Package com.metsci.glimpse.util.math.stat

Class BivariateGaussianDistributionUtils

java.lang.Object

com.metsci.glimpse.util.math.stat.BivariateGaussianDistributionUtils

public class BivariateGaussianDistributionUtils
extends Object

This class contains a collection of static methods for dealing with Bivariate Gaussian distributions.

Author:

moskowitz

Constructor Summary

Constructors

Constructor	Description
BivariateGaussianDistributionUtils()

Method Summary

Modifier and Type	Method	Description
static double[]	fromUnitCovarianceEllipse(double semiMajorAxisLength, double semiMinorAxisLength, double orientation)	Given the parameters defining the unit covariance ellipse for a Bivariate Gaussian distribution centered about the origin, this method returns sigmaX = Sqrt[Var(X)], sigmaY = Sqrt[Var(Y)], and correlation = Cov(X,Y) / (sigmaX sigmaY) for this probability distribution.
static void	main(String[] args)
static double[]	toUnitCovarianceEllipse(double sigmaX, double sigmaY, double correlation)	Returns the parameters defining the unit covariance ellipse for a Bivariate Gaussian distribution centered about the origin with given sigmaX, sigmaY, and correlation.

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

BivariateGaussianDistributionUtils

public BivariateGaussianDistributionUtils()

Method Detail

toUnitCovarianceEllipse

public static double[] toUnitCovarianceEllipse(double sigmaX,
                                               double sigmaY,
                                               double correlation)

Returns the parameters defining the unit covariance ellipse for a Bivariate Gaussian distribution centered about the origin with given sigmaX, sigmaY, and correlation. The unit covariance ellipse is a constant probability contour enclosing a 1-sigma area (probability of being inside the ellipse approximately equals 39.35%).

Note: correlation must be <= 1 and >= -1.

Ref: Data Analysis for Scientists and Engineers, Stuart Meyer, 1975, p.288-290.

Parameters:

sigmaX - X standard deviation = Sqrt[Var(X)]

sigmaY - Y standard deviation = Sqrt[Var(Y)]

correlation - correlation coefficient = Cov(X,Y) / (sigmaX sigmaY)

Returns:

array of size 3: {semi-major axis length, semi-minor axis length, orientation} of 1-sigma covariance ellipse

Throws:

IllegalArgumentException - if correlation is outside valid domain.

fromUnitCovarianceEllipse

public static double[] fromUnitCovarianceEllipse(double semiMajorAxisLength,
                                                 double semiMinorAxisLength,
                                                 double orientation)

Given the parameters defining the unit covariance ellipse for a Bivariate Gaussian distribution centered about the origin, this method returns sigmaX = Sqrt[Var(X)], sigmaY = Sqrt[Var(Y)], and correlation = Cov(X,Y) / (sigmaX sigmaY) for this probability distribution. The unit covariance ellipse is a constant probability contour enclosing a 1-sigma area (probability of being inside the ellipse approximately equals 39.35%).

Note: Calculation is based on COV = Q' R Q where Q is rotation matrix {cos,sin;-sin, cos} for given orientation and R is diagonal matrix {semiMaj, 0; 0, semiMin} for axis lengths. With COV computed, we get sigmaX = Sqrt[COV(0,0)], sigmaY = Sqrt[COV(1,1)], and finally correlation = COV(0,1)/(sigmaX * sigmaY).

Parameters:

semiMajorAxisLength - length of semi-major axis of 1-sigma covariance ellipse

semiMinorAxisLength - length of semi-minor axis of 1-sigma covariance ellipse

orientation - orientation of covariance ellipse (azimuth of semi-major axis)

Returns:

array of size 3: {sigmaX, sigmaY, correlation}

main

public static void main(String[] args)