Package org.drip.measure.exponential

Class R1ScaledDistribution

java.lang.Object
org.drip.measure.continuous.R1Distribution
org.drip.measure.exponential.R1ScaledDistribution
public class R1ScaledDistribution
extends R1Distribution
R1ScaledDistribution implements the Probability Density Function for the Scaled R1 Exponential Function. The References are:

  • Gradshteyn, I. S., I. M. Ryzhik, Y. V. Geronimus, M. Y. Tseytlin, and A. Jeffrey (2015): Tables of Integrals, Series, and Products Academic Press
  • Hilfer, J. (2002): H-function Representations for Stretched Exponential Relaxation and non-Debye Susceptibilities in Glassy Systems Physical Review E 65 (6) 061510
  • Wikipedia (2019): Stretched Exponential Function https://en.wikipedia.org/wiki/Stretched_exponential_function
  • Wuttke, J. (2012): Laplace-Fourier Transform of the Stretched Exponential Function: Analytic Error-Bounds, Double Exponential Transform, and Open Source Implementation libkw Algorithm 5 (4) 604-628
  • Zorn, R. (2002): Logarithmic Moments of Relaxation Time Distributions Journal of Chemical Physics 116 (8) 3204-3209
It provides the following Functionality:
  • R1ScaledDistribution Constructor
  • Retrieve the Scaled Exponential Estimator
  • Retrieve the Gamma Estimator
  • Lay out the Support of the PDF Range
  • Compute the Density under the Distribution at the given Variate
  • Compute the cumulative under the distribution to the given value
  • Compute the Incremental under the Distribution between the 2 variates
  • Retrieve the Mean of the Distribution
  • Retrieve the Variance of the Distribution
  • Retrieve the Normalizer
  • Retrieve the "Lambda" Parameter

Module Computational Core Module
Library Numerical Analysis Library
Project Rd Continuous/Discrete Probability Measures
Package R1 and Rd Continuous Random Measure

Author:
Lakshmi Krishnamurthy

  • Constructor Details

    • R1ScaledDistribution

      public R1ScaledDistribution​(ScaledExponentialEstimator scaledExponentialEstimator, R1ToR1 gammaEstimator) throws java.lang.Exception
      R1ScaledDistribution Constructor
      Parameters:
      scaledExponentialEstimator - Scaled Exponential Estimator
      gammaEstimator - Gamma Estimator
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid

  • Method Details

    • scaledExponentialEstimator

      public ScaledExponentialEstimator scaledExponentialEstimator()
      Retrieve the Scaled Exponential Estimator
      Returns:
      Scaled Exponential Estimator

    • gammaEstimator

      public R1ToR1 gammaEstimator()
      Retrieve the Gamma Estimator
      Returns:
      Gamma Estimator

    • support

      public double[] support()
      Lay out the Support of the PDF Range
      Specified by:
      support in class R1Distribution
      Returns:
      Support of the PDF Range

    • density

      public double density​(double t) throws java.lang.Exception
      Compute the Density under the Distribution at the given Variate
      Specified by:
      density in class R1Distribution
      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
      Compute the cumulative under the distribution to the given value
      Specified by:
      cumulative in class R1Distribution
      Parameters:
      t - Variate to which the cumulative is to be computed
      Returns:
      The cumulative
      Throws:
      java.lang.Exception - Thrown if the inputs are invalid

    • incremental

      public double incremental​(double t1, double t2) throws java.lang.Exception
      Compute the Incremental under the Distribution between the 2 variates
      Overrides:
      incremental in class R1Distribution
      Parameters:
      t1 - Left Variate to which the cumulative is to be computed
      t2 - Right Variate to which the cumulative is to be computed
      Returns:
      The Incremental under the Distribution between the 2 variates
      Throws:
      java.lang.Exception - Thrown if the inputs are invalid

    • mean

      public double mean() throws java.lang.Exception
      Retrieve the Mean of the Distribution
      Specified by:
      mean in class R1Distribution
      Returns:
      The Mean of the Distribution
      Throws:
      java.lang.Exception - Thrown if the Mean cannot be estimated

    • variance

      public double variance() throws java.lang.Exception
      Retrieve the Variance of the Distribution
      Specified by:
      variance in class R1Distribution
      Returns:
      The Variance of the Distribution
      Throws:
      java.lang.Exception - Thrown if the Variance cannot be estimated

    • normalizer

      public double normalizer()
      Retrieve the Normalizer
      Returns:
      Normalizer

    • lambda

      public double lambda()
      Retrieve the "Lambda" Parameter
      Returns:
      "Lambda" Parameter