Package org.drip.measure.gaussian

Class NormalQuadrature

java.lang.Object
org.drip.measure.gaussian.NormalQuadrature
public class NormalQuadrature
extends java.lang.Object
NormalQuadrature implements the Quadrature Metrics behind the Univariate Normal Distribution. It implements the Incremental, the Cumulative, and the Inverse Cumulative Distribution Densities.

Author:
Robert Sedgewick, Lakshmi Krishnamurthy

  • Constructor Summary

    Constructors
    Constructor Description
    NormalQuadrature()  

  • Method Summary

    Modifier and Type Method Description
    static double CDF​(double dblX)
    Compute the Cumulative Distribution Function up to the specified Variate
    static double Density​(double dblX)
    Retrieve the Density at the specified Point using Zero Mean and Unit Variance
    static double ERF​(double x)
    Compute the Error Function of x
    static double ERFC​(double x)
    Compute the Error Function Complement of x
    static double InverseCDF​(double dblY)
    Compute the Inverse CDF of the Distribution up to the specified Y
    static double Probit​(double p)
    Compute the Probit of the Distribution up to the specified p
    static double Random()
    Generate a Random Univariate Number following a Gaussian Distribution

    Methods inherited from class java.lang.Object

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

  • Constructor Details

    • NormalQuadrature

      public NormalQuadrature()

  • Method Details

    • Density

      public static final double Density​(double dblX) throws java.lang.Exception
      Retrieve the Density at the specified Point using Zero Mean and Unit Variance
      Parameters:
      dblX - The Ordinate
      Returns:
      The Density at the specified Point Zero Mean and Unit Variance
      Throws:
      java.lang.Exception - Thrown if Inputs are Invalid

    • CDF

      public static final double CDF​(double dblX) throws java.lang.Exception
      Compute the Cumulative Distribution Function up to the specified Variate
      Parameters:
      dblX - The Variate
      Returns:
      The Cumulative Distribution Function up to the specified Variate
      Throws:
      java.lang.Exception - thrown if the Inputs are Invalid

    • InverseCDF

      public static final double InverseCDF​(double dblY) throws java.lang.Exception
      Compute the Inverse CDF of the Distribution up to the specified Y
      Parameters:
      dblY - Y
      Returns:
      The Inverse CDF of the Distribution up to the specified Y
      Throws:
      java.lang.Exception - Thrown if Inputs are Invalid

    • Probit

      public static final double Probit​(double p) throws java.lang.Exception
      Compute the Probit of the Distribution up to the specified p
      Parameters:
      p - p
      Returns:
      The Probit of the Distribution up to the specified p
      Throws:
      java.lang.Exception - Thrown if Inputs are Invalid

    • Random

      public static final double Random() throws java.lang.Exception
      Generate a Random Univariate Number following a Gaussian Distribution
      Returns:
      The Random Univariate Number
      Throws:
      java.lang.Exception - Thrown the Random Number cannot be generated

    • ERF

      public static final double ERF​(double x) throws java.lang.Exception
      Compute the Error Function of x
      Parameters:
      x - x
      Returns:
      The Error Function of x
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid

    • ERFC

      public static final double ERFC​(double x) throws java.lang.Exception
      Compute the Error Function Complement of x
      Parameters:
      x - x
      Returns:
      The Error Function Complement of x
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid