Package com.irurueta.statistics

Class NormalDist

java.lang.Object
com.irurueta.statistics.NormalDist
public class NormalDist extends Object
Contains methods to work with normal (i.e. Gaussian) distributions. Methods of this class use methods of the Erf class. This class is based in code of Numerical Recipes 3rd ed. section 6.14.1.

  • Nested Class Summary

    Nested Classes
    Modifier and Type
    Class
    Description
    static interface 
    NormalDist.DerivativeEvaluator
    Interface to evaluate a one dimensional function at point x and to obtain its derivative at such point.

  • Field Summary

    Fields
    Modifier and Type
    Field
    Description
    private static final double
    GAUSSIAN_NORM
    Term to normalize Gaussian so that its integral from -infinity to infinity is one.
    private static final double
    HALF_SQRT2
    Square root of 2 divided by 2.
    private double
    mu
    Mean value of Gaussian distribution.
    private double
    sig
    Standard deviation of Gaussian distribution.
    private static final double
    SQRT2
    Square root of 2.

  • Constructor Summary

    Constructors
    Constructor
    Description
    NormalDist()
    Constructor.
    NormalDist(double mu, double sig)
    Constructor with mean and standard deviation.

  • Method Summary

    Modifier and Type
    Method
    Description
    double
    cdf(double x)
    Evaluates the cumulative distribution function (c.d.f.) of a Gaussian distribution having the mean and standard deviation of this instance at provided point x.
    static double
    cdf(double x, double mu, double sig)
    Evaluates the cumulative distribution function (c.d.f.) of a Gaussian distribution having mean mu and standard deviation sig at provided point x.
    double
    getMean()
    Gets mean value of Gaussian distribution.
    double
    getStandardDeviation()
    Gets standard deviation of Gaussian distribution.
    double
    getVariance()
    Gets variance of Gaussian distribution.
    private static double
    internalCdf(double x, double mu, double sig)
    Evaluates the cumulative distribution function (c.d.f.) of a Gaussian distribution having mean mu and standard deviation sig at provided point x.
    private static double
    internalInvcdf(double p, double mu, double sig)
    Evaluates the inverse cumulative distribution function of a Gaussian distribution having mean mu and standard deviation sig at provided point p.
    private static double
    internalMahalanobisDistance(double x, double mu, double sig)
    Computes the Mahalanobis distance of provided point x for provided mean and standard deviation values.
    private static double
    internalP(double x, double mu, double sig)
    Evaluates the probability density function (p.d.f.) of a Gaussian distribution having mean mu and standard deviation sig at provided point x.
    double
    invcdf(double p)
    Evaluates the inverse cumulative distribution function of a Gaussian distribution having the mean and standard deviation of this instance at provided point p.
    static double
    invcdf(double p, double mu, double sig)
    Evaluates the inverse cumulative distribution function of a Gaussian distribution having mean mu and standard deviation sig at provided point p.
    double
    mahalanobisDistance(double x)
    Computes the Mahalanobis distance of provided point x for current mean and standard deviation values.
    static double
    mahalanobisDistance(double x, double mu, double sig)
    Computes the Mahalanobis distance of provided point x for provided mean and standard deviation values.
    double
    p(double x)
    Evaluates the probability density function (p.d.f.) of a Gaussian distribution having the mean and standard deviation of this instance at provided point x.
    static double
    p(double x, double mu, double sig)
    Evaluates the probability density function (p.d.f.) of a Gaussian distribution having mean mu and standard deviation sig at provided point x.
    static NormalDist
    propagate(NormalDist.DerivativeEvaluator evaluator, double mean, double standardDeviation)
    Evaluates the derivative and a 1D function at a certain mean point and computes the non-linear propagation of Gaussian uncertainty through such function at such point.
    static void
    propagate(NormalDist.DerivativeEvaluator evaluator, double mean, double standardDeviation, NormalDist result)
    Evaluates the derivative and a 1D function at a certain mean point and computes the non-linear propagation of Gaussian uncertainty through such function at such point.
    static NormalDist
    propagate(NormalDist.DerivativeEvaluator evaluator, NormalDist dist)
    Evaluates the derivative and a 1D function at a certain mean point and computes the non-linear propagation of Gaussian uncertainty through such function at such point.
    static void
    propagate(NormalDist.DerivativeEvaluator evaluator, NormalDist dist, NormalDist result)
    Evaluates the derivative and a 1D function at a certain mean point and computes the non-linear propagation of Gaussian uncertainty through such function at such point.
    NormalDist
    propagateThisDistribution(NormalDist.DerivativeEvaluator evaluator)
    Evaluates the derivative and a 1D function at the mean point of this normal distribution and computes the non-linear propagation of Gaussian uncertainty through such function at such point.
    void
    propagateThisDistribution(NormalDist.DerivativeEvaluator evaluator, NormalDist result)
    Evaluates the derivative and a 1D function at the mean point of this normal distribution and computes the non-linear propagation of Gaussian uncertainty through such function at such point.
    final void
    setMean(double mu)
    Sets mean value of Gaussian distribution.
    final void
    setStandardDeviation(double sig)
    Sets standard deviation of Gaussian distribution.
    void
    setVariance(double variance)
    Sets variance of Gaussian distribution.

