Documentation of 'umontreal.iro.lecuyer.probdist.PiecewiseLinearEmpiricalDist' Java class
PiecewiseLinearEmpiricalDist
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umontreal.iro.lecuyer.probdist

Class PiecewiseLinearEmpiricalDist

  • All Implemented Interfaces:
    Distribution

    public class PiecewiseLinearEmpiricalDist
extends ContinuousDistribution
    Extends the class ContinuousDistribution for a piecewise-linear approximation of the empirical distribution function, based on the observations X(1),..., X(n) (sorted by increasing order), and defined as follows (e.g.,). The distribution function starts at X(1) and climbs linearly by 1/(n - 1) between any two successive observations. The density is

    f (x) = 1/[(n - 1)(X(i+1) - X(i))] for X(i) <= x < X(i+1) and i = 1, 2,..., n - 1.

    The distribution function is

    F(x) = 0          for x < X(1),
    F(x) = (i - 1)/(n - 1) + (x - X(i))/[(n - 1)(X(i+1) - X(i))]          for X(i) <= x < X(i+1),
    F(x) = 1          elsewhere,

    whose inverse is

    F-1(u) = X(i) + ((n - 1)u - i + 1)(X(i+1) - X(i))

    for (i - 1)/(n - 1) <= u <= i/(n - 1) and i = 1,..., n - 1.

    • Constructor Summary

      Constructors 
      Constructor and Description
      PiecewiseLinearEmpiricalDist(double[] obs)
      Constructs a new piecewise-linear distribution using all the observations stored in obs.
      PiecewiseLinearEmpiricalDist(java.io.Reader in)
      Constructs a new empirical distribution using the observations read from the reader in.

    • Method Summary

      All Methods Instance Methods Concrete Methods 
      Modifier and Type Method and Description
      double barF(double x)
      Returns the complementary distribution function.
      double cdf(double x)
      Returns the distribution function F(x).
      double density(double x)
      Returns f (x), the density evaluated at x.
      double getMean()
      Returns the mean.
      int getN()
      Returns n, the number of observations.
      double getObs(int i)
      Returns the value of X(i).
      double[] getParams()
      Return a table containing parameters of the current distribution.
      double getSampleMean()
      Returns the sample mean of the observations.
      double getSampleStandardDeviation()
      Returns the sample standard deviation of the observations.
      double getSampleVariance()
      Returns the sample variance of the observations.
      double getStandardDeviation()
      Returns the standard deviation.
      double getVariance()
      Returns the variance.
      double inverseF(double u)
      Returns the inverse distribution function x = F-1(u).
      java.lang.String toString()
      Returns a String containing information about the current distribution.

      • Methods inherited from class java.lang.Object

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

    • Constructor Detail

      • PiecewiseLinearEmpiricalDist

        public PiecewiseLinearEmpiricalDist(double[] obs)
        Constructs a new piecewise-linear distribution using all the observations stored in obs. These observations are copied into an internal array and then sorted.

      • PiecewiseLinearEmpiricalDist

        public PiecewiseLinearEmpiricalDist(java.io.Reader in)
                             throws java.io.IOException
        Constructs a new empirical distribution using the observations read from the reader in. This constructor will read the first double of each line in the stream. Any line that does not start with a +, -, or a decimal digit, is ignored. The file is read until its end. One must be careful about lines starting with a blank. This format is the same as in UNURAN.
        Throws:
        java.io.IOException

    • Method Detail

      • density

        public double density(double x)
        Description copied from class: ContinuousDistribution
        Returns f (x), the density evaluated at x.
        Specified by:
        density in class ContinuousDistribution
        Parameters:
        x - value at which the density is evaluated
        Returns:
        density function evaluated at x

      • cdf

        public double cdf(double x)
        Description copied from interface: Distribution
        Returns the distribution function F(x).
        Parameters:
        x - value at which the distribution function is evaluated
        Returns:
        distribution function evaluated at x

      • barF

        public double barF(double x)
        Description copied from class: ContinuousDistribution
        Returns the complementary distribution function. The default implementation computes bar(F)(x) = 1 - F(x).
        Specified by:
        barF in interface Distribution
        Overrides:
        barF in class ContinuousDistribution
        Parameters:
        x - value at which the complementary distribution function is evaluated
        Returns:
        complementary distribution function evaluated at x

      • inverseF

        public double inverseF(double u)
        Description copied from class: ContinuousDistribution
        Returns the inverse distribution function x = F-1(u). Restrictions: u∈[0, 1].
        Specified by:
        inverseF in interface Distribution
        Overrides:
        inverseF in class ContinuousDistribution
        Parameters:
        u - value at which the inverse distribution function is evaluated
        Returns:
        the inverse distribution function evaluated at u

      • getN

        public int getN()
        Returns n, the number of observations.

      • getObs

        public double getObs(int i)
        Returns the value of X(i).

      • getSampleMean

        public double getSampleMean()
        Returns the sample mean of the observations.

      • getSampleVariance

        public double getSampleVariance()
        Returns the sample variance of the observations.

      • getSampleStandardDeviation

        public double getSampleStandardDeviation()
        Returns the sample standard deviation of the observations.

      • getParams

        public double[] getParams()
        Return a table containing parameters of the current distribution.

      • toString

        public java.lang.String toString()
        Returns a String containing information about the current distribution.
        Overrides:
        toString in class java.lang.Object
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