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///////////////////////////////////////////////////////////////////////////////
// For information as to what this class does, see the Javadoc, below. //
// Copyright (C) 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, //
// 2007, 2008, 2009, 2010, 2014, 2015, 2022 by Peter Spirtes, Richard //
// Scheines, Joseph Ramsey, and Clark Glymour. //
// //
// This program is free software; you can redistribute it and/or modify //
// it under the terms of the GNU General Public License as published by //
// the Free Software Foundation; either version 2 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 General Public License for more details. //
// //
// You should have received a copy of the GNU General Public License //
// along with this program; if not, write to the Free Software //
// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA //
///////////////////////////////////////////////////////////////////////////////
package edu.cmu.tetrad.util;
import org.apache.commons.math3.special.Gamma;
import org.apache.commons.math3.util.FastMath;
/**
* Frequency function of partial correlation r(12|34...k), assuming that the true partial correlation is equal to zero.
* Uses the equation (29.13.4) from Cramer's _Mathematical Methods of Statistics_.
*
* @author josephramsey
* @version $Id: $Id
*/
public class PartialCorrelationPdf implements Function, TetradSerializable {
private static final long serialVersionUID = 23L;
/**
* Number of data points in the sample.
*
* @serial
*/
private final int n;
/**
* Number of compared variables--that is, 2 + (#conditioning variables).
*
* @serial
*/
private final int k;
/**
* The power to which the variable expression is raised in the distribution function for zero partial correlation.
*
* @serial
*/
private final double outsideExp;
/**
* The aggregate value of the constant expression in the distribution function for zero partial correlation.
*
* @serial
*/
private double constant = Double.NaN;
//===========================CONSTRUCTORS========================//
/**
* Constructs a new zero partial correlation distribution function with the given values for n and k.
*
* @param n sample size
* @param k the number of variables being compared.
*/
public PartialCorrelationPdf(int n, int k) {
this.n = n;
this.k = k;
/*
The ratio of the two gamma expressions in the distribution function for
zero partial correlation.
*/
double gammaRatio = gammaRatio(n, k);
this.constant = (1 / FastMath.pow(FastMath.PI, 0.5)) * gammaRatio;
this.outsideExp = (double) (n - k - 2) / 2.0;
}
/**
* Generates a simple exemplar of this class to test serialization.
*
* @return the examplar.
*/
@SuppressWarnings("UnusedDeclaration")
public static PartialCorrelationPdf serializableInstance() {
return new PartialCorrelationPdf(5, 2);
}
//==========================PUBLIC METHODS========================//
/**
* {@inheritDoc}
*
* Calculates the value of the function at the given domain point.
*/
public double valueAt(double x) {
return this.constant * FastMath.pow(1 - x * x, this.outsideExp);
}
/**
* Calculates the ratio of gamma values in the distribution equation.
*
* @param n sample size
* @param k the number of variables being compared.
* @return this ratio.
*/
private double gammaRatio(int n, int k) {
double top = (n - k + 1) / 2.0;
double bottom = (n - k) / 2.0;
double lngamma = Gamma.logGamma(top) - Gamma.logGamma(bottom);
return FastMath.exp(lngamma);
}
/**
*
toString.
*
* @return a description of the function.
*/
public String toString() {
return "Zero partial correlation distribution with n = " + getN() +
" and k = " + getK() + "\n\n";
}
private int getN() {
return this.n;
}
/**
* Getter for the field k.
*
* @return Ibid.
*/
public int getK() {
return this.k;
}
}