Classes de fonctions statistiques

Développeur

BOURSE

RUBRIQUES

Benchmark Group

L'internaute Magazine

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Classes de fonctions statistiques
Sous licence GPL 16 octobre 2001

Cette classe contient des méthodes statistiques acceptant en paramètre un ou deux tableaux monodimensionnels et renvoyant un ou deux tableaux de données statistiques. Le premier contient le minimum, le maximum, la somme, moyenne, valeur médiane et l'écart-type. Le second contient les valeurs caractéristiques d'une droite de regression linéaire (droite des moindres carrés).

Ci-dessous figure un exemple d'utilisation:

<?
/*
* Sample test code for the Statistic and the Linear Least square regression class: Stat1
* Alain M. Samoun 3/12/00
*/

echo "
<HTML>
<BODY BGCOLOR=\"white\">
<PRE>
";

require("Stat1.php");

/* create two arrays for testing*/

$X= array( 110, 116, 124, 129, 131, 138, 142, 150, 153, 155, 156, 159, 164, 168, 174);
$Y= array( 44, 31, 43, 45, 56, 79, 57, 56, 58, 92, 78, 64, 88, 112, 101);

/* create an instance w/o initialization */
$h = new Stat1;

/* do the calculation and print the results */
$h->create($X,$Y,"Test Stat1");

$h->printStats();

/* access the result arrays directly*/
$result = $h->getStats();
echo "\n\nresult is of type: ".pe($result)."\n";
while (list($key,$val) = each($result)) {
echo $key."\t".$val."\n";
}

echo"
</PRE>
</BODY></HTML>"

?>

Et le code:

<?php

/* 
* This is a statistic class that accepts one or two unidimensional arrays of data. 
* It returns a stat array using the getStats() method. 
* If only one array is sent, it will return the min,max, sum,  median, average and standard 
* deviation for this array. If two arrays are sent, in addition to these values for both 
* arrays, a linear regression line is computed: m is the slope b is the Yaxis intersect, 
* r is the correlation, a measure of the quality of the data fit by the regression line (r=1 
* being a perfect fit) and t is the "t"test, to test whether the association between X and Y 
* data is real or merely apparent, I leave the user to interpret this test himself. (See the 
* tutorial and the table at: http://www.bmj.com/collections/statsbk/apptabb.html). 
* The regression line will be calculated only if both arrays have the same number of samples. 
* Note that it is the responsibility of the user to make sure that his data are in linear form 
* (For the linear regression to work, Median and Average values should be close). 
* I tried to use the histogram class wrote by Jesus Castagnetto as an inheritance for 
* this script, but it was too complicated since that I needed two arrays. Probably the other 
* way around, using Stat1 as an inheritance for an histogram class, will be easier now. 
* Tested with PHP4 beta 4. 
* (c) Alain M. Samoun 3/12/00 alain@samoun.com 
* License: Same as the GNU's Free Software Foundation or the open source PHP license as you 
   prefer;-). 
     
    This library is distributed in the hope that it will be useful, 
    but WITHOUT ANY WARRANTY; without even the implied warranty of 
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU 
    Lesser General Public License for more details.

class Stat1 {

/* variables */

var $N,$NY,$MINX,$MAXX,$MAXY,$MINY,$AVGX,$AVGY,$STDVX,$STDVY,$SUMX,$SUMY,$SUMX2,$SUMY2,$SUMXY; 
    var $X = array(),$Y = array(); 
    var $MEDX,$MEDY,$DEV,$m,$b,$r; 
    var $STATS = array();

/* Constructor */ 
        function Stat1($X="", $Y="",$DEV=0, $title="") { 
        if ($X && $Y && $title) { 
            $this->create($X,$Y,$title); 
        } 
    }

/* Create the class */ 
     
    function create($X,$Y,$title="") { 
        /* Check if we got a valid set of data*/ 
        (($this->N = count($X))  > 1) or die("Not enough data, number of values : ".$this->N."\n"); 
         
        /* initialize values */ 
        $this->MINX = (float) min($X); 
        $this->MAXX= (float) max($X);     
         
        /* Compute X Median */ 
        # Sort values in array X 
        $XX = $X; 
        sort ($XX); 
        if ($this->N%2 == 0){ 
            $this->MEDX = (($XX[($this->N)/2])+($XX[-1+($this->N/2)]))/2; 
        }else{ 
            $this->MEDX = $XX[floor($this->N/2)]; 
        } 
         
        $this->NY = count($Y); 
        $this->MINY = (float) min($Y); 
        $this->MAXY= (float) max($Y); 
         
