/**
* File: NormalDistribution.java.
*
* Class representation of the Normal distribution
*
* @author Written by Joaquin Derrac (University of Granada) 1/12/2010
* @version 1.0
* @since JDK1.5
*/
package keel.GraphInterKeel.statistical.tests;
public class NormalDistribution{
private double mu;
private double sigma;
/**
* Set the mean of the distribution
*
* @param value Mean value
*/
public void setMean(double value){
mu=value;
}//end-method
/**
* Set the sigma value of the distribution
*
* @param value Sigma value
*/
public void setSigma(double value){
sigma=value;
}//end-method
/**
* Get the mean of the distribution
*
* @return Mean value
*/
public double getMean(){
return mu;
}//end-method
/**
* Get the sigma value of the distribution
*
* @return Sigma value
*/
public double getSigma(){
return sigma;
}//end-method
/**
* Default builder
*/
public NormalDistribution(){
}//end-method
/**
* Computes punctual probability for a given point
*
* @param x Point selected
* @return Punctual probability
*/
public double getProbability(double x){
double value=0.0;
value=Math.pow(Math.E,-(x-mu)*(x-mu)/(2.0*sigma*sigma));
value/=Math.sqrt(2.0*Math.PI*sigma*sigma);
return value;
}//end-method
/**
* Computes cumulated distribution frequency for a given value
*
* @param x Z value
* @return Cumulated distribution frequency
*/
public double getCumulatedProbability(double x){
double value;
double z= ((x-mu)/sigma);
value=getTipifiedProbability(z, false);
return value;
}//end-method
/**
*
* Computes cumulative N(0,1) distribution. Based om Algorithm AS66 Applied Statistics (1973) vol22 no.3
*
* @param z x value
* @param upper A boolean value, if true the integral is evaluated from z to infinity, from minus infinity to z otherwise
* @return The value of the cumulative N(0,1) distribution for z
*/
public double getTipifiedProbability(double z, boolean upper) {
//Algorithm AS 66: "The Normal Integral"
//Applied Statistics
double ltone = 7.0,
utzero = 18.66,
con = 1.28,
a1 = 0.398942280444,
a2 = 0.399903438504,
a3 = 5.75885480458,
a4 = 29.8213557808,
a5 = 2.62433121679,
a6 = 48.6959930692,
a7 = 5.92885724438,
b1 = 0.398942280385,
b2 = 3.8052e-8,
b3 = 1.00000615302,
b4 = 3.98064794e-4,
b5 = 1.986153813664,
b6 = 0.151679116635,
b7 = 5.29330324926,
b8 = 4.8385912808,
b9 = 15.1508972451,
b10 = 0.742380924027,
b11 = 30.789933034,
b12 = 3.99019417011;
double y, alnorm;
if (z < 0) {
upper = !upper;
z = -z;
}
if (z <= ltone || upper && z <= utzero) {
y = 0.5 * z * z;
if (z > con) {
alnorm = b1 * Math.exp( -y) /
(z - b2 +
b3 /
(z + b4 +
b5 /
(z - b6 +
b7 / (z + b8 - b9 / (z + b10 + b11 / (z + b12))))));
} else {
alnorm = 0.5 -
z *
(a1 - a2 * y / (y + a3 - a4 / (y + a5 + a6 / (y + a7))));
}
} else {
alnorm = 0;
}
if (!upper) {
alnorm = 1 - alnorm;
}
return (alnorm);
}//end-method
/*
* Computes inverse cumulative distribution.
* From http://home.online.no/~pjacklam/notes/invnorm/
* Error is bounded to 1.15E-09
*
* @param p CDF probability
*
* @return Z value associated
*/
public double inverseNormalDistribution(double p){
double a1 = -3.969683028665376e+01;
double a2 = 2.209460984245205e+02;
double a3 = -2.759285104469687e+02;
double a4 = 1.383577518672690e+02;
double a5 = -3.066479806614716e+01;
double a6 = 2.506628277459239e+00;
double b1 = -5.447609879822406e+01;
double b2 = 1.615858368580409e+02;
double b3 = -1.556989798598866e+02;
double b4 = 6.680131188771972e+01;
double b5 = -1.328068155288572e+01;
double c1 = -7.784894002430293e-03;
double c2 = -3.223964580411365e-01;
double c3 = -2.400758277161838e+00;
double c4 = -2.549732539343734e+00;
double c5 = 4.374664141464968e+00;
double c6 = 2.938163982698783e+00;
double d1 = 7.784695709041462e-03;
double d2 = 3.224671290700398e-01;
double d3 = 2.445134137142996e+00;
double d4 = 3.754408661907416e+00;
double p_low = 0.02425;
double p_high = 1.0 - p_low;
double q;
double x=0.0;
double r;
if(p<=0){
return Double.NEGATIVE_INFINITY;
}
if(p>=1){
return Double.POSITIVE_INFINITY;
}
//Rational approximation for lower region.
if (p < p_low){
q = Math.sqrt(-2.0*Math.log(p));
x = (((((c1*q+c2)*q+c3)*q+c4)*q+c5)*q+c6) /
((((d1*q+d2)*q+d3)*q+d4)*q+1.0);
return x;
}
//Rational approximation for central region.
if (p <= p_high){
q = p - 0.5;
r = q*q;
x = (((((a1*r+a2)*r+a3)*r+a4)*r+a5)*r+a6)*q /
(((((b1*r+b2)*r+b3)*r+b4)*r+b5)*r+1.0);
return x;
}
//Rational approximation for upper region.
if (p_high < p){
q = Math.sqrt(-2.0*Math.log(1.0-p));
x = -(((((c1*q+c2)*q+c3)*q+c4)*q+c5)*q+c6) /
((((d1*q+d2)*q+d3)*q+d4)*q+1.0);
return x;
}
return x;
}//end-method
}//end-class