Package org.drip.specialfunction.beta

Class IntegrandEstimator

java.lang.Object
org.drip.specialfunction.definition.BetaEstimator
org.drip.specialfunction.beta.IntegrandEstimator
All Implemented Interfaces:
R2ToR1
public abstract class IntegrandEstimator
extends BetaEstimator
IntegrandEstimator implements the Beta Function using Integrand Estimation Schemes. The References are:

  • Abramowitz, M., and I. A. Stegun (2007): Handbook of Mathematics Functions Dover Book on Mathematics
  • Davis, P. J. (1959): Leonhard Euler's Integral: A Historical Profile of the Gamma Function American Mathematical Monthly 66 (10) 849-869
  • Whitaker, E. T., and G. N. Watson (1996): A Course on Modern Analysis Cambridge University Press New York
  • Wikipedia (2019): Beta Function https://en.wikipedia.org/wiki/Beta_function
  • Wikipedia (2019): Gamma Function https://en.wikipedia.org/wiki/Gamma_function
It provides the following functionality:
  • Construct the Beta Estimator from the Trigonometric Integral
  • Construct the Beta Estimator from the Euler Integral of the First Kind
  • Construct the Beta Estimator from the Euler Integral of the First Kind Exponent N
  • Construct the Beta Estimator from the Euler Integral of the First Kind over the Right Half Plane
  • Retrieve the Quadrature Count

Module Product Core Module
Library Fixed Income Analytics
Project Special Function Implementation and Analysis
Package Estimation Techniques for Beta Function
Author:
Lakshmi Krishnamurthy

  • Method Summary

    Modifier and Type Method Description
    static IntegrandEstimator EulerFirst​(int quadratureCount)
    Construct the Beta Estimator from the Euler Integral of the First Kind
    static IntegrandEstimator EulerFirstN​(int quadratureCount, double exponent)
    Construct the Beta Estimator from the Euler Integral of the First Kind Exponent N
    static IntegrandEstimator EulerFirstRightPlane​(int quadratureCount)
    Construct the Beta Estimator from the Euler Integral of the First Kind over the Right Half Plane
    int quadratureCount()
    Retrieve the Quadrature Count
    static IntegrandEstimator Trigonometric​(int quadratureCount)
    Construct the Beta Estimator from the Trigonometric Integral

    Methods inherited from class org.drip.specialfunction.definition.BetaEstimator

    beta, jacobian

    Methods inherited from class java.lang.Object

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

    Methods inherited from interface org.drip.function.definition.R2ToR1

    evaluate

  • Method Details

    • Trigonometric

      public static final IntegrandEstimator Trigonometric​(int quadratureCount)
      Construct the Beta Estimator from the Trigonometric Integral
      Parameters:
      quadratureCount - Count of the Integrand Quadrature
      Returns:
      Beta Estimator from the Trigonometric Integral

    • EulerFirst

      public static final IntegrandEstimator EulerFirst​(int quadratureCount)
      Construct the Beta Estimator from the Euler Integral of the First Kind
      Parameters:
      quadratureCount - Count of the Integrand Quadrature
      Returns:
      Beta Estimator from the Euler Integral of the First Kind

    • EulerFirstN

      public static final IntegrandEstimator EulerFirstN​(int quadratureCount, double exponent)
      Construct the Beta Estimator from the Euler Integral of the First Kind Exponent N
      Parameters:
      quadratureCount - Count of the Integrand Quadrature
      exponent - Exponent
      Returns:
      Beta Estimator from the Euler Integral of the First Kind

    • EulerFirstRightPlane

      public static final IntegrandEstimator EulerFirstRightPlane​(int quadratureCount)
      Construct the Beta Estimator from the Euler Integral of the First Kind over the Right Half Plane
      Parameters:
      quadratureCount - Count of the Integrand Quadrature
      Returns:
      Beta Estimator from the Euler Integral of the First Kind over the Right Half Plane

    • quadratureCount

      public int quadratureCount()
      Retrieve the Quadrature Count
      Returns:
      The Quadrature Count