    Methods inherited from class java.lang.Object

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

  • Field Details

    • SQRT2

      private static final double SQRT2
      Square root of 2.

    • HALF_SQRT2

      private static final double HALF_SQRT2
      Square root of 2 divided by 2.

    • GAUSSIAN_NORM

      private static final double GAUSSIAN_NORM
      Term to normalize Gaussian so that its integral from -infinity to infinity is one.

    • mu

      private double mu
      Mean value of Gaussian distribution.

    • sig

      private double sig
      Standard deviation of Gaussian distribution.

  • Constructor Details

    • NormalDist

      public NormalDist()
      Constructor. Initializes a Gaussian distribution with zero mean and unitary standard deviation (i.e. N(0,1)).

    • NormalDist

      public NormalDist(double mu, double sig)
      Constructor with mean and standard deviation.
      Parameters:
      mu - mean value of Gaussian distribution.
      sig - standard deviation of Gaussian distribution.
      Throws:
      IllegalArgumentException - if provided standard deviation is zero or negative.

  • Method Details

    • getMean

      public double getMean()
      Gets mean value of Gaussian distribution.
      Returns:
      mean value of Gaussian distribution.

    • setMean

      public final void setMean(double mu)
      Sets mean value of Gaussian distribution.
      Parameters:
      mu - mean value of Gaussian distribution.

    • getStandardDeviation

      public double getStandardDeviation()
      Gets standard deviation of Gaussian distribution.
      Returns:
      standard deviation of Gaussian distribution.

    • setStandardDeviation

      public final void setStandardDeviation(double sig)
      Sets standard deviation of Gaussian distribution.
      Parameters:
      sig - standard deviation to be set.
      Throws:
      IllegalArgumentException - if provided standard deviation is zero or negative.

    • getVariance

      public double getVariance()
      Gets variance of Gaussian distribution.
      Returns:
      variance of Gaussian distribution.

    • setVariance

      public void setVariance(double variance)
      Sets variance of Gaussian distribution.
      Parameters:
      variance - variance of Gaussian distribution.
      Throws:
      IllegalArgumentException - if provided variance is zero or negative.

    • p

      public static double p(double x, double mu, double sig)
      Evaluates the probability density function (p.d.f.) of a Gaussian distribution having mean mu and standard deviation sig at provided point x.
      Parameters:
      x - point where p.d.f. is evaluated.
      mu - mean of Gaussian distribution.
      sig - standard deviation of Gaussian distribution.
      Returns:
      evaluation of p.d.f.
      Throws:
      IllegalArgumentException - if provided standard deviation is zero or negative.

    • p

      public double p(double x)
      Evaluates the probability density function (p.d.f.) of a Gaussian distribution having the mean and standard deviation of this instance at provided point x.
      Parameters:
      x - point where p.d.f. is evaluated.
      Returns:
      evaluation of p.d.f.

