Computes p(x;n,p) where x~B(n,p) : Math « Development Class « Java

Computes p(x;n,p) where x~B(n,p)

/* Copyright (C) 2003 Univ. of Massachusetts Amherst, Computer Science Dept.
   This file is part of "MALLET" (MAchine Learning for LanguagE Toolkit).
   This software is provided under the terms of the Common Public License,
   version 1.0, as published by  For further
   information, see the file `LICENSE' included with this distribution. */

//package cc.mallet.util;

 * @author <a href="">Charles Sutton</a>
 * @version $Id:,v 1.1 2007/10/22 21:37:40 mccallum Exp $
public class Util {

     * Computes p(x;n,p) where x~B(n,p)
    // Copied as the "classic" method from Catherine Loader.
    //  Fast and Accurate Computation of Binomial Probabilities.
    //   2001.  (This is not the fast and accurate version.)
    public static double logBinom (int x, int n, double p)
      return logFactorial (n) - logFactorial (x) - logFactorial (n - x)
              + (x*Math.log (p)) + ((n-x)*Math.log (1-p));
    public static double logFactorial (int n) {
        return logGamma(n+1);

  // From libbow, dirichlet.c
  // Written by Tom Minka <>
  public static final double logGamma (double x)
    double result, y, xnum, xden;
    int i;
    final double d1 = -5.772156649015328605195174e-1;
    final double p1[] = { 
      4.945235359296727046734888e0, 2.018112620856775083915565e2, 
      2.290838373831346393026739e3, 1.131967205903380828685045e4, 
      2.855724635671635335736389e4, 3.848496228443793359990269e4, 
      2.637748787624195437963534e4, 7.225813979700288197698961e3 
    final double q1[] = {
      6.748212550303777196073036e1, 1.113332393857199323513008e3, 
      7.738757056935398733233834e3, 2.763987074403340708898585e4, 
      5.499310206226157329794414e4, 6.161122180066002127833352e4, 
      3.635127591501940507276287e4, 8.785536302431013170870835e3
    final double d2 = 4.227843350984671393993777e-1;
    final double p2[] = {
      4.974607845568932035012064e0, 5.424138599891070494101986e2, 
      1.550693864978364947665077e4, 1.847932904445632425417223e5, 
      1.088204769468828767498470e6, 3.338152967987029735917223e6, 
      5.106661678927352456275255e6, 3.074109054850539556250927e6
    final double q2[] = {
      1.830328399370592604055942e2, 7.765049321445005871323047e3, 
      1.331903827966074194402448e5, 1.136705821321969608938755e6, 
      5.267964117437946917577538e6, 1.346701454311101692290052e7, 
      1.782736530353274213975932e7, 9.533095591844353613395747e6
    final double d4 = 1.791759469228055000094023e0;
    final double p4[] = {
      1.474502166059939948905062e4, 2.426813369486704502836312e6, 
      1.214755574045093227939592e8, 2.663432449630976949898078e9, 
      2.940378956634553899906876e10, 1.702665737765398868392998e11, 
      4.926125793377430887588120e11, 5.606251856223951465078242e11
    final double q4[] = {
      2.690530175870899333379843e3, 6.393885654300092398984238e5, 
      4.135599930241388052042842e7, 1.120872109616147941376570e9, 
      1.488613728678813811542398e10, 1.016803586272438228077304e11, 
      3.417476345507377132798597e11, 4.463158187419713286462081e11
    final double c[] = {
      -1.910444077728e-03, 8.4171387781295e-04, 
      -5.952379913043012e-04, 7.93650793500350248e-04, 
      -2.777777777777681622553e-03, 8.333333333333333331554247e-02, 
    final double a = 0.6796875;

    if((x <= 0.5) || ((x > a) && (x <= 1.5))) {
      if(x <= 0.5) {
        result = -Math.log(x);
        /*  Test whether X < machine epsilon. */
        if(x+1 == 1) {
          return result;
      else {
        result = 0;
        x = (x - 0.5) - 0.5;
      xnum = 0;
      xden = 1;
      for(i=0;i<8;i++) {
        xnum = xnum * x + p1[i];
        xden = xden * x + q1[i];
      result += x*(d1 + x*(xnum/xden));
    else if((x <= a) || ((x > 1.5) && (x <= 4))) {
      if(x <= a) {
        result = -Math.log(x);
        x = (x - 0.5) - 0.5;
      else {
        result = 0;
        x -= 2;
      xnum = 0;
      xden = 1;
      for(i=0;i<8;i++) {
        xnum = xnum * x + p2[i];
        xden = xden * x + q2[i];
      result += x*(d2 + x*(xnum/xden));
    else if(x <= 12) {
      x -= 4;
      xnum = 0;
      xden = -1;
      for(i=0;i<8;i++) {
        xnum = xnum * x + p4[i];
        xden = xden * x + q4[i];
      result = d4 + x*(xnum/xden);
    /*  X > 12  */
    else {
      y = Math.log(x);
      result = x*(y - 1) - y*0.5 + .9189385332046727417803297;
      x = 1/x;
      y = x*x;
      xnum = c[6];
      for(i=0;i<6;i++) {
        xnum = xnum * y + c[i];
      xnum *= x;
      result += xnum;
    return result;


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