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.TH "stable_test" 2 " 1 April 1997" "Fractales Group" "Scilab Function"
.so ../sci.an
.SH NAME
stable_test - stable law conformicy test
.sp
Author: Lotfi Belkacem
.sp
This routine tests the \fIstability property\fP of a signal.
.sp
.sp
.SH Usage
\f(CR[\fPparam,sd_param\f(CR]\fP=stable_test(maxr,data)
.SH Input parameters
.RS
.TP
o
\fBmaxr\fP : integer positive scalar.
maximum resolution witch depend on the size of the sample.
.TP
o
\fBdata\fP : real vector \f(CR[\fPsize,1\f(CR]\fP
corresponding to the data sample (increments of the signal).
.RE
.SH Output parameters
.RS
.TP
o
\fBparam\fP : real matrix \f(CR[\fPmaxr,4\f(CR]\fP
corresponding to the four estimated parameters of the fited stable law at each level of resolution.
param(i,:), for i=1, ...maxr, gives respectively alpha(characteristic exponent), beta (skewness parameter), mu (location parameter), gamma (scale parameter) estimated at the resolution i.
.TP
o
\fBsd_param\fP : real matrix \f(CR[\fPmaxr,4\f(CR]\fP
corresponding to the estimated standard deviations of the four previous parameters at each level of resolution.
sd_param(i,:), for i=1, ...maxr, gives respectively standard deviation of alpha, beta, mu and gamma estimated at the resolution i.
.RE
.SH Description
The stability test consists on estimating parameters of a fited alpha-satble law at different level of resolution. the variable is said to be stable if the charateristic exponent alpha remains approximatively constant at different resolution, and the scale parameter follows a scaling law with exponent (1/alpha)-1. .SH Example
under scilab type:
\f(CR[\fPproc1_5,inc1_5\f(CR]\fP=sim_stable(1.5,0,0,1,20000);
\f(CR[\fPparam,sd_param\f(CR]\fP=stable_test(7,inc1_5);
alpha=param(:,1);
m=(1:7)';
lnm=log(m);
plot2d(m,alpha,1,'111','alpha',\f(CR[\fP1,0,7,2\f(CR]\fP);
gamma=param(:,4);
lngamma=log(gamma);
plot(lnm,lngamma);
\f(CR[\fPa,b,sig\f(CR]\fP=reglin(lnm',lngamma');
slope=a
th_slope=1/1.5-1
.RS
.TP
o
we generate a standard 1.5-stable motion and its increments.
.TP
o
we test the stability property of the previous simutated 1.5-stable random variable "inc1_5" at 7 resolutions.
.TP
o
we list estimated alpha at different scales.
.TP
o
we visualize the stability of the shape parameter alpha.
.TP
o
we list estimated gamma at different scales.
.TP
o
we visualize the scaling law of the scale parameter gamma with a log-log plot in the space (scale,scale parameter).
.TP
o
we compute the slope "a" of the fited line which will be compared to (1/alpha-1).
.RE
.SH
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