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authorMichaël Baudin <michael.baudin@scilab.org>2009-02-13 11:37:58 +0100
committerMichaël Baudin <michael.baudin@scilab.org>2009-02-13 11:37:58 +0100
commita2ad12e7c446410387c70bf418f098cdd0aae17a (patch)
tree061e411c0158aa4b7e03bb03e16be2893bac0780 /scilab_doc
parent9a172b4b8d17d215ae2af1ab223355105371625d (diff)
downloadscilab-a2ad12e7c446410387c70bf418f098cdd0aae17a.zip
scilab-a2ad12e7c446410387c70bf418f098cdd0aae17a.tar.gz
Draft for Statistics with Scilab
Diffstat (limited to 'scilab_doc')
-rw-r--r--scilab_doc/statisticswithscilab/Makefile34
-rw-r--r--scilab_doc/statisticswithscilab/inscilab.tex340
-rw-r--r--scilab_doc/statisticswithscilab/introduction.sce93
-rw-r--r--scilab_doc/statisticswithscilab/introduction.tex149
-rw-r--r--scilab_doc/statisticswithscilab/introduction_convergencemoments.pngbin0 -> 4537 bytes
-rw-r--r--scilab_doc/statisticswithscilab/introduction_ecdfcomparison.pngbin0 -> 4875 bytes
-rw-r--r--scilab_doc/statisticswithscilab/introduction_ecdfnormal.pngbin0 -> 4147 bytes
-rw-r--r--scilab_doc/statisticswithscilab/missingfeatures.tex10
-rw-r--r--scilab_doc/statisticswithscilab/notes.txt286
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-rw-r--r--scilab_doc/statisticswithscilab/scilabstats.tex112
-rw-r--r--scilab_doc/statisticswithscilab/statisticsscilab.bib175
-rw-r--r--scilab_doc/statisticswithscilab/statstoolboxes.tex23
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diff --git a/scilab_doc/statisticswithscilab/Makefile b/scilab_doc/statisticswithscilab/Makefile
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1#!/bin/sh
2
3RAPPORT = scilabstats
4
5LT = pdflatex
6
7pdf:
8 $(LT) $(RAPPORT)
9 bibtex $(RAPPORT)
10 $(LT) $(RAPPORT)
11 $(LT) $(RAPPORT)
12
13
14dvi:
15 $(LT) ${RAPPORT}
16 bibtex ${RAPPORT}
17 $(LT) ${RAPPORT}
18
19clean:
20 rm -f *.aux
21 rm -f *.bbl
22 rm -f *.blg
23 rm -f *.log
24 rm -f *.out
25 rm -f *.toc
26
27spell:
28 ispell -t ${RAPPORT}.tex
29
30distclean:
31 make clean
32 rm -f ${RAPPORT}.pdf
33 rm -f ${RAPPORT}.dvi
34
diff --git a/scilab_doc/statisticswithscilab/inscilab.tex b/scilab_doc/statisticswithscilab/inscilab.tex
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1\chapter{Scilab statistical features}
2
3In this chapter, we describe the features which are provided
4in Scilab's core, that is, "out of the box".
5Indeed, Scilab provide features such as general statistical
6description of datas, many cumulated density functions
7and can generate uniform and non uniform random variates.
8These features are based on several open source libraries, that
9we are analysing in the first section.
10A complete overview of these features is provided in the
11second section, where we analyse the full list of functions and
12the numerical methods they use. For the most important
13functions, we provide a sample session where the function is
14used and some plots of the results.
15
16\section{The sources}
17
18In this section, we analyse the libraries which are available
19in Scilab and which provide its statistical features.
20The figure \ref{inscilab-libraries} is an overview of the
21libraries which are either Scilab macros or source code, provided
22in C, Fortran 77 or as Scilab macros.
23
24\begin{figure}[htbp]
25\begin{tabular}{|l|l|}
26\hline
27Commands & calerf, erf, erfc, erfcx \\
28Routines & CALERF\\
29Directory & scilab/modules/elementary\_functions/src/fortran\\
30Language & Fortran\\
31Download & \url{http://www.kurims.kyoto-u.ac.jp/~ooura/index.html} \\
32Author & Takuya Ooura \\
33Year & 1996 \\
34References & \cite{Algorithm715} \\
35\hline
36\hline
37Name & Labostat \\
38Directory & scilab/modules/elementary\_functions/src/fortran\\
39Commands & General description functions (center, variance, etc...) \\
40Language & Scilab scripts \\
41Author & Carlos Klimann \\
42Year & 2000 \\
43References & \cite{Wonacott1990}, \cite{Saporta2006}\\
44\hline
45\hline
46Name & DCDFLIB \\
47Directory & scilab/modules/statistics/src/dcdflib\\
48Download & \url{http://www.netlib.org/random/}\\
49Commands & Cumulated Density Functions (cdfbet, cdfbin, etc...) \\
50Language & Fortran \\
51Author & Barry Brown, W. J. Cody, Alfred H. Morris Jr \\
52Year & 1994 for library, 1992 for code by Cody, 1991 for code by Morris \\
53References & \cite{abramowitz+stegun1964}, \cite{HartEtAl:1968}, \cite{Algorithm715}, \cite{Kennedy1980}
54\cite{Algo708}, \cite{DiDonato1986}\\
55\hline
56\hline
57Name & Randlib \\
58Directory & scilab/modules/randlib/src/fortran\\
59Download & \url{ftp://odin.mda.uth.tmc.edu/pub/source}\\
60& (unavailable at the time of the writing of this report)\\
61Commands & grand (for distributions like normal, gamma, chi, etc...) \\
62Language & Fortran \\
63Author & Barry Brown, James Lovato, Kathy Russell, John Venier \\
64Year & 1997 \\
65References & \cite{Ahrens1972}, \cite{358390}, \cite{Devroye86non-uniformrandom},
66\cite{AhrensDieter1973}\\
67\hline
68\end{tabular}
69\caption{Statistical libraries available in Scilab}
70\label{inscilab-libraries}
71\end{figure}
72
73
74\section{Overview of functions}
75
76The figure \ref{inscilab-fulllist} presents a complete list
77of Scilab statistical functions.
