chi-squared/cdf.js

characteristic functions for chi-squared distributions

var LogGamma = require('gamma').log

// The following code liberated from
// http://www.math.ucla.edu/~tom/distributions/chisq.html

function Gcf(X,A) {        // Good for X>A+1
  with (Math) {
    var A0=0;
    var B0=1;
    var A1=1;
    var B1=X;
    var AOLD=0;
    var N=0;
    while (abs((A1-AOLD)/A1)>.00001) {
      AOLD=A1;
      N=N+1;
      A0=A1+(N-A)*A0;
      B0=B1+(N-A)*B0;
      A1=X*A0+N*A1;
      B1=X*B0+N*B1;
      A0=A0/B1;
      B0=B0/B1;
      A1=A1/B1;
      B1=1;
    }
    var Prob=exp(A*log(X)-X-LogGamma(A))*A1;
  }
  return 1-Prob
}

function Gser(X,A) {        // Good for X<A+1.
    with (Math) {
    var T9=1/A;
    var G=T9;
    var I=1;
    while (T9>G*.00001) {
      T9=T9*X/(A+I);
      G=G+T9;
      I=I+1;
    }
    G=G*exp(A*log(X)-X-LogGamma(A));
    }
    return G
}

function Gammacdf(x,a) {
  var GI;
  if (x<=0) {
    GI=0
  } else if (x<a+1) {
    GI=Gser(x,a)
  } else {
    GI=Gcf(x,a)
  }
  return GI
}

module.exports = function (Z, DF) {
  if (DF<=0) {
    throw new Error("Degrees of freedom must be positive")
  }
  return Gammacdf(Z/2,DF/2)
}