/*
* Concept profile generation tool suite
* Copyright (C) 2015 Biosemantics Group, Erasmus University Medical Center,
* Rotterdam, The Netherlands
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU Affero General Public License as published
* by the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program 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 Affero General Public License for more details.
*
* You should have received a copy of the GNU Affero General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>
*/
package org.erasmusmc.math;
public class GaussianDistribution {
public static void main(String[] args){
System.out.println(cdf(0.01,1,1));
}
// 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, mu, signma) = 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 csf(z) = standard Gaussian cdf using Taylor approximation
public static double cdf(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 cdf(double z, double mu, double sigma) {
return cdf((z - mu) / sigma);
}
// Compute z such that Phi(z) = y via bisection search
public static double PhiInverse(double y) {
return PhiInverse(y, .00000001, -8, 8);
}
// bisection search
private static double PhiInverse(double y, double delta, double lo, double hi) {
double mid = lo + (hi - lo) / 2;
if (hi - lo < delta) return mid;
if (cdf(mid) > y) return PhiInverse(y, delta, lo, mid);
else return PhiInverse(y, delta, mid, hi);
}
}