78
79\begin{figure}[htbp]
80\begin{tabular}{|l|l|}
81\hline
82\textbf{Description} & \\
83\textbf{of Data} & \\
84\hline
85center & cmoment \\
86correl & covar \\
87ftest & ftuneq \\
88geomean & harmean \\
89iqr & labostat \\
90mad & mean \\
91meanf & median \\
92moment & msd \\
93mvvacov & nancumsum \\
94nand2mean & nanmax \\
95nanmean & nanmeanf \\
96nanmedian & nanmin \\
97nanstdev & nansum \\
98nfreq & pca \\
99perctl & princomp \\
100quart & regress \\
101sample & samplef \\
102samwr & show\_pca \\
103st\_deviation & stdevf \\
104strange & tabul \\
105thrownan & trimmean \\
106variance & variancef \\
107wcenter & \\
108\hline
109\end{tabular}
110\begin{tabular}{|l|l|}
111\hline
112\textbf{Special} & \\
113\textbf{Functions} & \\
114\hline
115beta & calerf \\
116erf & erfc \\
117erfcx & erfinv \\
118gamma & gammaln \\
119\hline
120\hline
121\textbf{Random} &\\
122\textbf{Number} &\\
123\textbf{Generation} &\\
124\hline
125grand & prbs\_a \\
126rand & sprand \\
127randpencil &\\
128\hline
129\hline
130\textbf{Cumulated} &\\
131\textbf{Density} &\\
132\textbf{Functions} &\\
133\hline
134cdfbet & cdfbin \\
135cdfchi & cdfchn \\
136cdff & cdffnc \\
137cdfgam & cdfnbn \\
138cdfnor & cdfpoi \\
139cdft & \\
140\hline
141\end{tabular}
142\caption{Complete list of statistical features in Scilab}
143\label{inscilab-fulllist}
144\end{figure}
145
146\subsection{General description functions}
147
148The figure \ref{inscilab-descriptionfunctions} presents the
149general description functions available in Scilab.
150
151\begin{figure}[htbp]
152\begin{tabular}{|l|l|}
153\hline
154Name & Feature\\
155\hline
156center & center \\
157wcenter & center and weight \\
158cmoment & central moments of all orders \\
159correl & correlation of two variables \\
160covar & covariance of two variables \\
161ftest & Fischer ratio \\
162ftuneq & Fischer ratio for samples of unequal size. \\
163geomean & geometric mean \\
164harmean & harmonic mean \\
165iqr & interquartile range \\
166mad & mean absolute deviation \\
167mean & mean (row mean, column mean) of vector/matrix entries \\
168meanf & weighted mean of a vector or a matrix \\
169median & median (row median, column median,...) of vector/matrix/array entries \\
170moment & non central moments of all orders \\
171msd & mean squared deviation \\
172mvvacov & computes variance-covariance matrix \\
173nancumsum & cumulative sum of the values of a matrix \\
174nand2mean & difference of the means of two independent samples \\
175nanmax & max (ignoring Nan's) \\
176nanmean & mean (ignoring Nan's) \\
177nanmeanf & mean (ignoring Nan's) with a given frequency. \\
178nanmedian & median of the values of a numerical vector or matrix \\
179nanmin & min (ignoring Nan's) \\
180nanstdev & standard deviation (ignoring the Nans). \\
181nansum & sum of values ignoring Nan's \\
182nfreq & frequence of the values in a vector or matrix \\
183pca & computes principal components analysis with standardized variables \\
184perctl & computation of percentils \\
185princomp & Principal components analysis \\
186quart & computation of quartiles \\
187regress & regression coefficients of two variables \\
188sample & sampling with replacement \\
189samplef & sample with replacement from a population and frequences of his values. \\
190samwr & sampling without replacement \\
191show\_pca & visualization of principal components analysis results \\
192st\_deviation & standard deviation (row or column-wise) of vector/matrix entries \\
193stdevf & standard deviation \\
194strange & range \\
195tabul & frequency of values of a matrix or vector \\
196thrownan & eliminates nan values \\
197trimmean & trimmed mean of a vector or a matrix \\
198variance & variance of the values of a vector or matrix \\
199variancef & standard deviation of the values of a vector or matrix \\
200\hline
201\end{tabular}
202\caption{Description of Data functions}
203\label{inscilab-descriptionfunctions}
204\end{figure}
205
206\subsection{Special functions}
207
208The figure \ref{inscilab-specialfunctions} presents the special functions
209available in Scilab.
210
211\begin{figure}[htbp]
212\begin{tabular}{|l|l|}
213\hline
214Name & Feature\\
215\hline
216beta & beta function \\
217calerf & computes error functions \\
218erf & error function \\
219erfc & complementary error function \\
220erfcx & scaled complementary error function \\
221erfinv & inverse of the error function \\
222gamma & gamma function \\
223gammaln & logarithm of gamma function \\
224\hline
225\end{tabular}
226\caption{Special functions}
227\label{inscilab-specialfunctions}
228\end{figure}
229
230The figure \ref{inscilab-specialfunctionsdetailed} presents
231a detailed analysis of the location and internal design
232of the special functions available in Scilab.
233
234\begin{figure}[htbp]
235\begin{tabular}{|l|l|}
236\hline
237Name & Location / Internals \\
238\hline
239beta & modules/special\_functions/sci\_gateway/c/sci\_beta.c \\
240& switch to dgammacody by W. J. Cody and \\
241& L. Stoltz and to betaln from DCDFLIB \\
242\hline
243calerf & modules/elementary\_functions/src/fortran \\
244& by Takuya OOURA \\
245\hline
246erf & modules/elementary\_functions/macros/erf.sci \\
247& call to calerf \\
248\hline
249erfc & modules/elementary\_functions/macros/erfc.sci \\
250& call to calerf \\
251\hline
252erfcx & modules/elementary\_functions/macros/erfcx.sci \\
253& call to calerf \\
254\hline
255erfinv & modules/special\_functions/macros/erfinv.sci \\
256& rational aproximation of erfinv + 2 Newton's steps\\
257\hline
258gamma & modules/special\_functions/sci\_gateway/fortran/sci\_f\_gamma.f \\
259& based on dgammacody by W. J. Cody and L. Stoltz \\
260\hline
261gammaln & modules/elementary\_functions/src/fortran/dlgama.f \\
262& by W. J. Cody and L. Stoltz \\
263\hline
264\end{tabular}
265\caption{Detailed analysis of special functions}
266\label{inscilab-specialfunctionsdetailed}
267\end{figure}
268
269\subsection{Cumulated density functions}
270
271The figure \ref{inscilab-cdffunctions} presents the cumulated
272density functions available in Scilab.
