Package org.drip.function.e2erf

Class ErrorFunctionInverse

java.lang.Object
org.drip.function.definition.R1ToR1
org.drip.numerical.estimation.R1ToR1Estimator
org.drip.function.e2erf.ErrorFunctionInverse
public abstract class ErrorFunctionInverse
extends R1ToR1Estimator
ErrorFunctionInverse implements the E2 erf Inverse erf-1. The References are:

  • Abramowitz, M., and I. A. Stegun (2007): Handbook of Mathematics Functions Dover Book on Mathematics
  • Chang, S. H., P. C. Cosman, L. B. Milstein (2011): Chernoff-Type Bounds for Gaussian Error Function IEEE Transactions on Communications 59 (11) 2939-2944
  • Cody, W. J. (1991): Algorithm 715: SPECFUN – A Portable FORTRAN Package of Special Function Routines and Test Drivers ACM Transactions on Mathematical Software 19 (1) 22-32
  • Schopf, H. M., and P. H. Supancic (2014): On Burmann’s Theorem and its Application to Problems of Linear and Non-linear Heat Transfer and Diffusion https://www.mathematica-journal.com/2014/11/on-burmanns-theorem-and-its-application-to-problems-of-linear-and-nonlinear-heat-transfer-and-diffusion/#more-39602/
  • Wikipedia (2019): Error Function https://en.wikipedia.org/wiki/Error_function


Author:
Lakshmi Krishnamurthy

  • Method Details

    • Winitzki2008

      public static final ErrorFunctionInverse Winitzki2008​(double a)
      Construct Winitzki (2008) Version of the Analytical E2 erf Inverse
      Parameters:
      a - a
      Returns:
      Winitzki (2008) Version of the Analytical E2 erf Inverse

    • Winitzki2008a

      public static final ErrorFunctionInverse Winitzki2008a()
      Construct Winitzki (2008a) Version of the Analytical E2 erf Inverse
      Returns:
      Winitzki (2008a) Version of the Analytical E2 erf Inverse

    • Winitzki2008b

      public static final ErrorFunctionInverse Winitzki2008b()
      Construct Winitzki (2008b) Version of the Analytical E2 erf Inverse
      Returns:
      Winitzki (2008b) Version of the Analytical E2 erf Inverse

    • MacLaurin

      public static final ErrorFunctionInverse MacLaurin​(int termCount)
      Construct the Euler-MacLaurin Instance of the E2 erf Inverse
      Parameters:
      termCount - The Count of Approximation Terms
      Returns:
      The Euler-MacLaurin Instance of the E2 erf Inverse

    • seriesEstimateNative

      public R1Estimate seriesEstimateNative​(double x)
      Description copied from class: R1ToR1Estimator
      Compute the Built-in Higher Order Series Estimates
      Overrides:
      seriesEstimateNative in class R1ToR1Estimator
      Parameters:
      x - X
      Returns:
      The Built-in Higher Order Series Estimates

    • probit

      public double probit​(double p) throws java.lang.Exception
      Compute the Probit Value for the given p
      Parameters:
      p - P
      Returns:
      The Probit Value
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid

    • inverseCDF

      public double inverseCDF​(double p) throws java.lang.Exception
      Compute the Inverse CDF Value for the given p
      Parameters:
      p - P
      Returns:
      The Inverse CDF Value
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid