agi.foundation

(agi.foundation.core-2024r3.jar)

Class GaussianStatistics

java.lang.Object

agi.foundation.GaussianStatistics

public final class GaussianStatistics
extends Object

Provides static methods helpful when working with Gaussian functions.

Method Summary

Modifier and Type	Method and Description
static double	complementaryErrorFunction(double x) Calculates the complement of GaussianStatistics.errorFunction(double).
static double	errorFunction(double x) Calculates the error function for all values of x.
static double	inverseComplementaryErrorFunction(double p) Calculates the inverse of the complementary error function.
static double	inverseErrorFunction(double p) Calculates the inverse of the error function.
static double	multiDimensionalConfidenceIntervals(int dimension, double sigmas) Calculates the fraction of the probability distribution of a specified dimension that lies within the confidence interval described by the specified number of standard deviations.
static double	multiDimensionalStandardDeviationFactor(int dimension, double probability) Calculates the number of standard deviations that describe the confidence interval which makes up the given portion of the probability distribution.

Methods inherited from class java.lang.Object

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

Method Detail

errorFunction

public static double errorFunction(double x)

Calculates the error function for all values of x.

Parameters:

x - The value to calculate the error function of.

Returns:

The error function of the given value.

complementaryErrorFunction

public static double complementaryErrorFunction(double x)

Calculates the complement of GaussianStatistics.errorFunction(double). By definition this complement plus the error function are equal to one.

Parameters:

x - The value to use to calculate the complement of the error function.

Returns:

The complement of the error function of the given value.

inverseComplementaryErrorFunction

public static double inverseComplementaryErrorFunction(double p)

Calculates the inverse of the complementary error function.

The GaussianStatistics.complementaryErrorFunction(double) approaches its asymptote very quickly, at double precision its solutions are rounded to 0.0 or 2.0 at an input of +-5.93. If this method returns negative or positive infinity and a finite value must be used instead, anything outside of that range would make an acceptable substitute.

Parameters:

p - The value to use to calculate the inverse of the complementary error function, from 0.0 to 2.0.

Returns:

The inverse of the complementary error function.

inverseErrorFunction

public static double inverseErrorFunction(double p)

Calculates the inverse of the error function.

The GaussianStatistics.errorFunction(double) approaches its asymptote very quickly, at double precision its solutions are rounded to -1.0 or 1.0 at an input of +-5.93. If this method returns negative or positive infinity and a finite value must be used instead, anything outside of that range would make an acceptable substitute.

Parameters:

p - The value to use to calculate the inverse of the error function, from -1.0 to 1.0.

Returns:

The inverse of the error function.

multiDimensionalConfidenceIntervals

public static double multiDimensionalConfidenceIntervals(int dimension,
                                                         double sigmas)

Calculates the fraction of the probability distribution of a specified dimension that lies within the confidence interval described by the specified number of standard deviations.

Parameters:

dimension - The dimension of the gaussian probability distribution.

sigmas - The width of the confidence interval in standard deviations.

Returns:

The fraction of the probability distribution within the confidence interval, between 0.0 and 1.0.

multiDimensionalStandardDeviationFactor

public static double multiDimensionalStandardDeviationFactor(int dimension,
                                                             double probability)

Calculates the number of standard deviations that describe the confidence interval which makes up the given portion of the probability distribution.

Parameters:

dimension - The dimension of the gaussian probability distribution.

probability - The desired probability that an event in the probability distribution lies in the confidence interval described by the returned number of standard deviations, from 0.0 to 1.0;

Returns:

The number of standard deviations necessary to provide the specified confidence interval.