Analyse statistique des données expérimentales by Demailly J P

By Demailly J P

P D.J. examine numerique et équations differentielles (EDP Sciences, 1996)(ISBN 2868834566)(149s)

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Ainsi ('expression de la transformation de Fourier directe (40) nous donne la formule (39). Nous sommes en presence d'une distribution pour laquelle les definitions generates des valeurs moyennes ne sont pas valables. Cette particularity de la distribution de Lorentz a des consequences tres importantes. Nous verrons au paragraphe suivant que c'est la seule distribution qui ne se transforme pas en une distribution de Gauss lorsque le nombre de mesures devient grand. 4 ANALYSE STATISTIQUE DBS DONNEES EXPERIMENTALES DISTRIBUTION GAMMA Cette distribution herite son nom d'une fonction speciale dite fonction F ou integrate d'Euler de deuxieme espece.

On peut voir facilement que cette distribution est symetrique par rapport a XQ qui est aussi le maximum de cette fonction. En ce qui concerne le coefficient a, son interpretation est aussi claire : il represente la moitie de la largeur a mi-hauteur et caracterise ainsi 1'etalement de cette fonction. Cependant, on rencontre de vrais problemes quand on veut trouver la moyenne et la variance en utilisant nos definitions habituelles. 9 : La distribution de Lorentz D'apres la definition (6), la valeur moyenne de x est egale a Pour calculer cette integrale, faisons le changement de variable Le deuxieme terme est egal a XQ en vertu de la normalisation de la distribution.

2 que la distribution de Poisson peut etre obtenue a partir de la distribution binomiale lorsque le nombre de mesures N est grand et que p est petit, le produit p = Np restant constant. Cela signifie egalement que, dans le cas d'un grand nombre de mesures, la distribution binomiale tend vers 48 ANALYSE STATISTIQUE DBS DONNEES EXPERIMENTALES la distribution de Gauss. Cependant, il faut interpreter ces limites avec precaution. On ne peut pas dire que la distribution de Gauss est un cas particulier de celle de Poisson lorsque fj, —>• oo.

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