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//---------------------------------------------------------------------------
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#pragma hdrstop
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#include "ot_statistique.h"
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//---------------------------------------------------------------------------
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#pragma package(smart_init)
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/// ecart type dans le cas d'une serie discrete
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/// racine carree de la moyenne de carrés moins le carré de la moyenne
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double OT_STATISTIQUE::ecart_type (double * x, int n)
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{
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int i;
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double moyenne_x = 0;
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for (i=0;i<n;i++)
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moyenne_x += x[i];
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moyenne_x /= n;
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double moyenne_x2 = 0;
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for (i=0;i<n;i++)
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moyenne_x2 += x[i]*x[i];
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moyenne_x2 /= n;
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return sqrt(moyenne_x2-moyenne_x*moyenne_x);
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}
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/// la moyenne des produits moins le produit des moyennes
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double OT_STATISTIQUE::covariance (double * x, double * y, int n)
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{
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int i;
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double moyenne_xy = 0;
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for (i=0;i<n;i++)
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moyenne_xy += x[i]*y[i];
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moyenne_xy /= n;
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double moyenne_x = 0;
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for (i=0;i<n;i++)
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moyenne_x += x[i];
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moyenne_x /= n;
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double moyenne_y = 0;
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for (i=0;i<n;i++)
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moyenne_y += y[i];
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moyenne_y /= n;
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return moyenne_xy - moyenne_x * moyenne_y;
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}
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/// la moyenne des carrés moins le carré de la moyenne
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double OT_STATISTIQUE::variance (double * x, int n)
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{
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int i;
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double moyenne_carres = 0;
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for (i=0;i<n;i++)
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moyenne_carres += x[i]*x[i];
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moyenne_carres /= n;
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double moyenne = 0;
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for (i=0;i<n;i++)
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moyenne += x[i];
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moyenne /= n;
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return moyenne_carres - moyenne*moyenne;
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}
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///
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void OT_STATISTIQUE::regression_lineaire(double *x, double *y, int n, double *pente, double *valY0)
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{
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int i;
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// coef directeur de la droite
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double a = variance(y,n) / covariance(x,y,n);
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// b = valeur de y (0) par moindre carrés
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double b = 0;
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for (i=0; i<n; i++)
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b += y[i] - a*x[i];
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b /= n;
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*pente = a;
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*valY0 = b;
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}
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double OT_STATISTIQUE::max(double *x, int n)
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{
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if (n==0)
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return 0;
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double max_x = x[0];
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for (int i=0;i<n;i++)
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if (x[i] > max_x)
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max_x = x[i];
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return max_x;
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}
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double OT_STATISTIQUE::min(double *x, int n)
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{
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if (n==0)
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return 0;
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double min_x = x[0];
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for (int i=0;i<n;i++)
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if (x[i] < min_x)
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min_x = x[i];
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return min_x;
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}
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