Module org.bzdev.math
Package org.bzdev.math.stats

Class GaussianDistr

java.lang.Object
org.bzdev.math.stats.ProbDistribution
org.bzdev.math.stats.GaussianDistr
All Implemented Interfaces:
RealValuedDomainOps
public class GaussianDistr extends ProbDistribution
Class providing methods for Gaussian/Normal distributions. The use of A, P and Q follows the convention in Abramowitz and Stegun, "Handbook of Mathematical Functions" (10th printing [1972], 9th Dover printing), chapter 26. Some of the methods have names that start with an upper-case letter, contrary to the usual Java convention, in order to conform to this text.

  • Constructor Summary

    Constructors
    Constructor
    Description
    GaussianDistr()
    Constructor.
    GaussianDistr(double mu, double sigma)
    Constructor given a mean and standard deviation.

  • Method Summary

    Modifier and Type
    Method
    Description
    double
    A(double x)
    Get the probability that a value is within the range [-x, x].
    static double
    A(double x, double mu, double sigma)
    Compute the probability that a value deviates from 0 by no more than a specified amount given a Gaussian distribution with a variance of σ2 and a mean of μ.
    boolean
    isSymmetric(double x)
    Determine if this distribution is symmetric about x.
    double
    P(double x)
    Get the probability that a value is no larger than the argument
    static double
    P(double x, double mu, double sigma)
    Compute the cumulative probability function for a Gaussian distribution with a variance of σ2 and a mean of μ.
    double
    pd(double x)
    Get the probability density
    static double
    pd(double x, double mu, double sigma)
    Compute the probability density for a Gaussian distribution with a variance of σ2 and a mean of μ.
    double
    Q(double x)
    Get the probability that a value is no smaller than the argument
    static double
    Q(double x, double mu, double sigma)
    Compute the complement of the cumulative probability function for a Gaussian distribution with a variance of σ2 and a mean of μ.

    Methods inherited from class org.bzdev.math.stats.ProbDistribution

    cdf, cdfc, domainMaxClosed, domainMinClosed, getDomainMax, getDomainMin, inverseA, inverseP, inverseQ, isInDomain

    Methods inherited from class java.lang.Object

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

  • Constructor Details

    • GaussianDistr

      public GaussianDistr()
      Constructor. The mean is 0.0 and the standard deviation is 1.0.

    • GaussianDistr

      public GaussianDistr(double mu, double sigma)
      Constructor given a mean and standard deviation.
      Parameters:
      mu - the mean value for the distribution (μ)
      sigma - the standard deviation for the distribution (σ)

  • Method Details

    • isSymmetric

      public boolean isSymmetric(double x)
      Description copied from class: ProbDistribution
      Determine if this distribution is symmetric about x. A distribution is symmetric if its probability density f satisfies f(x+y) = f(x-y) and that if x+y is in f's domain, so is x-y. Equivalently, it must satisfy Q(x+y) = P(x-y).
      Specified by:
      isSymmetric in class ProbDistribution
      Parameters:
      x - the point about which to test if this distribution is symmaetric
      Returns:
      true if it is symmetric; false otherwise.

    • pd

      public double pd(double x)
      Description copied from class: ProbDistribution
      Get the probability density
      Overrides:
      pd in class ProbDistribution
      Parameters:
      x - the value for which the density is to be computed
      Returns:
      the probability density

    • P

      public double P(double x)
      Description copied from class: ProbDistribution
      Get the probability that a value is no larger than the argument
      Specified by:
      P in class ProbDistribution
      Parameters:
      x - the argument
      Returns:
      the probability

    • Q

      public double Q(double x)
      Description copied from class: ProbDistribution
      Get the probability that a value is no smaller than the argument
      Overrides:
      Q in class ProbDistribution
      Parameters:
      x - the argument
      Returns:
      the probability

    • A

      public double A(double x)
      Description copied from class: ProbDistribution
      Get the probability that a value is within the range [-x, x]. This method is meaningful for distributions that are symmetric about 0. When this is not the case, an UnsupportedOperationException should be thrown.
      Overrides:
      A in class ProbDistribution
      Parameters:
      x - the argument
      Returns:
      the probability that a value is in the range [-x, x]

    • pd

      public static double pd(double x, double mu, double sigma)
      Compute the probability density for a Gaussian distribution with a variance of σ2 and a mean of μ.
      Parameters:
      x - a value in the range [-∞,∞]
      mu - the mean μ
      sigma - the standard deviation σ
      Returns:
      the probability density

    • P

      public static double P(double x, double mu, double sigma)
      Compute the cumulative probability function for a Gaussian distribution with a variance of σ2 and a mean of μ.
      Parameters:
      x - a value in the range [-∞,∞]
      mu - the mean μ
      sigma - the standard deviation σ
      Returns:
      the cumulative probability P(x,μ,σ)

    • Q

      public static double Q(double x, double mu, double sigma)
      Compute the complement of the cumulative probability function for a Gaussian distribution with a variance of σ2 and a mean of μ. This is equal to 1 - P(x,μ σ) when the computation is exact.
      Parameters:
      x - a value in the range [-∞,∞]
      mu - the mean μ
      sigma - the standard deviation σ
      Returns:
      the complement, 1 - P(x,μ σ), of the cumulative probability

    • A

      public static double A(double x, double mu, double sigma)
      Compute the probability that a value deviates from 0 by no more than a specified amount given a Gaussian distribution with a variance of σ2 and a mean of μ. of 1.0. The probability is equal to the integral of the probability density from -x to x.
      Parameters:
      x - the maximum value for an interval.
      mu - the mean μ
      sigma - the standard deviation σ
      Returns:
      the probability that a value is in the range [-x,x]