CODEWITHSUNDEEP
phpalgorithm
Javit
Javit

Reputation: 21

Bell Curve Algorithm With PHP

I am working on a personal project in which IQ ranges will be randomly assignes to fake characters. This asignment will be random, yet realistic, so IQ ranges must be distributed along a bell curve. There are 3 range categories: low, normal, and high. The half of the fake characters will fall within normal, but about 25% will either fall into the low or high range.

How can I code this?

Upvotes: 1

Views: 3699

Answers (4)

Mark Baker
Mark Baker

Reputation: 212452

It might look long and complicated (and was written procedural for PHP4) but I used to use the following for generating non-linear random distributions:

function random_0_1()
{
    //  returns random number using mt_rand() with a flat distribution from 0 to 1 inclusive
    //
    return (float) mt_rand() / (float) mt_getrandmax() ;
}

function random_PN()
{
    //  returns random number using mt_rand() with a flat distribution from -1 to 1 inclusive
    //
    return (2.0 * random_0_1()) - 1.0 ;
}


function gauss()
{
    static $useExists = false ;
    static $useValue ;

    if ($useExists) {
        //  Use value from a previous call to this function
        //
        $useExists = false ;
        return $useValue ;
    } else {
        //  Polar form of the Box-Muller transformation
        //
        $w = 2.0 ;
        while (($w >= 1.0) || ($w == 0.0)) {
            $x = random_PN() ;
            $y = random_PN() ;
            $w = ($x * $x) + ($y * $y) ;
        }
        $w = sqrt((-2.0 * log($w)) / $w) ;

        //  Set value for next call to this function
        //
        $useValue = $y * $w ;
        $useExists = true ;

        return $x * $w ;
    }
}

function gauss_ms( $mean,
                   $stddev )
{
    //  Adjust our gaussian random to fit the mean and standard deviation
    //  The division by 4 is an arbitrary value to help fit the distribution
    //      within our required range, and gives a best fit for $stddev = 1.0
    //
    return gauss() * ($stddev/4) + $mean;
}

function gaussianWeightedRnd( $LowValue,
                                 $maxRand,
                                 $mean=0.0,
                                 $stddev=2.0 )
{
    //  Adjust a gaussian random value to fit within our specified range
    //      by 'trimming' the extreme values as the distribution curve
    //      approaches +/- infinity
    $rand_val = $LowValue + $maxRand ;
    while (($rand_val < $LowValue) || ($rand_val >= ($LowValue + $maxRand))) {
        $rand_val = floor(gauss_ms($mean,$stddev) * $maxRand) + $LowValue ;
        $rand_val = ($rand_val + $maxRand) / 2 ;
    }

    return $rand_val ;
}

function bellWeightedRnd( $LowValue,
                             $maxRand )
{
    return gaussianWeightedRnd( $LowValue, $maxRand, 0.0, 1.0 ) ;
}

For the simple bell distribution, just call bellWeightedRnd() with the min and max values; for a more sophisticated distribution, gaussianWeightedRnd() allows you to specify the mean and stdev for your distribution as well.

The gaussian bell curve is well suited to IQ distribution, although I also have similar routines for alternative distribution curves such as poisson, gamma, logarithmic, &c.

Upvotes: 5

Peng Qi
Peng Qi

Reputation: 1462

first assume you have 3 function to provide high medium and low IQs, then simply

function randomIQ(){
    $dice = rand(1,100);
    if($dice <= 25) $iq = low_iq();
    elseif($dice <= 75) $iq = medium_iq();
    else $iq = high_iq();
    return $iq;
}

Upvotes: 1

iwalkbarefoot
iwalkbarefoot

Reputation: 955

Using the link that ithcy posted I created the following function:

function RandomIQ()
{  
    return round((rand(-1000,1000) + rand(-1000,1000) + rand(-1000,1000))/100,0) * 2 + 100;
}

It's a little messy but some quick checking gives it a mean of approximately 100 and a roughly Normal Distribution. It should fall in line with the information that I got from this site.

Upvotes: 0

Brandon Frohbieter
Brandon Frohbieter

Reputation: 18139

You could randomize multiple 'dice', random number from each adding up to the highest point. This will generate a normal distribution (approximately).

Upvotes: 0

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