    • cdf

      public static double cdf(double x, double mu, double sig)
      Evaluates the cumulative distribution function (c.d.f.) of a Gaussian distribution having mean mu and standard deviation sig at provided point x. The c.d.f is equivalent to the probability of the Gaussian distribution of having a value less than x, and it is computed as the integral from -infinity to x of the Gaussian p.d.f.
      Parameters:
      x - point where c.d.f. is evaluated.
      mu - mean of Gaussian distribution.
      sig - standard deviation of Gaussian distribution.
      Returns:
      evaluation of c.d.f.
      Throws:
      IllegalArgumentException - if provided standard deviation is zero or negative.

    • cdf

      public double cdf(double x)
      Evaluates the cumulative distribution function (c.d.f.) of a Gaussian distribution having the mean and standard deviation of this instance at provided point x. The c.d.f is equivalent to the probability of the Gaussian distribution of having a value less than x, and it is computed as the integral from -infinity to x of the Gaussian p.d.f. Because the c.d.f is a probability, it always returns values between 0.0 and 1.0.
      Parameters:
      x - point where c.d.f. is evaluated.
      Returns:
      evaluation of c.d.f.

    • invcdf

      public static double invcdf(double p, double mu, double sig)
      Evaluates the inverse cumulative distribution function of a Gaussian distribution having mean mu and standard deviation sig at provided point p. Because the c.d.f is a monotonically increasing function with values between 0.0 and 1.0, its inverse is uniquely defined between such range of values.
      Parameters:
      p - value to evaluate the inverse c.d.f. at. This value is equivalent to a probability and must be between 0.0 and 1.0.
      mu - mean of Gaussian distribution.
      sig - standard deviation of Gaussian distribution.
      Returns:
      the value x for which the c.d.f. has value p.
      Throws:
      IllegalArgumentException - if provided standard deviation is zero or negative, or if provided probability value is not between 0.0 and 1.0.

    • invcdf

      public double invcdf(double p)
      Evaluates the inverse cumulative distribution function of a Gaussian distribution having the mean and standard deviation of this instance at provided point p. Because the c.d.f is a monotonically increasing function with values between 0.0 and 1.0, its inverse is uniquely defined between such range of values.
      Parameters:
      p - value to evaluate the inverse c.d.f. at. This value is equivalent to a probability and must be between 0.0 and 1.0.
      Returns:
      the value x for which the c.d.f. has value p.
      Throws:
      IllegalArgumentException - if provided probability value is not between 0.0 and 1.0.

    • mahalanobisDistance

      public static double mahalanobisDistance(double x, double mu, double sig)
      Computes the Mahalanobis distance of provided point x for provided mean and standard deviation values.
      Parameters:
      x - point where Mahalanobis distance is evaluated.
      mu - mean of Gaussian distribution.
      sig - standard deviation of Gaussian distribution.
      Returns:
      Mahalanobis distance of provided point respect to mean.
      Throws:
      IllegalArgumentException - if provided standard deviation is zero or negative.

    • mahalanobisDistance

      public double mahalanobisDistance(double x)
      Computes the Mahalanobis distance of provided point x for current mean and standard deviation values.
      Parameters:
      x - point where Mahalanobis distance is evaluated.
      Returns:
      Mahalanobis distance of provided point respect to current mean.

    • internalP

      private static double internalP(double x, double mu, double sig)
      Evaluates the probability density function (p.d.f.) of a Gaussian distribution having mean mu and standard deviation sig at provided point x. This method is used internally.
      Parameters:
      x - point where p.d.f. is evaluated.
      mu - mean of Gaussian distribution.
      sig - standard deviation of Gaussian distribution.
      Returns:
      evaluation of p.d.f.
      Throws:
      IllegalArgumentException - if provided standard deviation is zero or negative.

    • internalCdf

      private static double internalCdf(double x, double mu, double sig)
      Evaluates the cumulative distribution function (c.d.f.) of a Gaussian distribution having mean mu and standard deviation sig at provided point x. The c.d.f is equivalent to the probability of the Gaussian distribution of having a value less than x, and it is computed as the integral from -infinity to x of the Gaussian p.d.f. This method is used internally.
      Parameters:
      x - point where c.d.f. is evaluated.
      mu - mean of Gaussian distribution.
      sig - standard deviation of Gaussian distribution.
      Returns:
      evaluation of c.d.f.
      Throws:
      IllegalArgumentException - if provided standard deviation is zero or negative.

