File:Somme tirage 1 a 6d6 et loi normale.svg
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DescriptionSomme tirage 1 a 6d6 et loi normale.svg |
English: Convergence of the sum of nd6 towards a normal distribution (central limit theorem).
Français : Convergence de la somme de nd6 vers une loi normale (théorème central limite). |
Date | |
Source | Own work |
Author | Christophe Dang Ngoc Chan (Cdang (talk)) |
Other versions | see also File:Somme n tirages d6 1 a 5.svg |
Scilab source
This media was created with Scilab, a free open-source software. Here is a listing of the Scilab source used to create this file. |
// Trace la fonction de densité de n tirages de dés à 6 faces
// et la loi normale selon le théorème central limite
// initialisation
clear;
clf;
nbmax = 6; // nombre max de tirages
cmap = [coolcolormap(nbmax); 0, 0, 0];
xset("colormap", cmap);
// Fonctions
function [frequences]=tirages(n)
// calcule les fréquences de n tirage de dés par dénombrement
// entrées : n : nombre de tirages (entier)
// sorties : frequences : matrice de fréquences (réels)
N = 6^n; // nombre de valeurs possibles
resultats = zeros(N, n); // initialisation : résultats des tirages
for i = 1:n // n° de colonne
k = 6^(n - i); //à la colonne i : k valeurs 1, puis k valeurs 2...
for j=0:6^(i - 1) - 1
for jj = 1:6
resultats((6*j + jj - 1)*k + 1:(6*j + jj)*k, i) = jj;
end
end
end
//disp(resultats);
somme = sum(resultats, "c");
frequences_non_triees = tabul(somme);
frequences = gsort(frequences_non_triees, "lr", "i");
frequences(:,2) = frequences(:,2)/N; // normalisation des fréquences
endfunction
// Programme principal
mu0 = mean(1:6);
sigma0 = st_deviation(1:6);
for i=1:nbmax
XY = tirages(i);
sigma = sigma0*sqrt(i);
mu = i*mu0;
x = 0:0.25:XY($, 1);
y = pdfnormal(x, mu, sigma);
subplot(2, 3, i)
plot2d(x, y, style = nbmax+1)
plot2d3(XY(:, 1), XY(:, 2), style = i)
titre = string(i)+"d6";
xtitle(titre, "valeur", "fréquence")
end
Licensing[edit]
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Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
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File history
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 12:29, 5 November 2013 | 609 × 446 (110 KB) | Cdang (talk | contribs) | One more case. Parameters of the normal law calculated from the central limit theorem and not from the data. | |
09:21, 5 November 2013 | 605 × 455 (89 KB) | Cdang (talk | contribs) | {{Information |Description={{en|1=Convergence of the sum of ''n''d6 towards a normal distribution (central limit theorem).}} {{fr|1=Convergence de la somme de ''n''d6 vers une loi normale (théorème central limite).}} |Source={{own}} |Date=2013-11-05 ... |
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Short title | Convergence de la somme de nd6 vers une loi normale |
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Width | 609 |
Height | 446 |