package org.seqcode.math.probability;
public class NormalDistributionGio {
private double mean, variance, stddev;
private double coeff, logcoeff;
private double denom;
/**
* constructor
* @param m mean
* @param v variance
*/
public NormalDistributionGio(Double m, Double v)
{
mean = m;
variance = v;
coeff = 1.0 / Math.sqrt(2.0 * Math.PI * variance);
logcoeff = (Math.log(Math.PI) + Math.log(variance) + Math.log(2.0)) / -2.0;
denom = 2.0 * variance;
stddev = Math.sqrt(variance);
}//end of constructor method
/**
* <tt>value</tt> is following a normal distribution <tt>N(m,v)</tt>
* @param value the value whose z-score will be calculated
* @return the z-score of this <tt>value</tt>
*/
public double calcZScore(Double value) {
double diff = value - mean;
return Math.abs(diff / stddev);
}//end of calcZScore method
/**
* <tt>value</tt> is following a normal distribution <tt>N(m,v)</tt>
* @param value the value whose likelihood will be calculated
* @return the likelihood of this <tt>value</tt>
*/
public double calcProbability(Double value) {
return Math.exp(calcLogProbability(value));
}//end of calcProbability method
/**
* <tt>value</tt> is following a normal distribution <tt>N(m,v)</tt>
* @param value the value whose log-likelihood will be calculated
* @return the log-likelihood of this <tt>value</tt>
*/
public double calcLogProbability(Double value) {
double diff = value - mean;
double exponent = - (diff*diff) / denom;
return exponent + logcoeff;
}//end of calcLogProbability method
/**
* static method when we don't initialize the constructor<br>
* <tt>value</tt> is following a normal distribution <tt>N(mean,var)</tt>
* @param value the last value of a set of <tt>n</tt> data points whose (the set) total log-likelihood will be calculated
* @param n # of data points
* @param prevMean previous mean (of <tt>n-1</tt> data points)
* @param prevVar previous variance (of <tt>n-1</tt> data points)
* @return the likelihood of the set of <tt>n</tt> data points
*/
public double dynCalcTotalProbability(Double value, int n, Double prevMean, Double prevVar) {
return Math.exp(dynCalcTotalLogProbability(value, n, prevMean, prevVar));
}//end of dynCalcProbability method
/**
* <b>Total Log-likelihood</b><br>
* <pre>
* 1 n
* mean_n = mu_n = ---* Sum {y_i}
* n i=1
*
* 1 n
* var_n = (sigma_n)^2 = ---* Sum {(y_i - mean_n)^2} , where: sigma_n: standard deviation
* n i=1
*
* n 1
* total-log-lik_n = - --- * log(2*pi*var_n) - ------- * [(n-1)*( var_(n-1) + ( mean_n - mean_(n-1) )^2 ) + (y_n-mean_n)^2]
* 2 2*var_n
* </pre>
* where:
* <pre>
* n 1 (y_i - mean_n)^2
* total-log-lik_n = Sum { log(-----------------) - ----------------- }
* i=1 sqrt(2*pi*var_n) 2*var_n
* </pre>
*
* static method when we don't initialize the constructor<br>
* <tt>value</tt> is following a normal distribution <tt>N(mean,var)</tt>
* @param value the last value of a set of <tt>n</tt> data points whose (the set) total log-likelihood will be calculated
* @param n # of data points
* @param prevMean previous mean (of <tt>n-1</tt> data points)
* @param prevVar previous variance (of <tt>n-1</tt> data points)
* @return the log-likelihood of the set of <tt>n</tt> data points
*/
public double dynCalcTotalLogProbability(Double value, int n, Double prevMean, Double prevVar) {
return -((double)n/2)*Math.log(2.0*Math.PI*variance) - (1/(2.0*variance))*((n-1)*(prevVar + (mean-prevMean)*(mean-prevMean)) + (value-mean)*(value-mean));
}//end of dynCalcLogProbability method
/**********************
*** STATIC METHODS ***
**********************/
/**
* static method when we don't initialize the constructor<br>
* <tt>value</tt> is following a normal distribution <tt>N(mean,var)</tt>
* @param value value the value whose z-score will be calculated