    • internalInvcdf

      private static double internalInvcdf(double p, double mu, double sig) throws IllegalArgumentException
      Evaluates the inverse cumulative distribution function of a Gaussian distribution having mean mu and standard deviation sig at provided point p. Because the c.d.f is a monotonically increasing function with values between 0.0 and 1.0, its inverse is uniquely defined between such range of values. This method is used internally.
      Parameters:
      p - value to evaluate the inverse c.d.f. at. This value is equivalent to a probability and must be between 0.0 and 1.0.
      mu - mean of Gaussian distribution.
      sig - standard deviation of Gaussian distribution.
      Returns:
      the value x for which the c.d.f. has value p.
      Throws:
      IllegalArgumentException - if provided probability value is not between 0.0 and 1.0.

    • internalMahalanobisDistance

      private static double internalMahalanobisDistance(double x, double mu, double sig)
      Computes the Mahalanobis distance of provided point x for provided mean and standard deviation values.
      Parameters:
      x - point where Mahalanobis distance is evaluated.
      mu - mean of Gaussian distribution.
      sig - standard deviation of Gaussian distribution.
      Returns:
      Mahalanobis distance of provided point respect to mean.

    • propagate

      public static void propagate(NormalDist.DerivativeEvaluator evaluator, double mean, double standardDeviation, NormalDist result)
      Evaluates the derivative and a 1D function at a certain mean point and computes the non-linear propagation of Gaussian uncertainty through such function at such point.
      Parameters:
      evaluator - interface to evaluate derivative of a function at a certain point.
      mean - mean of original Gaussian distribution to be propagated.
      standardDeviation - standard deviation of original Gaussian distribution to be propagated.
      result - instance where propagated Gaussian distribution will be stored.
      See Also:

    • propagate

      public static NormalDist propagate(NormalDist.DerivativeEvaluator evaluator, double mean, double standardDeviation)
      Evaluates the derivative and a 1D function at a certain mean point and computes the non-linear propagation of Gaussian uncertainty through such function at such point.
      Parameters:
      evaluator - interface to evaluate derivative of a function at a certain point.
      mean - mean of original Gaussian distribution to be propagated.
      standardDeviation - standard deviation of original Gaussian distribution to be propagated.
      Returns:
      a new propagated Gaussian distribution.
      See Also:

    • propagate

      public static void propagate(NormalDist.DerivativeEvaluator evaluator, NormalDist dist, NormalDist result)
      Evaluates the derivative and a 1D function at a certain mean point and computes the non-linear propagation of Gaussian uncertainty through such function at such point.
      Parameters:
      evaluator - interface to evaluate derivative of a function at a certain point.
      dist - 1D Gaussian distribution to be propagated.
      result - instance where propagated Gaussian distribution will be stored.
      See Also:

    • propagate

      public static NormalDist propagate(NormalDist.DerivativeEvaluator evaluator, NormalDist dist)
      Evaluates the derivative and a 1D function at a certain mean point and computes the non-linear propagation of Gaussian uncertainty through such function at such point.
      Parameters:
      evaluator - interface to evaluate derivative of a function at a certain point.
      dist - 1D Gaussian distribution to be propagated.
      Returns:
      a new propagated Gaussian distribution.
      See Also:

    • propagateThisDistribution

      public void propagateThisDistribution(NormalDist.DerivativeEvaluator evaluator, NormalDist result)
      Evaluates the derivative and a 1D function at the mean point of this normal distribution and computes the non-linear propagation of Gaussian uncertainty through such function at such point.
      Parameters:
      evaluator - interface to evaluate derivative of a function at the mean point of this normal distribution.
      result - instance where propagated Gaussian distribution will be stored.
      See Also:

    • propagateThisDistribution

      public NormalDist propagateThisDistribution(NormalDist.DerivativeEvaluator evaluator)
      Evaluates the derivative and a 1D function at the mean point of this normal distribution and computes the non-linear propagation of Gaussian uncertainty through such function at such point.
      Parameters:
      evaluator - interface to evaluate derivative of a function at the mean point of this normal distribution.
      Returns:
      a new propagated Gaussian distribution.
      See Also: