Class TwoIIDSum

java.lang.Object
org.drip.measure.continuous.R1Univariate
org.drip.measure.exponential.TwoIIDSum

public class TwoIIDSum
extends R1Univariate
TwoIIDSum implements the PDF of the Sum of Two IID Exponential Random Variables. The References are:

  • Devroye, L. (1986): Non-Uniform Random Variate Generation Springer-Verlag New York
  • Exponential Distribution (2019): Exponential Distribution https://en.wikipedia.org/wiki/Exponential_distribution
  • Norton, M., V. Khokhlov, and S. Uryasev (2019): Calculating CVaR and bPOE for Common Probability Distributions with Application to Portfolio Optimization and Density Estimation Annals of Operations Research 299 (1-2) 1281-1315
  • Ross, S. M. (2009): Introduction to Probability and Statistics for Engineers and Scientists 4th Edition Associated Press New York, NY
  • Schmidt, D. F., and D. Makalic (2009): Universal Models for the Exponential Distribution IEEE Transactions on Information Theory 55 (7) 3087-3090


Author:
Lakshmi Krishnamurthy
  • Constructor Details

    • TwoIIDSum

      public TwoIIDSum​(R1RateDistribution firstR1RateDistribution, R1RateDistribution secondR1RateDistribution) throws java.lang.Exception
      TwoIIDSum Constructor
      Parameters:
      firstR1RateDistribution - First R1 Exponential Distribution
      secondR1RateDistribution - Second R1 Exponential Distribution
      Throws:
      java.lang.Exception - Thrown if Inputs are Invalid
  • Method Details

    • largerR1RateDistribution

      public R1RateDistribution largerR1RateDistribution()
      Retrieve the Larger Exponential Distribution
      Returns:
      The Larger Exponential Distribution
    • smallerR1RateDistribution

      public R1RateDistribution smallerR1RateDistribution()
      Retrieve the Smaller Exponential Distribution
      Returns:
      The Smaller Exponential Distribution
    • 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
    • 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
    • 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
    • cumulative

      public double cumulative​(double upper) 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:
      upper - Variate to which the cumulative is to be computed
      Returns:
      The cumulative
      Throws:
      java.lang.Exception - Thrown if the inputs are invalid
    • differentialEntropy

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