o
\fBproc\fP : real vector \f(CR[\fPsize,1\f(CR]\fP
corresponding to the data sample.
.RE
.SH Output 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.
.RE
.SH Example
\f(CR[\fPproc1,inc1\f(CR]\fP=sim_stable(1,0,0,1,10000);
generates a standard 1-stable motion (Cauchy process).
\f(CR[\fPalpha,beta,mu,gamma\f(CR]\fP=Koutrouvelis(inc1);
estimates parameters of the previous simutated 1-stable random variable inc1.
.SH Remarque
Skewness and location parameters are badly estimated with this methode.
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