273
274\begin{figure}[htbp]
275\begin{tabular}{|l|l|}
276\hline
277Name & Feature\\
278\hline
279cdfbet & Beta distribution \\
280cdfbin & Binomial distribution \\
281cdfchi & chi-square distribution \\
282cdfchn & non-central chi-square distribution \\
283cdff & F distribution \\
284cdffnc & non-central F distribution \\
285cdfgam & gamma distribution \\
286cdfnbn & negative binomial distribution \\
287cdfnor & normal distribution \\
288cdfpoi & poisson distribution \\
289cdft & Student's T distribution\\
290\hline
291\end{tabular}
292\caption{Cumulated density functions}
293\label{inscilab-cdffunctions}
294\end{figure}
295
296
297\subsection{Random number generation}
298
299The figure \ref{inscilab-randomnumbercommands} presents the random
300number generators available in Scilab.
301
302\begin{figure}[htbp]
303\begin{tabular}{|l|l|}
304\hline
305Name & Feature\\
306\hline
307grand & Random number generators \\
308prbs\_a & pseudo random binary sequences generation \\
309rand & random number generator \\
310sprand & sparse random matrix \\
311randpencil & random pencil \\
312\hline
313\end{tabular}
314\caption{Random number commands}
315\label{inscilab-randomnumbercommands}
316\end{figure}
317
318The figure \ref{inscilab-randomnumbercommands} presents a detailed
319analysis of the location and design of the random
320number generators available in Scilab.
321
322\begin{figure}[htbp]
323\begin{tabular}{|l|l|}
324\hline
325Name & Location / Internals \\
326\hline
327grand & modules/randlib/sci\_gateway/c/sci\_grand.c \\
328& based on several random number generators\\
329prbs\_a & modules/cacsd/macros/prbs\_a.sci \\
330& based on rand \\
331rand & modules/elementary\_functions/src/fortran/urand.f \\
332& by Michael A. Malcolm And Cleve B. Moler \\
333sprand & (todo)\\
334randpencil & (todo)\\
335\hline
336\end{tabular}
337\caption{Detailed analysis of random number commands}
338\label{inscilab-detailrandomnumbercommands}
339\end{figure}
340
diff --git a/scilab_doc/statisticswithscilab/introduction.sce b/scilab_doc/statisticswithscilab/introduction.sce
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1// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
2// Copyright (C) 2008 - INRIA - Michael Baudin
3//
4// This file must be used under the terms of the CeCILL.
5// This source file is licensed as described in the file COPYING, which
6// you should have received as part of this distribution. The terms
7// are also available at
8// http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
9//
10// introduction.sce --
11// The scripts used in the introduction chapter of "Scilab and Statistics".
12//
13//
14// Empirical Cumulated Density Function of Normal Law with 200 samples
15//
16N=200;
17x = rand(1,N,"normal");
18Xsorted =gsort(x,"g","i");
19Ydata = (1:N)/N;
20plot(Xsorted,Ydata);
21f=gcf();
22f.children.title.text="Empirical Cumulated Density Function of Normal Law";
23compound=f.children.children(1);
24h1=captions(compound.children,"rand() with Polar method");
25h1.legend_location="in_upper_left";
26nbplots = 1;
27for i = 1:nbplots
28 mypoly = f.children.children(2).children(i);
29 mypoly.thickness=2;
30 mypoly.mark_size=2;
31 mypoly.mark_size_unit="tabulated";
32end
33filename = "introduction_ecdfnormal.png";
34xs2png(0,filename);
35
36//
37// Empirical Cumulated Density Function of Normal Law with 200 samples
38// Compared with "exact" Cumulated Density Function.
39//
40N=200;
41x = rand(1,N,"normal");
42Xsorted =gsort(x,"g","i");
43Ydata = (1:N)/N;
44x=linspace(-3,3,100);
45P=cdfnor("PQ",x,zeros(x),ones(x));
46plot(Xsorted,Ydata,x,P);
47f=gcf();
48f.children.title.text="Empirical Cumulated Density Function of Normal Law";
49compound=f.children.children(1);
50h1=captions(compound.children,["cdfnor() with Rational Functions","rand() with Polar method"]);
51h1.legend_location="in_upper_left";
52nbplots = 2;
53for i = 1:nbplots
54 mypoly = f.children.children(2).children(i);
55 mypoly.thickness=2;
56 mypoly.mark_size=2;
57 mypoly.mark_size_unit="tabulated";
58end
59filename = "introduction_ecdfcomparison.png";
60xs2png(0,filename);
61
62//
63// Observe convergence of mean and variance as N > infinity
64//
65nbpoints = 5;
66means=zeros(nbpoints,1);
67vars=zeros(nbpoints,1);
68stdevs=zeros(nbpoints,1);
69nlist = 1:nbpoints;
70for i = nlist
71 N=10^i;
72 x = rand(1,N,"normal");
73 means(i) = mean(x);
74 vars(i) = variance(x);
75 stdevs(i) = stdev(x);
76end
77plot(nlist,[means,vars,stdevs]);
78f=gcf();
79f.children.x_label.text="Log - Number of Samples";
80f.children.title.text="Convergence of moments of Normal Law";
81compound=f.children.children(1);
82h1=captions(compound.children,["Standard Deviation","Variance","Mean"]);
83h1.legend_location="in_upper_right";
84nbplots = 3;
85for i = 1:nbplots
86 mypoly = f.children.children(2).children(i);
87 mypoly.thickness=2;
88 mypoly.mark_size=2;
89 mypoly.mark_size_unit="tabulated";
90end
91filename = "introduction_convergencemoments.png";
92xs2png(0,filename);
93
diff --git a/scilab_doc/statisticswithscilab/introduction.tex b/scilab_doc/statisticswithscilab/introduction.tex
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1\chapter{Introduction}
2
3As stated in \cite{scilabstats2001}, Scilab's core provide
4a complete set of features related to simulation and statistical
5computations.