        /* Compute Y Median */ 
        # Sort values in array Y 
        $YY = $Y; 
        sort ($YY); 
        if ($this->NY%2 == 0){ 
            $this->MEDY = (($YY[($this->NY)/2])+($YY[-1+($this->NY/2)]))/2; 
        }else{ 
            $this->MEDY = $YY[floor($this->NY/2)]; 
        } 
         
         
        $this->setTitle($title); 
         
         
         
         
        /* stats */ 
        for ($i = 0; $i < $this->N ; $i++) { 
            $this->SUMX += (float) $X[$i]; 
            $this->SUMX2 += (float) pow($X[$i],2); 
            $this->SUMXY += (float) $X[$i]* (float)$Y[$i]; 
        } 
        $this->AVGX = (float) $this->SUMX/ (float) $this->N; 
        $this->STDVX = (float) sqrt(($this->SUMX2 - $this->N*pow($this->AVGX,2))/(float)($this->N - 1));

for ($i = 0; $i < $this->NY ; $i++) { 
            $this->SUMY += (float) $Y[$i]; 
            $this->SUMY2 += (float) pow($Y[$i],2); 
        } 
        $this->AVGY = (float) $this->SUMY/ (float)$this->NY; 
        $this->STDVY = (float) sqrt(($this->SUMY2 - $this->NY*pow($this->AVGY,2))/(float)($this->NY - 1)); 
         
        if ($this->NY == $this->N){ 
            $this->DEV = (float) (($this->SUMX2 * $this->N)- ($this->SUMX * $this->SUMX)); 
            $this->m = (float)(($this->SUMXY * $this->N)- ($this->SUMX * $this->SUMY))/$this->DEV; 
            $this->b = (float)(($this->SUMX2 * $this->SUMY)- ($this->SUMXY * $this->SUMX))/$this->DEV; 
            $this->r = (float) ($this->SUMXY -($this->N * $this->AVGX * $this->AVGY))/(($this->N-1)*$this->STDVX * $this->STDVY); 
            $this->t = (float) $this->r * sqrt(($this->N -2)/(1- pow($this->r,2))); 
        } 
    /* make the STATS array */ 
        $this->STATS =    array ( 
                                    N=>$this->N, 
                                    NY=>$this->NY, 
                                    MINX=>$this->MINX, 
                                    MAXX=>$this->MAXX, 
                                    SUMX=>$this->SUMX, 
                                    MEDX=>$this->MEDX, 
                                    AVGX=>$this->AVGX, 
                                    STDVX=>$this->STDVX, 
                                    MINY=>$this->MINY, 
                                    MAXY=>$this->MAXY, 
                                    SUMY=>$this->SUMY, 
                                    MEDY=>$this->MEDY, 
                                    AVGY=>$this->AVGY, 
                                    STDVY=>$this->STDVY, 
                                    m=>$this->m, 
                                    b=>$this->b, 
                                    r=>$this->r, 
                                    t=>$this->t 
                                     
                                );

} 
     
     
    /* sets the Title */ 
    function setTitle($title) { 
        $this->TITLE=$title; 
    }

/* send back STATS array */ 
    function getStats() { 
        return $this->STATS; 
    } 
     
     
    /* simple printStats */ 
    function printStats() { 
        $s = "Statistics for : ".$this->TITLE."\n"; 
        $s .= "Number of data in X axis: $this->N \n"; 
        $s .= sprintf("Min = %-2.4f\tMax = %-2.4f\tAvg = %-2.4f\tMED = %-2.4f\tStDev = %-2.4f \n",$this->MINX,$this->MAXX,$this->AVGX,$this->MEDX, $this->STDVX  ); 
        $s .= "\nNumber of data in Y axis: $this->NY \n"; 
        $s .= sprintf("Min = %-2.4f\tMax = %-2.4f\tAvg = %-2.4f\tMED = %-2.4f\tStDev = %-2.4f \n",$this->MINY,$this->MAXY,$this->AVGY,$this->MEDY, $this->STDVY  ); 
        if($this->NY ==$this->N){     
            $s .= "\nLinear regression line: \n"; 
            if ($this->b >=0){ 
                $s .= "Y = $this->m X + $this->b   with correlation (r)= $this->r\n  \"t\"test (df=$this->N-2) = $this->t"; 
            }else{ 
                $s .= "Y = $this->m X  $this->b    with correlation (r)= $this->r\n  \"t\"test (df=$this->N-2) = $this->t"; 
            } 
        } 
        echo $s; 
         
         
    } 
     
     
     
} /* end of Stat1 class */



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