Package com.opttek.optquest

Class COptQuestParetoDistribution

java.lang.Object
com.opttek.optquest.COptQuestParetoDistribution
All Implemented Interfaces:
com.opttek.optquest.IProbabilityDistribution
public class COptQuestParetoDistribution extends Object implements com.opttek.optquest.IProbabilityDistribution
Pareto distribution implementation. Verified - these functions return the same results as scipy.stats.pareto. Inspired by / Based on NIST's DataPlot implementation.

  • Constructor Summary

    Constructors
    Constructor
    Description
    COptQuestParetoDistribution(double gamma, double a, double loc, double scale)
     

  • Method Summary

    Modifier and Type
    Method
    Description
    double
    cdf(double x)
     
    static double
    CDF(double x, double gamma)
    Pareto Cumulative Distribution Function with default parameters Uses standard parameterization with a=1, loc=0, scale=1.
    static double
    CDF(double x, double gamma, double a, double loc, double scale)
    Pareto Cumulative Distribution Function (CDF) Computes P(X ≤ x) where X follows a Pareto distribution with shape parameter gamma and support parameters.
    double
    chaz(double x)
     
    static double
    CHAZ(double x, double gamma)
    Pareto Cumulative Hazard Function with default parameters Uses standard parameterization with a=1, loc=0, scale=1.
    static double
    CHAZ(double x, double gamma, double a, double loc, double scale)
    Pareto Cumulative Hazard Function Computes the cumulative hazard H(x) = -ln(S(x)) where S(x) = 1 - F(x) is the survival function.
    double
    haz(double x)
     
    static double
    HAZ(double x, double gamma)
    Pareto Hazard Function with default parameters Uses standard parameterization with a=1, loc=0, scale=1.
    static double
    HAZ(double x, double gamma, double a, double loc, double scale)
    Pareto Hazard Function Computes the hazard rate h(x) = f(x) / S(x) where f(x) is the PDF and S(x) is the survival function.
    double
    pdf(double x)
     
    static double
    PDF(double x, double gamma)
    Pareto Probability Density Function with default parameters Uses standard parameterization with a=1, loc=0, scale=1.
    static double
    PDF(double x, double gamma, double a, double loc, double scale)
    Pareto Probability Density Function (PDF) Computes the probability density at x for a Pareto distribution with given parameters.
    double
    ppf(double x)
     
    static double
    PPF(double p, double gamma)
    Pareto Percent Point Function with default parameters Uses standard parameterization with a=1, loc=0, scale=1.
    static double
    PPF(double p, double gamma, double a, double loc, double scale)
    Pareto Percent Point Function (PPF) - Inverse CDF Computes the value x such that P(X ≤ x) = p, where X follows a Pareto distribution with given parameters.
    double
    sf(double x)
     

    Methods inherited from class java.lang.Object

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

  • Constructor Details

    • COptQuestParetoDistribution

      public COptQuestParetoDistribution(double gamma, double a, double loc, double scale)

  • Method Details

    • pdf

      public double pdf(double x)
      Specified by:
      pdf in interface com.opttek.optquest.IProbabilityDistribution

    • cdf

      public double cdf(double x)
      Specified by:
      cdf in interface com.opttek.optquest.IProbabilityDistribution

    • ppf

      public double ppf(double x)
      Specified by:
      ppf in interface com.opttek.optquest.IProbabilityDistribution

    • sf

      public double sf(double x)
      Specified by:
      sf in interface com.opttek.optquest.IProbabilityDistribution

    • chaz

      public double chaz(double x)
      Specified by:
      chaz in interface com.opttek.optquest.IProbabilityDistribution

    • haz

      public double haz(double x)
      Specified by:
      haz in interface com.opttek.optquest.IProbabilityDistribution

    • CDF

      public static double CDF(double x, double gamma, double a, double loc, double scale)
      Pareto Cumulative Distribution Function (CDF) Computes P(X ≤ x) where X follows a Pareto distribution with shape parameter gamma and support parameters. The CDF is given by: F(x; γ, a) = 1 - (a/x)^γ for x ≥ a, 0 otherwise
      Parameters:
      x - the value at which to evaluate the CDF (must be finite)
      gamma - the tail length shape parameter (must be positive)
      a - the lower bound parameter (must be positive, default 1.0)
      loc - the location parameter (default 0.0)
      scale - the scale parameter (must be positive, default 1.0)
      Returns:
      the cumulative probability P(X ≤ x)

