File:Maximum de vraisemblance surface loi normale centree reduite.svg
| Uploaded by | Cdang |
|---|---|
| Upload date | 2013-06-20T12:59:54Z |
| MIME type | image/svg+xml |
| Dimensions | 545 × 372 px |
| File size | 505.0 KB |
Summary
| Description |
Français : Surface représentant la vraisemblance L (en z) en fonction des paramètres μ et σ de la loi normale.
Pour les valeurs de la variable aléatoire, nous avons pris les déciles de la loi normale centrée réduite. Créé avec Scilab, modifié avec Inkscape.English: Surface representing the likehood L (z axis) versus the parameters μ and σ of the normal law.
The values of the random variable are the deciles of the standard normal distribution. Created with Scilab, modified with Inkscape. |
| Date | |
| Source | Own work |
| Author | Cdang |
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. |
// L'exécution de ce script nécessite le module CASCI
clear;
clf;
// déciles
Y = 0.1:0.1:0.9;
X = idfnormal(Y, 0, 1);
n = size(Y, "*");
// fonctions
function [L] = vraisemblance(x, mu, sigma)
// calcule le maximum de vraisemblance de la loi normale
// entrées : x : réalisations de la variable aléatoire (vectuer de réels)
// mu, sigma : paramètres de la loi normale (réels)
// sortie : L : vraisemblance (réel)
y = pdfnormal(x, mu, sigma);
L = prod(y);
endfunction
// Programme principal
// espace de recherche
m = 20;
mu = linspace(-0.5, 0.5, m);
n = 20;
sigma = linspace(0.5, 1.5, n);
L = zeros(m, n); // initialisation
for i = 1:m
for j = 1:n
L(i,j) = vraisemblance(X, mu(i), sigma(j));
end
end
// tracé
cmap = coolcolormap(30);
xset("colormap", cmap);
plot3d1(mu', sigma', 1e5*L)
xtitle("Vraisemblance", "$\mu$", "$\sigma$", "$\mathrm{L} \times 10^5$")
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