* @param mean mean
* @param var variance
* @return the z-score of this <tt>value</tt>
*/
public static double calcZScore(Double value, Double mean, Double var)
{
double diff = value - mean;
double stddev = Math.sqrt(var);
return Math.abs(diff / stddev);
}//end of static calcZScore method
/**
* static method when we don't initialize the constructor<br>
* <tt>value</tt> is following a normal distribution <tt>N(mean,var)</tt>
* @param value the value whose likelihood will be calculated
* @param mean mean
* @param var variance
* @return the likelihood of this <tt>value</tt>
*/
public static double calcProbability(Double value, Double mean, Double var) {
return Math.exp(calcLogProbability(value, mean, var));
}//end of static calcProbability method
/**
* static method when we don't initialize the constructor<br>
* <tt>value</tt> is following a normal distribution <tt>N(mean,var)</tt>
* @param value the value whose log-likelihood will be calculated
* @param mean mean
* @param var variance
* @return the log-likelihood of this <tt>value</tt>
*/
public static double calcLogProbability(Double value, Double mean, Double var) {
double logcoeff = (Math.log(Math.PI) + Math.log(var) + Math.log(2.0)) / -2.0;
double denom = 2.0*var;
double diff = value - mean;
double exponent = - (diff*diff) / denom;
return exponent + logcoeff;
}//end of static calcLogProbability method
/**
* static method when we don't initialize the constructor<br>
* <tt>value</tt> is following a normal distribution <tt>N(mean,var)</tt>
* @param value the last value of a set of <tt>n</tt> data points whose (the set) total log-likelihood will be calculated
* @param n # of data points
* @param mean current mean (of <tt>n</tt> data points)
* @param var current variance (of <tt>n</tt> data points)
* @param prevMean previous mean (of <tt>n-1</tt> data points)
* @param prevVar previous variance (of <tt>n-1</tt> data points)
* @return the likelihood of the set of <tt>n</tt> data points
*/
public static double dynCalcTotalProbability(Double value, int n, Double mean, Double var, Double prevMean, Double prevVar) {
return Math.exp(dynCalcTotalLogProbability(value, n, mean, var, prevMean, prevVar));
}//end of static dynCalcProbability method
/**
* <b>Total Log-likelihood</b><br>
* <pre>
* 1 n
* mean_n = mu_n = ---* Sum {y_i}
* n i=1
*
* 1 n
* var_n = (sigma_n)^2 = ---* Sum {(y_i - mean_n)^2} , where: sigma_n: standard deviation
* n i=1
*
* n 1
* total-log-lik_n = - --- * log(2*pi*var_n) - ------- * [(n-1)*( var_(n-1) + ( mean_n - mean_(n-1) )^2 ) + (y_n-mean_n)^2]
* 2 2*var_n
* </pre>
* where:
* <pre>
* n 1 (y_i - mean_n)^2
* total-log-lik_n = Sum { log(-----------------) - ----------------- }
* i=1 sqrt(2*pi*var_n) 2*var_n
* </pre>
*
* static method when we don't initialize the constructor<br>
* <tt>value</tt> is following a normal distribution <tt>N(mean,var)</tt>
* @param value the last value of a set of <tt>n</tt> data points whose (the set) total log-likelihood will be calculated
* @param n # of data points
* @param mean current mean (of <tt>n</tt> data points)
* @param var current variance (of <tt>n</tt> data points)
* @param prevMean previous mean (of <tt>n-1</tt> data points)
* @param prevVar previous variance (of <tt>n-1</tt> data points)
* @return the log-likelihood of the set of <tt>n</tt> data points
*/
public static double dynCalcTotalLogProbability(Double value, int n, Double mean, Double var, Double prevMean, Double prevVar) {
return -((double)n/2)*Math.log(2.0*Math.PI*var) - (1/(2.0*var))*((n-1)*(prevVar + (mean-prevMean)*(mean-prevMean)) + (value-mean)*(value-mean));
}//end of static dynCalcLogProbability method
}//end of NormalDistributionGio class