    • CDF

      public static double CDF(double x, double gamma)
      Pareto Cumulative Distribution Function with default parameters Uses standard parameterization with a=1, loc=0, scale=1.
      Parameters:
      x - the value at which to evaluate the CDF
      gamma - the tail length shape parameter (must be positive)
      Returns:
      the cumulative probability P(X ≤ x)

    • PDF

      public static double PDF(double x, double gamma, double a, double loc, double scale)
      Pareto Probability Density Function (PDF) Computes the probability density at x for a Pareto distribution with given parameters. The PDF is given by: f(x; γ, a) = (γ * a^γ) / x^(γ+1) for x ≥ a, 0 otherwise
      Parameters:
      x - the value at which to evaluate the PDF (must be finite)
      gamma - the tail length shape parameter (must be positive)
      a - the lower bound parameter (must be positive, default 1.0)
      loc - the location parameter (default 0.0)
      scale - the scale parameter (must be positive, default 1.0)
      Returns:
      the probability density at x

    • PDF

      public static double PDF(double x, double gamma)
      Pareto Probability Density Function with default parameters Uses standard parameterization with a=1, loc=0, scale=1.
      Parameters:
      x - the value at which to evaluate the PDF
      gamma - the tail length shape parameter (must be positive)
      Returns:
      the probability density at x

    • PPF

      public static double PPF(double p, double gamma, double a, double loc, double scale)
      Pareto Percent Point Function (PPF) - Inverse CDF Computes the value x such that P(X ≤ x) = p, where X follows a Pareto distribution with given parameters. Uses the closed-form inverse: x = a * (1-p)^(-1/γ)
      Parameters:
      p - the probability (must be between 0 and 1, exclusive)
      gamma - the tail length shape parameter (must be positive)
      a - the lower bound parameter (must be positive, default 1.0)
      loc - the location parameter (default 0.0)
      scale - the scale parameter (must be positive, default 1.0)
      Returns:
      the value x such that CDF(x, gamma, a, loc, scale) = p

    • PPF

      public static double PPF(double p, double gamma)
      Pareto Percent Point Function with default parameters Uses standard parameterization with a=1, loc=0, scale=1.
      Parameters:
      p - the probability (must be between 0 and 1, exclusive)
      gamma - the tail length shape parameter (must be positive)
      Returns:
      the value x such that CDF(x, gamma) = p

    • CHAZ

      public static double CHAZ(double x, double gamma, double a, double loc, double scale)
      Pareto Cumulative Hazard Function Computes the cumulative hazard H(x) = -ln(S(x)) where S(x) = 1 - F(x) is the survival function. For Pareto distribution: H(x; γ, a) = γ * ln(x/a) for x ≥ a, 0 otherwise
      Parameters:
      x - the value at which to evaluate the cumulative hazard
      gamma - the tail length shape parameter (must be positive)
      a - the lower bound parameter (must be positive, default 1.0)
      loc - the location parameter (default 0.0)
      scale - the scale parameter (must be positive, default 1.0)
      Returns:
      the cumulative hazard value

    • CHAZ

      public static double CHAZ(double x, double gamma)
      Pareto Cumulative Hazard Function with default parameters Uses standard parameterization with a=1, loc=0, scale=1.
      Parameters:
      x - the value at which to evaluate the cumulative hazard
      gamma - the tail length shape parameter (must be positive)
      Returns:
      the cumulative hazard value

    • HAZ

      public static double HAZ(double x, double gamma, double a, double loc, double scale)
      Pareto Hazard Function Computes the hazard rate h(x) = f(x) / S(x) where f(x) is the PDF and S(x) is the survival function. For Pareto distribution: h(x; γ, a) = γ/x for x ≥ a, 0 otherwise
      Parameters:
      x - the value at which to evaluate the hazard rate
      gamma - the tail length shape parameter (must be positive)
      a - the lower bound parameter (must be positive, default 1.0)
      loc - the location parameter (default 0.0)
      scale - the scale parameter (must be positive, default 1.0)
      Returns:
      the hazard rate value

    • HAZ

      public static double HAZ(double x, double gamma)
      Pareto Hazard Function with default parameters Uses standard parameterization with a=1, loc=0, scale=1.
      Parameters:
      x - the value at which to evaluate the hazard rate
      gamma - the tail length shape parameter (must be positive)
      Returns:
      the hazard rate value