Package org.drip.measure.continuous

Class R1ParetoDistribution

java.lang.Object
org.drip.measure.continuous.R1Distribution
org.drip.measure.continuous.R1ParetoDistribution
public class R1ParetoDistribution
extends R1Distribution
R1ParetoDistribution implements the R1 Pareto Distribution. 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
It provides the following Functionality:
  • R1ParetoDistribution Constructor
  • Retrieve k
  • Retrieve Lambda
  • Lay out the Support of the PDF Range
  • Compute the Density under the Distribution at the given Variate
  • Retrieve the Mode of the Distribution
  • Compute the cumulative under the distribution to the given value
  • Retrieve the Quantile Variate of the Distribution
  • Retrieve the Mean of the Distribution
  • Retrieve the Median of the Distribution
  • Retrieve the Variance of the Distribution

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

    • R1ParetoDistribution

      public R1ParetoDistribution​(double lambda, double k) throws java.lang.Exception
      R1ParetoDistribution Constructor
      Parameters:
      lambda - Rate Parameter
      k - K Parameter
      Throws:
      java.lang.Exception - Thrown if the Inputs are invalid

  • Method Details

    • k

      public double k()
      Retrieve k
      Returns:
      k

    • lambda

      public double lambda()
      Retrieve Lambda
      Returns:
      Lambda

    • 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

    • mode

      public double mode() throws java.lang.Exception
      Retrieve the Mode of the Distribution
      Overrides:
      mode in class R1Distribution
      Returns:
      The Mode of the Distribution
      Throws:
      java.lang.Exception - Thrown if the Mode cannot be estimated

    • 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

    • quantile

      public double quantile​(double p) throws java.lang.Exception
      Retrieve the Quantile Variate of the Distribution
      Overrides:
      quantile in class R1Distribution
      Parameters:
      p - The Quantile Fraction
      Returns:
      The Quantile Variate of the Distribution
      Throws:
      java.lang.Exception - Thrown if the Quantile Variate cannot be estimated

    • 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

    • median

      public double median() throws java.lang.Exception
      Retrieve the Median of the Distribution
      Overrides:
      median in class R1Distribution
      Returns:
      The Median of the Distribution
      Throws:
      java.lang.Exception - Thrown if the Median 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