Package org.drip.measure.chisquare

Class R1WilsonHilferty

java.lang.Object
org.drip.measure.continuous.R1Univariate
org.drip.measure.chisquare.R1WilsonHilferty
Direct Known Subclasses:
R1CentralWilsonHilferty, R1NonCentralWilsonHaferty
public abstract class R1WilsonHilferty
extends R1Univariate
R1CentralWilsonHilferty implements the Normal Proxy Version for the R1 Chi-Square Distribution using the Wilson-Hilferty Transformation. The References are:

  • Abramowitz, M., and I. A. Stegun (2007): Handbook of Mathematics Functions Dover Book on Mathematics
  • Backstrom, T., and J. Fischer (2018): Fast Randomization for Distributed Low Bit-rate Coding of Speech and Audio IEEE/ACM Transactions on Audio, Speech, and Language Processing 26 (1) 19-30
  • Chi-Squared Distribution (2019): Chi-Squared Function https://en.wikipedia.org/wiki/Chi-squared_distribution
  • Johnson, N. L., S. Kotz, and N. Balakrishnan (1994): Continuous Univariate Distributions 2nd Edition John Wiley and Sons
  • National Institute of Standards and Technology (2019): Chi-Squared Distribution https://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm


Author:
Lakshmi Krishnamurthy

  • Method Details

    • degreesOfFreedom

      public double degreesOfFreedom()
      Retrieve the Degrees of Freedom
      Returns:
      The Degrees of Freedom

    • r1UnivariateNormal

      public R1UnivariateNormal r1UnivariateNormal()
      Retrieve the R1 Univariate Normal
      Returns:
      The R1 Univariate Normal

    • transform

      public abstract double transform​(double x)
      Transform x into the Wilson-Hilferty Variate
      Parameters:
      x - X
      Returns:
      The Wilson-Hilferty Variate

    • inverseTransform

      public abstract double inverseTransform​(double wilsonHilferty)
      Transform the Wilson-Hilferty Variate into x
      Parameters:
      wilsonHilferty - The Wilson-Hilferty Variate
      Returns:
      The Wilson-Hilferty Variate transformed back to x

    • support

      public double[] support()
      Description copied from class: R1Univariate
      Lay out the Support of the PDF Range
      Specified by:
      support in class R1Univariate
      Returns:
      Support of the PDF Range

    • density

      public double density​(double t) throws java.lang.Exception
      Description copied from class: R1Univariate
      Compute the Density under the Distribution at the given Variate
      Specified by:
      density in class R1Univariate
      Parameters:
      t - Variate at which the Density needs to be computed
      Returns:
      The Density
      Throws:
      java.lang.Exception - Thrown if the input is invalid

    • cumulative

      public double cumulative​(double t) throws java.lang.Exception
      Description copied from class: R1Univariate
      Compute the cumulative under the distribution to the given value
      Specified by:
      cumulative in class R1Univariate
      Parameters:
      t - Variate to which the cumulative is to be computed
      Returns:
      The cumulative
      Throws:
      java.lang.Exception - Thrown if the inputs are invalid

    • invCumulative

      public double invCumulative​(double y) throws java.lang.Exception
      Description copied from class: R1Univariate
      Compute the inverse cumulative under the distribution corresponding to the given value
      Overrides:
      invCumulative in class R1Univariate
      Parameters:
      y - Value corresponding to which the inverse cumulative is to be computed
      Returns:
      The inverse cumulative
      Throws:
      java.lang.Exception - Thrown if the Input is invalid

    • mean

      public double mean() throws java.lang.Exception
      Description copied from class: R1Univariate
      Retrieve the Mean of the Distribution
      Specified by:
      mean in class R1Univariate
      Returns:
      The Mean of the Distribution
      Throws:
      java.lang.Exception - Thrown if the Mean cannot be estimated

    • median

      public double median() throws java.lang.Exception
      Description copied from class: R1Univariate
      Retrieve the Median of the Distribution
      Overrides:
      median in class R1Univariate
      Returns:
      The Median of the Distribution
      Throws:
      java.lang.Exception - Thrown if the Median cannot be estimated

    • mode

      public double mode() throws java.lang.Exception
      Description copied from class: R1Univariate
      Retrieve the Mode of the Distribution
      Overrides:
      mode in class R1Univariate
      Returns:
      The Mode of the Distribution
      Throws:
      java.lang.Exception - Thrown if the Mode cannot be estimated

    • variance

      public double variance() throws java.lang.Exception
      Description copied from class: R1Univariate
      Retrieve the Variance of the Distribution
      Specified by:
      variance in class R1Univariate
      Returns:
      The Variance of the Distribution
      Throws:
      java.lang.Exception - Thrown if the Variance cannot be estimated

    • skewness

      public double skewness() throws java.lang.Exception
      Description copied from class: R1Univariate
      Retrieve the Skewness of the Distribution
      Overrides:
      skewness in class R1Univariate
      Returns:
      The Skewness of the Distribution
      Throws:
      java.lang.Exception - Thrown if the Skewness cannot be estimated

    • excessKurtosis

      public double excessKurtosis() throws java.lang.Exception
      Description copied from class: R1Univariate
      Retrieve the Excess Kurtosis of the Distribution
      Overrides:
      excessKurtosis in class R1Univariate
      Returns:
      The Excess Kurtosis of the Distribution
      Throws:
      java.lang.Exception - Thrown if the Skewness cannot be estimated

    • momentGeneratingFunction

      public R1ToR1 momentGeneratingFunction()
      Description copied from class: R1Univariate
      Construct the Moment Generating Function
      Overrides:
      momentGeneratingFunction in class R1Univariate
      Returns:
      The Moment Generating Function

    • probabilityGeneratingFunction

      public R1ToR1 probabilityGeneratingFunction()
      Description copied from class: R1Univariate
      Construct the Probability Generating Function
      Overrides:
      probabilityGeneratingFunction in class R1Univariate
      Returns:
      The Probability Generating Function