6Indeed, Scilab provide uniform pseudo-random number generators, functions to
7compute the moments of a distribution and a complete set of
8distributions. In this document, we will make a complete
9overview on these features.
10
11It must be noticed, though, that these features
12are not as complete as in other languages, like R for example.
13This is why several toolboxes have developped in order to extend
14the features of Scilab. In this document, we will present two
15major toolboxes, that is the Sci\_R toolbox and the Stix toolbox.
16
17In the last chapter, we will analyse the missing statistical
18features and will analyse how these features are available in other
19tools, such as Matlab, R, or Octave.
20
21\section{A sample session}
22
23A good introduction on the statistical features of Scilab is \cite{scilabintro2007}.
24In the remaining of this introductin chapter, we will try to have
25a flavour of how to perform statistical computations with Scilab.
26We focus on the algorithms which are used inside Scilab, to show what
27exact algorithms perform the computations.
28
29As a first example, we will generate a sequence of numbers from a
30normal law with mean 0 and standard deviation 1 (example inspired and simplified
31from \cite{scilabintro2007}). The probability density function (pdf)
32and the cumulated probability density function of the normal law is
33\begin{eqnarray}
34f(x) &=& \frac{1}{\sqrt{2\pi}} e^{-\frac{t^2}{2}},\\
35P(x) &=& \frac{1}{\sqrt{2\pi}} \int_{-\infty}^x e^{-\frac{t^2}{2}}.
36\end{eqnarray}
37
38The empirical cumulated density function \cite{artcomputerKnuthVol2} of a given
39set of data $\{x_i\}_{i=1,N}$ is given by
40\begin{eqnarray}
41F_N(x) &=& \frac{\textrm{number of } x_1,x_2,\ldots,x_n \textrm{ that are }\leq x}{N}.
42\end{eqnarray}
43
44
45The numerical method used by Scilab to generate such numbers is the Polar
46method for normal deviates, as presented in \cite{artcomputerKnuthVol2}.
47
48\lstset{language=Scilab}
49\lstset{numbers=left}
50\lstset{basicstyle=\footnotesize}
51\lstset{keywordstyle=\color{green}\bfseries}
52\begin{lstlisting}
53N=200;
54x = rand(1,N,"normal");
55Xsorted =gsort(x,"g","i");
56Ydata = (1:N)/N;
57plot(Xsorted,Ydata);
58e=gce();
59e.children.polyline_style=2;
60xtitle("Empirical Cumulated Density Function of Normal Law with 200 samples")
61filename = "introduction_ecdfnormal.png";
62xs2png(0,filename);
63\end{lstlisting}
64
65The empirical cumulated density function
66is presented in figure \ref{introduction_ecdfnormal}.
67
68\begin{figure}[htbp]
69\begin{center}
70\includegraphics[height=10cm]{introduction_ecdfnormal.png}
71\end{center}
72\caption{Empirical Cumulated Density Function of Normal Law with 200 samples}
73\label{introduction_ecdfnormal}
74\end{figure}
75
76To compare the data which is produced by rand with the
77cumulated density function of the normal law, we use the
78\emph{cdfnor} primitive. This primitive is based on \cite{Algorithm715}
79and uses rational functions that theoretically approximate the normal
80distribution function to at least 18 significant decimal digits. The same
81primitive can be used to compute the inverse of the cumulated density
82function. In that case, rational functions are used as starting values to
83Newton's Iterations which compute the inverse standard normal.
84
85\lstset{language=Scilab}
86\lstset{numbers=left}
87\lstset{basicstyle=\footnotesize}
88\lstset{keywordstyle=\color{green}\bfseries}
89\begin{lstlisting}
90N=200;
91x = rand(1,N,"normal");
92Xsorted =gsort(x,"g","i");
93Ydata = (1:N)/N;
94x=linspace(-3,3,100);
95P=cdfnor("PQ",x,zeros(x),ones(x));
96plot(Xsorted,Ydata,x,P);
97\end{lstlisting}
98
99The comparison plot between the empirical cdf and the
100computed cdf is presented in figure \ref{introduction_ecdcomparison}.
101
102\begin{figure}[htbp]
103\begin{center}
104\includegraphics[height=10cm]{introduction_ecdfcomparison.png}
105\end{center}
106\caption{Cumulated Density Function of Normal Law : comparison of cdf from
107rational functions and empirical cdf from Polar method }
108\label{introduction_ecdcomparison}
109\end{figure}
110
111The moments of a distribution can be computed with the
112\emph{mean}, \emph{variance} and \emph{stdev} Scilab macros,
113which are implementations of the moments. For the variance
114and standard deviation, the scaling factor is $N-1$.
115In the following script, one computes these moment for
116an increasing number of samples, from $10^1$ to $10^5$.
117
118\lstset{language=Scilab}
119\lstset{numbers=left}
120\lstset{basicstyle=\footnotesize}
121\lstset{keywordstyle=\color{green}\bfseries}
122\begin{lstlisting}
123nbpoints = 5;
124means=zeros(nbpoints,1);
125vars=zeros(nbpoints,1);
126stdevs=zeros(nbpoints,1);
127nlist = 1:nbpoints;
128for i = nlist
129 N=10^i;
130 x = rand(1,N,"normal");
131 means(i) = mean(x);
132 vars(i) = variance(x);
133 stdevs(i) = stdev(x);
134end
135plot(nlist,[means,vars,stdevs]);
136\end{lstlisting}
137
138The convergence plot of the moments is presented in
139figure \ref{introduction_convergencemoments}.
140
141\begin{figure}[htbp]
142\begin{center}
143\includegraphics[height=10cm]{introduction_convergencemoments.png}
144\end{center}
145\caption{Convergence of the moments of the normal law}
146\label{introduction_convergencemoments}
147\end{figure}
148
149
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1\chapter{Missing features}
2
3\begin{itemize}
4\item Empirical Cumulated Density Function
5\item Robust implementation of variance, standard deviation.
6See in "Art of Computer Programming" \cite{artcomputerKnuthVol2}, chapter 4.2.2, "Accuracy of Floating
7Point Arithmetic", section A or in "Numerical Recipes" \cite{NumericalRecipes},
8chapter 14.1, "Moments of a Distribution: Mean, Variance, Skewness, and so Forth".
9\end{itemize}
10
diff --git a/scilab_doc/statisticswithscilab/notes.txt b/scilab_doc/statisticswithscilab/notes.txt
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@@ -0,0 +1,286 @@
1* Faire le lien entre erf et cdfnor
2
3Voici l'intégralité des fonctionnalités à présenter
4
5XLV. Special Functions
6
7 beta : beta function (modules\special_functions\sci_gateway\c\sci_beta.c : switch to dgammacody by W. J. Cody and L. Stoltz and to betaln from DCDFLIB)
8 calerf : computes error functions (modules\elementary_functions\src/fortran from Takuya OOURA)
9 erf : The error function (modules\elementary_functions\macros\erf.sci with call to calerf)
10 erfc : The complementary error function (modules\elementary_functions\macros\erfc.sci with call to calerf)
11 erfcx : scaled complementary error function (modules\elementary_functions\macros\erfcx.sci with call to calerf)
12 erfinv : The inverse of the error function (modules\special_functions\macros\erfinv.sci)
13 gamma : The gamma function (modules\special_functions\sci_gateway\fortran\sci_f_gamma.f based on dgammacody by W. J. Cody and L. Stoltz)
14 gammaln : The logarithm of gamma function (modules\elementary_functions\src\fortran\dlgama.f by W. J. Cody and L. Stoltz)
15XLVII. Statistics
16
17 cdfbet ? cumulative distribution function Beta distribution
18 cdfbin ? cumulative distribution function Binomial distribution
19 cdfchi ? cumulative distribution function chi-square distribution
20 cdfchn ? cumulative distribution function non-central chi-square distribution
21 cdff ? cumulative distribution function F distribution
22 cdffnc ? cumulative distribution function non-central f-distribution
23 cdfgam ? cumulative distribution function gamma distribution
24 cdfnbn ? cumulative distribution function negative binomial distribution
25 cdfnor ? cumulative distribution function normal distribution
26 cdfpoi ? cumulative distribution function poisson distribution
27 cdft ? cumulative distribution function Student's T distribution
28 center ? center
29 wcenter ? center and weight
30 cmoment ? central moments of all orders
31 correl ? correlation of two variables
32 covar ? covariance of two variables
33 ftest ? Fischer ratio
34 ftuneq ? Fischer ratio for samples of unequal size.
35 geomean ? geometric mean
36 harmean ? harmonic mean
37 iqr ? interquartile range
38 labostat ? Statistical toolbox for Scilab
39 mad ? mean absolute deviation
40 mean ? mean (row mean, column mean) of vector/matrix entries
41 meanf ? weighted mean of a vector or a matrix
42 median ? median (row median, column median,...) of vector/matrix/array entries
43 moment ? non central moments of all orders
44 msd ? mean squared deviation
45 mvvacov ? computes variance-covariance matrix
46 nancumsum ? Thos function returns the cumulative sum of the values of a matrix
47 nand2mean ? difference of the means of two independent samples
48 nanmax ? max (ignoring Nan's)
49 nanmean ? mean (ignoring Nan's)
50 nanmeanf ? mean (ignoring Nan's) with a given frequency.
51 nanmedian ? median of the values of a numerical vector or matrix
52 nanmin ? min (ignoring Nan's)
53 nanstdev ? standard deviation (ignoring the NANs).
54 nansum ? Sum of values ignoring NAN's
55 nfreq ? frequence of the values in a vector or matrix
56 pca ? Computes principal components analysis with standardized variables
57 perctl ? computation of percentils
58 princomp ? Principal components analysis
59 quart ? computation of quartiles
60 regress ? regression coefficients of two variables
61 sample ? Sampling with replacement
62 samplef ? sample with replacement from a population and frequences of his values.
63 samwr ? Sampling without replacement
64 show_pca ? Visualization of principal components analysis results
65 st_deviation ? standard deviation (row or column-wise) of vector/matrix entries ? standard deviation (row or column-wise) of vector/matrix entries
66 stdevf ? standard deviation
67 strange ? range
68 tabul ? frequency of values of a matrix or vector
69 thrownan ? eliminates nan values
70 trimmean ? trimmed mean of a vector or a matrix
71 variance ? variance of the values of a vector or matrix
72 variancef ? standard deviation of the values of a vector or matrix
73
74Miscelanous
75
76 grand ? Random number generator(s) (modules\randlib\sci_gateway\c\sci_grand.c based on several random number generators)
77 prbs_a ? pseudo random binary sequences generation (modules\cacsd\macros\prbs_a.sci based on rand)
78 rand ? random number generator (modules\elementary_functions\src\fortran\urand.f BY MICHAEL A. MALCOLM and CLEVE B. MOLER)
79 sprand ? sparse random matrix
80 randpencil ? random pencil
81
82***************************************************
83
84C http://www.kurims.kyoto-u.ac.jp/~ooura/index.html
85C Takuya OOURA, Research Institute for Mathematical Sciences
86C Kyoto University, Kyoto 606-01 Japan
87C e-mail : ooura@kurims.kyoto-u.ac.jp
88
89Directory : scilab\modules\elementary_functions\src\fortran
90Language : Fortran
91Download : http://www.kurims.kyoto-u.ac.jp/~ooura/index.html
92Author : Takuya OOURA
93
94***************************************************
95DCDFLIB
96Language : Fortran
97Directory : scilab\modules\statistics\src\dcdflib
98Download : http://www.netlib.org/random/
99Author : Barry Brown, James Lovato, Kathy Russell
100
101Barry Brown, James Lovato, Kathy Russell,
102Department of Biomathematics,
103University of Texas,
104Houston, Texas.
105
106 DCDFLIB
107
108 Library of Fortran Routines for Cumulative Distribution
109 Functions, Inverses, and Other Parameters
110
111 (February, 1994)
112
113 SUMMARY OF DCDFLIB
114
115This library contains routines to compute cumulative distribution
116functions, inverses, and parameters of the distribution for the
117following set of statistical distributions:
118
119 (1) Beta
120 (2) Binomial
121 (3) Chi-square
122 (4) Noncentral Chi-square
123 (5) F
124 (6) Noncentral F
125 (7) Gamma
126 (8) Negative Binomial
127 (9) Normal
128 (10) Poisson
129 (11) Student's t
130
131Given values of all but one parameter of a distribution, the other is
132computed. These calculations are done with FORTRAN Double Precision
133variables.
134
135
136***************************************************
137
138randlib-1.3
139
140C library routines for Random Number Generation
141Description: Randlib is a large library for random variate generation from many univariate and multivariate distributions. The bottom level routines provide 32 virtual random number generators. Each generator can provide 1,048,576 blocks of numbers, and each block is of length 1,073,741,824. Any generator can be set to the beginning or end of the current block or to its starting value.
142
143
144Directory : D:\Baudin\ProjetScilab\git\scilab\scilab\modules\randlib\src\fortran
145Language : Fortran
146Download : ftp://odin.mda.uth.tmc.edu/pub/source/ (unavailable at the time of the writing of this report)
147Author: Barry Brown, James Lovato, Kathy Russell, John Venier
148
149****************************************************
150Directory : D:\Baudin\ProjetScilab\git\scilab\scilab\modules\randlib\src\c
151Language : C
152Download : "My offer of RNG's for C was an invitation to dance"
153http://groups.google.com/group/sci.crypt/msg/eb4ddde782b17051?pli=1
154Author : G. Marsaglia
155
156Kiss
157
158 * the kiss generator of G. Marsaglia
159 * generate random integers (uint) in [0, 2^32 - 1]
160 * the state is given by 4 integers (z, w, jsr, jcong)
161 *
162 * NOTES
163 * The code was given by G. Marsaglia at the end of a
164 * thread concerning RNG in C in several newsgroups
165 * (whom sci.math.num-analysis) "My offer of RNG's for
166 * C was an invitation to dance..."
167 *
168 * Slight modifications by Bruno Pincon for inclusion in
169 * Scilab (added set/get state routines)
170 *
171 * kiss is made of combinaison of severals others but
172 * they are not interfaced at the scilab level.
173 *
174 * Need that it is assumed that the
175 * unsigned long arithmetic is the classic 32 bits
176 * unsigned arithmetic modulo 2^32 (ie all is exact
177 * modulo 2^32)
178****************************************************
179clcg2
180Directory : D:\Baudin\ProjetScilab\git\scilab\scilab\modules\randlib\src\c
181Language : C
182Download : ?
183Author : Luc Devroye
184
185 * PURPOSE
186 * uniform random number generator developed by Pierre
187 * Lecuyer based on a clever and tested combination of
188 * two linear congruential sequences
189 *
190 * s1 <- a1*s1 mod m1 , a1 = 40014, m1 = 2147483563
191 * s2 <- a2*s2 mod m2 , a2 = 40692, m2 = 2147483399
192 *
193 * output <- s1-s2 mod (m1 - 1)
194 *
195 * so output is in [0, 2147483561], period about 2.3 10^18
196 *
197 * The state is given by (s1, s2). In case of a user
198 * modification of the state we must have :
199 *
200 * s1 in [1, m1-1]
201 * s2 in [1, m2-1]
202 *
203 * ORIGIN
204 * The basic code is provided at the Luc Devroye 's home page.
205 * Modifications by Bruno Pincon (in particular added routines
206 * to set and get the state, and modify the generator to get
207 * exactly s1-s2 mod (m1 - 1) for "coherence" with the others
208 * generators : provides numbers in [0, MaxRngInt(generator)]
209 * (see NOTE some lines after)
210
211@article{Ecuyer1988,
212 author = {L'Ecuyer,, P.},
213 title = {Efficient and portable combined random number generators},
214 journal = {Commun. ACM},
215 volume = {31},
216 number = {6},
217 year = {1988},
218 issn = {0001-0782},
219 pages = {742--751},
220 doi = {http://doi.acm.org/10.1145/62959.62969},
221 publisher = {ACM},
222 address = {New York, NY, USA},
223 }
224
225****************************************************
226clcg4
227Directory : D:\Baudin\ProjetScilab\git\scilab\scilab\modules\randlib\src\c
228Language : C
229Download : http://www.iro.umontreal.ca/~lecuyer/myftp/papers/
230Author : L'Ecuyer and Andres
231
232 * clcg4 generator stuff
233 *
234 * AUTHORS
235 * The following code is from L'Ecuyer and Andres "A Randow Number based
236 * on the combinaison of Four LCG" (distributed at the Pierre L'Ecuyer
237 * home page with a corresponding paper).
238****************************************************
239FSULTRA
240Directory : D:\Baudin\ProjetScilab\git\scilab\scilab\modules\randlib\src\c
241Download : http://archives.math.utk.edu/software/msdos/miscellaneous/fsultra1/
242Language : C
243Authors : Arif Zaman and George Marsaglia
244
245FSU - ULTRA The greatest random number generator that ever was
246 or ever will be. Way beyond Super-Duper.
247 (Just kidding, but we think its a good one.)
248
249Authors: Arif Zaman (arif@stat.fsu.edu) and
250 George Marsaglia (geo@stat.fsu.edu).
251
252Date: 27 May 1992
253
254Version: 1.05
255
256Copyright: To obtain permission to incorporate this program into
257 any commercial product, please contact the authors at
258 the e-mail address given above or at
259
260 Department of Statistics and
261 Supercomputer Computations Research Institute
262 Florida State University
263 Tallahassee, FL 32306.
264
265See Also: README for a brief description
266 ULTRA.DOC for a detailed description
267
268
269 File: ULTRA.C
270
271 This is the ULTRA random number generator written entirely in C.
272
273 This may serve as a model for an assembler version of this routine.
274 The programmer should avoid simply duplicating and instead use the
275 usual assembler features to increase the speed of this routine.
276
277 Especially the subroutine SWB should be replaced by the one
278 machine instruction (usually called subtract-with-borrow) that
279 is available in almost every hardware.
280
281 For people not familiar with 8086 assembler, it may help to
282 consult this when reading the assembler code. This program should
283 be a dropin replacement for the assembler versions, but is about
284 half as fast.
285
286
diff --git a/scilab_doc/statisticswithscilab/scilabstats.pdf b/scilab_doc/statisticswithscilab/scilabstats.pdf
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1%
2% scilabstats.tex --
3% Some notes about Scilab statistical features in Scilab.
4%
5% Copyright 2008 Michael Baudin
6%
7\documentclass[12pt]{report}
8
9%% Good fonts for PDF
10\usepackage[cyr]{aeguill}
11
12%% Package for page headers
13\usepackage{fancyhdr}
14
15%% Package to include graphics
16%% Comment for DVI
17\usepackage[pdftex]{graphicx}
18
19%% Figures formats: jpeg or pdf
20%% Comment for DVI
21\DeclareGraphicsExtensions{.jpg,.pdf}
22
23%% Package to create Hyperdocuments
24%% Comment for DVI
25\usepackage[pdftex,colorlinks=true,linkcolor=blue,citecolor=blue,urlcolor=blue]{hyperref}
26
27%% Package to control printed area size
28\usepackage{anysize}
29%% ...by defining margins {left}{right}{top}{bottom}
30\marginsize{22mm}{14mm}{12mm}{25mm}
31
32%% Package used to include a bibliography
33\usepackage{natbib}
34
35%% R for real numbers
36\usepackage{amssymb}
37
38%% User defined commands
39
40\usepackage{url}
41
42% Scilab macros
43\newcommand{\scimacro}[1]{\textit{#1}}
44\newcommand{\scicommand}[1]{\textit{#1}}
45
46% To highlight source code
47\usepackage{listings}
48
49% Define theorem environments
50\newtheorem{theorem}{Theorem}[section]
51\newtheorem{lemma}[theorem]{Lemma}
52\newtheorem{proposition}[theorem]{Proposition}
53\newtheorem{corollary}[theorem]{Corollary}
54
55\newenvironment{proof}[1][Proof]{\begin{trivlist}
56\item[\hskip \labelsep {\bfseries #1}]}{\end{trivlist}}
57\newenvironment{definition}[1][Definition]{\begin{trivlist}
58\item[\hskip \labelsep {\bfseries #1}]}{\end{trivlist}}
59\newenvironment{example}[1][Example]{\begin{trivlist}
60\item[\hskip \labelsep {\bfseries #1}]}{\end{trivlist}}
61\newenvironment{remark}[1][Remark]{\begin{trivlist}
62\item[\hskip \labelsep {\bfseries #1}]}{\end{trivlist}}
63
64\newcommand{\qed}{\nobreak \ifvmode \relax \else
65 \ifdim\lastskip<1.5em \hskip-\lastskip
66 \hskip1.5em plus0em minus0.5em \fi \nobreak
67 \vrule height0.75em width0.5em depth0.25em\fi}
68
69% Maths shortcuts
70\newcommand{\RR}{\mathbb{R}}
71
72% Algorithms
73\usepackage{algorithm2e}
74
75\begin{document}
76\author{Michael Baudin}
77\date{February 2009}
78\title{Scilab and Statistics}
79\begin{abstract}
80In this document, we describe the statistical features of Scilab.
81We analyse the features available in Scilab's core (i.e. provided
82"out of the box") and Scilab Statistical Toolboxes.
83For Scilab's core statistical features, we analyse the different
84libraries used by Scilab and provide a complete overview of
85the functions. For the most important features, we present Scilab
86sessions with a sample use of the command. Several Scilab Toolboxes
87are analysed in this document, including Sci\_R and Stixbox.
88We also analyse the missing features (not provided in the core and not in the
89toolboxes) with the tools which are available in other languages,
90including Matlab and R.
91\end{abstract}
92
93\maketitle
94
95\tableofcontents
96
97\include{introduction}
98\include{inscilab}
99\include{statstoolboxes}
100\include{missingfeatures}
101
102\clearpage
103
104%% Bibliography
105
106
107\addcontentsline{toc}{chapter}{Bibliography}
108\bibliographystyle{plain}
109\bibliography{statisticsscilab}
110
111\end{document}
112
diff --git a/scilab_doc/statisticswithscilab/statisticsscilab.bib b/scilab_doc/statisticswithscilab/statisticsscilab.bib
new file mode 100644
index 0000000..95cfada
--- /dev/null
+++ b/scilab_doc/statisticswithscilab/statisticsscilab.bib
@@ -0,0 +1,175 @@
1#
2# scilabstats.bib --
3#
4
5@book{scilabintro2007,
6author = {J.-P. Chancelier and F. Delebecque and C. Gomez and M. Goursat and R. Nikoukhah and S. Steer},
7title = {Introduction à Scilab},
8year = {2007},
9publisher= {Springer},
10}
11
12@UNPUBLISHED{scilabstats2001,
13author = {Bernard Ycart},
14title = {Démarrer en Scilab suivi de Statistiques en Scilab},
15year = {2001},
16note = {\url{http://ljk.imag.fr/membres/Bernard.Ycart/polys/demarre_scilab/node21.html}}
17}
18
19@book{artcomputerKnuthVol2,
20author = {D. E. Knuth},
21title = {The Art of Computer Programming, Volume 2, Seminumerical Algorithms},
22year = {1998},
23publisher= {Third Edition, Addison Wesley, Reading, MA},
24}
25
26
27@book{NumericalRecipes,
28author = {W. H. Press and Saul A. Teukolsky and William T. Vetterling and Brian P. Flannery},
29title = {Numerical Recipes in C, Second Edition},
30year = {1992},
31publisher= {}}
32
33@book{Wonacott1990,
34author = {T.H. Wonacott and R.J. Wonacott},
35title = {Introductory statistics},
36year = {1990},
37publisher= {John Wiley and Sons, New York}}
38
39@book{Saporta2006,
40 author = {Saporta, Gilbert },
41 citeulike-article-id = {2795256},
42 isbn = {2710808145},
43 keywords = {2006, books, francais, my-books, probability-theory, statistics},
44 month = {June},
45 posted-at = {2008-05-13 16:02:22},
46 priority = {2},
47 publisher = {{Editions Technip}},
48 title = {Probabilit\'{e}s, analyses des donn\'{e}es et statistiques},
49 url = {http://www.amazon.de/exec/obidos/redirect?tag=citeulike01-21\&amp;path=ASIN/2710808145},
50 year = {}
51}
52
53
54@article{Algorithm715,
55 author = {Cody,, W. J.},
56 title = {Algorithm 715: SPECFUN--a portable FORTRAN package of special function routines and test drivers},
57 journal = {ACM Trans. Math. Softw.},
58 volume = {19},
59 number = {1},
60 year = {1993},
61 issn = {0098-3500},
62 pages = {22--30},
63 doi = {http://doi.acm.org/10.1145/151271.151273},
64 publisher = {ACM},
65 address = {New York, NY, USA},
66 }
67
68
69@Book{abramowitz+stegun1964,
70 author = "Milton Abramowitz and Irene A. Stegun",
