ExpRand

Version: 1

Type: Function

Category: Math Functions

License: GNU Library Public License

Description: Exponentially weighted random number generator. Generates random number useing the formula f(x)=x^a where x is a random number and a is the weight.

Function imputs are $min, $max, and $average.
Function returns random float between $min and $max. If run multiple times the average should be near $average.

File contain test code (all code outside the function) which can be removed.

Math behind the code:
f(x)=x^a where x is a random number between 0 and $maxrand

From hear on $min is assumed to be 0, x is assumed to be $maxrand, and avg is $average
Average value is equil to area under the curve devided by x
A(x)=(x^(a+1)/(a+1) where A(x) is area
avg=(x^(a+1))/(a+1)x
simplify
avg=(x^a)/(a+1)

F(x)=x^a becomes
y=x^a where y is $max
x = y^(1/a)
avg=(x^a)/(a+1)
avg=((y^(1/a))^a)/(a+1) substitution
avg=y/(a+1) simplify
a=(y/avg)-1 solve for a
since y($max) is given and avg($average) is give you now have a
$exp = ($max/$average)-1;

x = y^(1/a)
since y($max) is given and a is now knowen you now have x($maxrand)
$maxrand = pow($max,(1/$exp));

f(x)=x^a where x is a random number between 0 and $maxrand can now be calculated
$rand = mt_rand(0,$maxrand);
$resault = pow($rand,$exp);

L0ok at the code to see how $min was added

<?php

$min_val = 3;
$max_val = 20;
$average_val = 5;

$loops = 0;

while ($loops < 100) {
	
	$total += exprand($min_val, $max_val, $average_val);
	
	$loops ++;
	}

$average = $total/$loops;
echo '<br>';
echo gettype($total);
echo "<br> $total <br> $loops <br>";
echo $average;

//exponentially weighted random number generator
//generates random numbers throught the base formula
//f(x)=x^a where x is a random number and a is the weight
//function imputs are $min, $max, and $average
//function returns random float between $min and $max
//if run multiple times the average should be near $average
function exprand($min, $max, $average) {
	//the origional exprand didn't accept $min
	//the next 2 lines and the second $resault line add $min functionality
	$max -=$min;
	$average -=$min;
	
	//calculating exponent
	$exp = ($max/$average)-1;
	//calculating max value for mt_rand
	$maxrand = pow($max,(1/$exp));
	
	//mt_rand returns integers
	//rounding errors were causing major problems
	//next 3 lines of code generate a random number with accuracy to the millionth
	$maxrand *= 1000000;
	$rand = mt_rand(0,$maxrand);
	$rand /= 1000000;
	
	//applying curve to $rand
	$resault = pow($rand,$exp);
	
	//add $min back in
	$resault += $min;
	
	return $resault;
	}
?>