Statistical simulations in PHP

stats.inc

<?php


class St
{
	/**
	 * Generate a random number in the interval (0,1).
	 * 
	 * Using the parameters $closed_left and/or $closed_right, the interval may
	 * be closed to [0,1), (0,1], or [0,1].
	 **/
	public static function uniform( $closed_left = false, $closed_right = false )
	{
		// A large prime for the denominator
		$D = 17638261;

		$l = $closed_left  ?  0 :  1;
		$r = $closed_right ? $D : $D-1;

		return mt_rand( $l, $r ) / $D;
	}

	/** 
	 * Generate a random variable with a Gauss distribution
	 **/
	public static function normal( $mu = 0, $sigma = 1 )
	{
		if ( count(self::$_norm_buffer) == 0 )
			self::_fill_norm_buffer();

		return ( $sigma * array_shift(self::$_norm_buffer) ) + $mu;
	}
	private static $_norm_buffer = array();
	/**
	 * Generate two random variables with standard Gauss distribution, using
	 * the Box-Muller method.
	 **/
	private static function _fill_norm_buffer()
	{
		$U = self::uniform();
		$V = self::uniform();

		self::$_norm_buffer[] = sqrt(-2*log($U)) * cos(2*M_PI*$V);
		self::$_norm_buffer[] = sqrt(-2*log($U)) * sin(2*M_PI*$V);
	}


	/**
	 * Generate a random variable with an exponential distribution, 
	 * with mean ( 1/$lambda ).
	 **/
	public static function exponential( $lambda = 1 )
	{
		return ( -1*log(self::uniform()) ) / $lambda;
	}
}