71 title = "Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables",
72 publisher = "Dover",
73 year = 1964,
74 address = "New York",
75 edition = "ninth Dover printing, tenth GPO printing",
76 isbn = "0-486-61272-4"
77}
78@book{HartEtAl:1968,
79 author = {Hart, John F. and Cheney, E. W. and Lawson, Charles L. and Maehly, Hans J. and Mesztenyi, Charles K. and Rice, John R. and Thacher and Witzgall, Christoph },
80 citeulike-article-id = {2931998},
81 keywords = {numerics, programming},
82 posted-at = {2008-06-26 20:34:54},
83 priority = {2},
84 publisher = {John wiley \& Sons},
85 series = {SIAM Series on Applied Mathematics},
86 title = {Computer Approximations},
87 year = {1968}
88}
89
90@book{Kennedy1980,
91 author = {Kennedy, William J. and James E. Gentle},
92 publisher = {Marcel Dekker, Inc., New York},
93 title = {Statistical Computing},
94 year = {1980}
95}
96@article{Algo708,
97 author = {Didonato,, Armido R. and Morris,Jr., Alfred H.},
98 title = {Algorithm 708: Significant digit computation of the incomplete beta function ratios},
99 journal = {ACM Trans. Math. Softw.},
100 volume = {18},
101 number = {3},
102 year = {1992},
103 issn = {0098-3500},
104 pages = {360--373},
105 doi = {http://doi.acm.org/10.1145/131766.131776},
106 publisher = {ACM},
107 address = {New York, NY, USA},
108 }
109@article{DiDonato1986,
110 author = {DiDonato,, Armido R and Morris,Jr., Alfred H},
111 title = {Computation of the incomplete gamma function ratios and their inverse},
112 journal = {ACM Trans. Math. Softw.},
113 volume = {12},
114 number = {4},
115 year = {1986},
116 issn = {0098-3500},
117 pages = {377--393},
118 doi = {http://doi.acm.org/10.1145/22721.23109},
119 publisher = {ACM},
120 address = {New York, NY, USA},
121 }
122
123@article{Ahrens1972,
124 author = {Ahrens,, J. H. and Dieter,, U.},
125 title = {Computer methods for sampling from the exponential and normal distributions},
126 journal = {Commun. ACM},
127 volume = {15},
128 number = {10},
129 year = {1972},
130 issn = {0001-0782},
131 pages = {873--882},
132 doi = {http://doi.acm.org/10.1145/355604.361593},
133 publisher = {ACM},
134 address = {New York, NY, USA},
135 }
136@article{358390,
137 author = {Ahrens,, J. H. and Dieter,, U.},
138 title = {Generating gamma variates by a modified rejection technique},
139 journal = {Commun. ACM},
140 volume = {25},
141 number = {1},
142 year = {1982},
143 issn = {0001-0782},
144 pages = {47--54},
145 doi = {http://doi.acm.org/10.1145/358315.358390},
146 publisher = {ACM},
147 address = {New York, NY, USA},
148 }
149@MISC{Devroye86non-uniformrandom,
150 author = {Luc Devroye},
151 title = {Non-Uniform Random Variate Generation},
152 year = {1986},
153 note={\url{http://cg.scs.carleton.ca/~luc/rnbookindex.html}}
154}
155
156@article{AhrensDieter1973,
157 jstor_articletype = {primary_article},
158 title = {Extensions of Forsythe's Method for Random Sampling from the Normal Distribution},
159 author = {Ahrens, J. H. and Dieter, U.},
160 journal = {Mathematics of Computation},
161 jstor_issuetitle = {},
162 volume = {27},
163 number = {124},
164 jstor_formatteddate = {Oct., 1973},
165 pages = {927--937},
166 url = {http://www.jstor.org/stable/2005527},
167 ISSN = {00255718},
168 abstract = {This article is an expansion of G. E. Forsythe's paper "Von Neumann's comparison method for random sampling from the normal and other distributions" [5]. It is shown that Forsythe's method for the normal distribution can be adjusted so that the average number $\bar N$ of uniform deviates required drops to 2.53947 in spite of a shorter program. In a further series of algorithms, $\bar N$ is reduced to values close to 1 at the expense of larger tables. Extensive computational experience is reported which indicates that the new methods compare extremely well with known sampling algorithms for the normal distribution.},
169 publisher = {American Mathematical Society},
170 language = {},
171 copyright = {Copyright © 1973 American Mathematical Society},
172 year = {1973},
173 }
174
175
diff --git a/scilab_doc/statisticswithscilab/statstoolboxes.tex b/scilab_doc/statisticswithscilab/statstoolboxes.tex
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@@ -0,0 +1,23 @@
1\chapter{Statistical Toolboxes}
2
3\url{http://www.scilab.org/contrib/index_contrib.php?page=download&category=DATA%20ANALYSIS%20AND%20STATISTICS}
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5GLMBOX :generalized statistical linear models analysis. (Dec 2003).
6\url{http://www.scilab.org/contrib/index_contrib.php?page=displayContribution&fileID=183}
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8grocer 1.2 : Comprehensive econometric toolbox
9\url{http://www.scilab.org/contrib/index_contrib.php?page=displayContribution&fileID=248}
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11Hurst : Exponent estimators v2.0
12\url{http://www.scilab.org/contrib/index_contrib.php?page=displayContribution&fileID=988}
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14multilinear regression
15\url{http://www.scilab.org/contrib/index_contrib.php?page=displayContribution&fileID=339}
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17Sci\_R for scilab 5.x
18\url{http://www.scilab.org/contrib/index_contrib.php?page=displayContribution&fileID=1138}
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20stixbox 1.2.5
21\url{http://www.scilab.org/contrib/index_contrib.php?page=displayContribution&fileID=184}
22statistics toolbox designed for the french examination "agregation de mathematiques"
23