Package com.opttek.optquest

Class COptQuestExponentialDistribution

java.lang.Object
com.opttek.optquest.COptQuestExponentialDistribution
All Implemented Interfaces:
com.opttek.optquest.IProbabilityDistribution
public class COptQuestExponentialDistribution extends Object implements com.opttek.optquest.IProbabilityDistribution
This class provides static methods for computing functions of the exponential distribution, including the cumulative distribution function (CDF), probability density function (PDF), percent point function (PPF), survival function (SF), hazard function (HAZ), and cumulative hazard function (CHAZ). The implementations are verified to match scipy.stats.expon and are inspired by NIST's DataPlot implementation. The exponential distribution is parameterized by a positive scale parameter (mean = scale, rate λ = 1/scale).

  • Constructor Summary

    Constructors
    Constructor
    Description
    COptQuestExponentialDistribution(double scale)
     

  • Method Summary

    Modifier and Type
    Method
    Description
    double
    cdf(double x)
     
    static double
    CDF(double x)
    Exponential Cumulative Distribution Function with default scale parameter Equivalent to expcdf(x, 1.0).
    static double
    CDF(double x, double scale)
    Exponential Cumulative Distribution Function (CDF) Computes P(X ≤ x) where X follows an exponential distribution with the given scale parameter.
    double
    chaz(double x)
     
    static double
    CHAZ(double x)
    Exponential Cumulative Hazard Function with default scale parameter Equivalent to expchaz(x, 1.0).
    static double
    CHAZ(double x, double scale)
    Exponential Cumulative Hazard Function Computes the cumulative hazard H(x) = -ln(S(x)) where S(x) is the survival function.
    double
    haz(double x)
     
    static double
    HAZ(double x)
    Exponential Hazard Function with default scale parameter Equivalent to exphaz(x, 1.0).
    static double
    HAZ(double x, double scale)
    Exponential 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)
    Exponential Probability Density Function with default scale parameter Equivalent to exppdf(x, 1.0).
    static double
    PDF(double x, double scale)
    Exponential Probability Density Function (PDF) Computes the probability density at x for an exponential distribution with the given scale parameter.
    double
    ppf(double x)
     
    static double
    PPF(double p)
    Exponential Percent Point Function with default scale parameter Equivalent to expppf(p, 1.0).
    static double
    PPF(double p, double scale)
    Exponential Percent Point Function (PPF) - Inverse CDF Computes the value x such that P(X ≤ x) = p, where X follows an exponential distribution with the given scale parameter.
    double
    sf(double x)
     
    static double
    SF(double x)
    Exponential Survival Function with default scale parameter Equivalent to expsf(x, 1.0).
    static double
    SF(double x, double scale)
    Exponential Survival Function Computes the survival probability S(x) = P(X > x) = 1 - F(x) where F(x) is the CDF.

    Methods inherited from class java.lang.Object

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

  • Constructor Details

    • COptQuestExponentialDistribution

      public COptQuestExponentialDistribution(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 scale)
      Exponential Cumulative Distribution Function (CDF) Computes P(X ≤ x) where X follows an exponential distribution with the given scale parameter. The CDF is defined as: F(x) = 1 - exp(-x/scale) for x ≥ 0, and 0 for x < 0. The exponential distribution models the time between events in a Poisson point process, where events occur continuously and independently at a constant average rate.
      Parameters:
      x - the value at which to evaluate the CDF (any real number)
      scale - the scale parameter (must be positive, λ = 1/scale)
      Returns:
      the cumulative probability P(X ≤ x)

    • CDF

      public static double CDF(double x)
      Exponential Cumulative Distribution Function with default scale parameter Equivalent to expcdf(x, 1.0). Uses the standard exponential distribution with rate parameter λ = 1.
      Parameters:
      x - the value at which to evaluate the CDF
      Returns:
      the cumulative probability P(X ≤ x) for standard exponential distribution

