Package com.opttek.optquest

Class COptQuestPoissonDistribution

java.lang.Object
com.opttek.optquest.COptQuestPoissonDistribution
All Implemented Interfaces:
com.opttek.optquest.IProbabilityDistribution
public class COptQuestPoissonDistribution extends Object implements com.opttek.optquest.IProbabilityDistribution

  • Constructor Summary

    Constructors
    Constructor
    Description
    COptQuestPoissonDistribution(double lambda)
     

  • Method Summary

    Modifier and Type
    Method
    Description
    double
    cdf(double x)
     
    static double
    CDF(int k, double lambda)
    Poisson Cumulative Distribution Function (CDF) Computes P(X ≤ k) where X follows a Poisson distribution with rate parameter lambda.
    double
    chaz(double x)
     
    double
    haz(double x)
     
    double
    pdf(double x)
     
    static double
    PDF(int k, double lambda)
    Poisson Probability Density Function (PDF) Computes P(X = k) where X follows a Poisson distribution with rate parameter lambda.
    double
    ppf(double x)
     
    static int
    PPF(double p, double lambda)
    Poisson Percent Point Function (PPF), the inverse CDF Computes the value k such that P(X ≤ k) ≥ p, where X follows a Poisson distribution with rate parameter lambda.
    double
    sf(double x)
     
    static double
    SF(double k, double lambda)
    Poisson survival function, S(k) = P(X > k) = P(k+1, lambda), where P is the regularized lower incomplete gamma function.

    Methods inherited from class java.lang.Object

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

  • Constructor Details

    • COptQuestPoissonDistribution

      public COptQuestPoissonDistribution(double lambda)

  • 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

    • SF

      public static double SF(double k, double lambda)
      Poisson survival function, S(k) = P(X > k) = P(k+1, lambda), where P is the regularized lower incomplete gamma function.

      Uses the standard identity directly rather than 1 - CDF(k), which loses all significance in the upper tail.

      k is floored, matching the step shape of a discrete survival function.

    • haz

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

    • chaz

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

    • PDF

      public static double PDF(int k, double lambda)
      Poisson Probability Density Function (PDF) Computes P(X = k) where X follows a Poisson distribution with rate parameter lambda. Formula: P(X = k) = (lambda^k * e^(-lambda)) / k!
      Parameters:
      k - the value (must be non-negative integer)
      lambda - the rate parameter (must be positive)
      Returns:
      the probability density at k

    • CDF

      public static double CDF(int k, double lambda)
      Poisson Cumulative Distribution Function (CDF) Computes P(X ≤ k) where X follows a Poisson distribution with rate parameter lambda. Uses the relationship: CDF(k, lambda) = 1 - Q(k+1, lambda) where Q is the regularized upper incomplete gamma function.
      Parameters:
      k - the value (must be non-negative integer)
      lambda - the rate parameter (must be positive)
      Returns:
      the cumulative probability P(X ≤ k)

    • PPF

      public static int PPF(double p, double lambda)
      Poisson Percent Point Function (PPF), the inverse CDF Computes the value k such that P(X ≤ k) ≥ p, where X follows a Poisson distribution with rate parameter lambda. Uses sequential search starting from an estimated initial value based on the normal approximation for large lambda, with safety bounds to prevent infinite loops.
      Parameters:
      p - the probability (must be between 0 and 1, inclusive)
      lambda - the rate parameter (must be positive)
      Returns:
      the smallest integer k such that CDF(k, lambda) ≥ p