package statistics;// Gaussian CDF Taylor approximation// Code borrowed from http://www.cs.princeton.edu/introcs/21function/Gaussian.java.html 19/9 2006/**************************************************************************  Compilation:  javac Gaussian.java*  Execution:    java Gaussian x mu sigma**  Function to compute the Gaussian pdf (probability density function)*  and the Gaussian cdf (cumulative density function)**  % java Gaussian 820 1019 209*  0.17050966869132111**  % java Gaussian 1500 1019 209*  0.9893164837383883**  % java Gaussian 1500 1025 231*  0.9801220907365489**************************************************************************/public class Gaussian { // return phi(x) = standard Gaussian pdf public static double phi(double x) {     return Math.exp(-x*x / 2) / Math.sqrt(2 * Math.PI); } // return phi(x) = Gaussian pdf with mean mu and stddev sigma public static double phi(double x, double mu, double sigma) {     return phi((x - mu) / sigma) / sigma; } // return Phi(z) = standard Gaussian cdf using Taylor approximation public static double Phi(double z) {     if (z < -8.0) return 0.0;     if (z >  8.0) return 1.0;     double sum = 0.0, term = z;     for (int i = 3; sum + term != sum; i += 2) {         sum  = sum + term;         term = term * z * z / i;     }     return 0.5 + sum * phi(z); } // return Phi(z, mu, sigma) = Gaussian cdf with mean mu and stddev sigma public static double Phi(double z, double mu, double sigma) {     return Phi((z - mu) / sigma); }  public static void main(String[] args) {     double z     = Double.parseDouble(args[0]);     double mu    = Double.parseDouble(args[1]);     double sigma = Double.parseDouble(args[2]);     System.out.println(Phi(z, mu, sigma)); }}