    • CHAZ

      public static double CHAZ(double x, double scale)
      Exponential Cumulative Hazard Function Computes the cumulative hazard H(x) = -ln(S(x)) where S(x) is the survival function. For the exponential distribution: H(x) = x/scale for x ≥ 0. The cumulative hazard represents the total accumulated risk up to time x. In reliability analysis, it quantifies the total exposure to failure risk.
      Parameters:
      x - the value at which to evaluate the cumulative hazard (any real number)
      scale - the scale parameter (must be positive)
      Returns:
      the cumulative hazard H(x)

    • CHAZ

      public static double CHAZ(double x)
      Exponential Cumulative Hazard Function with default scale parameter Equivalent to expchaz(x, 1.0). Uses the standard exponential distribution.
      Parameters:
      x - the value at which to evaluate the cumulative hazard
      Returns:
      the cumulative hazard H(x) for standard exponential distribution

    • HAZ

      public static double HAZ(double x, double scale)
      Exponential 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 the exponential distribution, the hazard rate is constant: h(x) = 1/scale = λ. This constant hazard property is the defining characteristic of the exponential distribution, reflecting the "memoryless" property where the probability of an event in the next instant is independent of how much time has already elapsed.
      Parameters:
      x - the value at which to evaluate the hazard (not used due to constant hazard)
      scale - the scale parameter (must be positive)
      Returns:
      the constant hazard rate 1/scale

    • HAZ

      public static double HAZ(double x)
      Exponential Hazard Function with default scale parameter Equivalent to exphaz(x, 1.0). Returns the constant hazard rate for the standard exponential distribution.
      Parameters:
      x - the value at which to evaluate the hazard
      Returns:
      the constant hazard rate 1.0 for standard exponential distribution

    • PDF

      public static double PDF(double x, double scale)
      Exponential Probability Density Function (PDF) Computes the probability density at x for an exponential distribution with the given scale parameter. The PDF is defined as: f(x) = (1/scale) * exp(-x/scale) for x ≥ 0, and 0 for x < 0. The PDF represents the relative likelihood of observing a value in an infinitesimal neighborhood around x. For the exponential distribution, this decreases exponentially from its maximum at x = 0.
      Parameters:
      x - the value at which to evaluate the PDF (any real number)
      scale - the scale parameter (must be positive)
      Returns:
      the probability density at x

    • PDF

      public static double PDF(double x)
      Exponential Probability Density Function with default scale parameter Equivalent to exppdf(x, 1.0). Uses the standard exponential distribution.
      Parameters:
      x - the value at which to evaluate the PDF
      Returns:
      the probability density at x for standard exponential distribution

    • PPF

      public static double PPF(double p, double scale)
      Exponential Percent Point Function (PPF) - Inverse CDF Computes the value x such that P(X ≤ x) = p, where X follows an exponential distribution with the given scale parameter. Uses the analytical inverse: F^(-1)(p) = -scale * ln(1 - p). This closed-form solution provides exact results without numerical iteration. The PPF is useful for generating random samples and computing confidence intervals.
      Parameters:
      p - the probability (must be between 0 and 1, exclusive of 1)
      scale - the scale parameter (must be positive)
      Returns:
      the quantile x such that CDF(x, scale) = p

    • PPF

      public static double PPF(double p)
      Exponential Percent Point Function with default scale parameter Equivalent to expppf(p, 1.0). Uses the standard exponential distribution.
      Parameters:
      p - the probability (must be between 0 and 1, exclusive of 1)
      Returns:
      the quantile x such that CDF(x, 1.0) = p

    • SF

      public static double SF(double x, double scale)
      Exponential Survival Function Computes the survival probability S(x) = P(X > x) = 1 - F(x) where F(x) is the CDF. For the exponential distribution: S(x) = exp(-x/scale) for x ≥ 0, and 1 for x < 0. The survival function represents the probability that a random variable X exceeds a given value x. In reliability analysis, this gives the probability that a system survives beyond time x.
      Parameters:
      x - the value at which to evaluate the survival function (any real number)
      scale - the scale parameter (must be positive)
      Returns:
      the survival probability S(x) = P(X > x)

    • SF

      public static double SF(double x)
      Exponential Survival Function with default scale parameter Equivalent to expsf(x, 1.0). Uses the standard exponential distribution.
      Parameters:
      x - the value at which to evaluate the survival function
      Returns:
      the survival probability S(x) for standard exponential distribution