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

Class EmpiricalDist

  • All Implemented Interfaces:
    Distribution

    public class EmpiricalDist
extends DiscreteDistribution
    Extends DiscreteDistribution to an empirical distribution function, based on the observations X(1),..., X(n) (sorted by increasing order). The distribution is uniform over the n observations, so the distribution function has a jump of 1/n at each of the n observations.

    • Constructor Summary

      Constructors 
      Constructor and Description
      EmpiricalDist(double[] obs)
      Constructs a new empirical distribution using all the observations stored in obs, and which are assumed to have been sorted in increasing numerical order.
      EmpiricalDist(java.io.Reader in)
      Constructs a new empirical distribution using the observations read from the reader in.

    • Method Summary

      All Methods Static Methods Instance Methods Concrete Methods 
      Modifier and Type Method and Description
      double barF(double x)
      Returns bar(F)(x) = 1 - F(x).
      double cdf(double x)
      Returns the distribution function F(x).
      double getInterQuartileRange()
      Returns the interquartile range of the observations, defined as the difference between the third and first quartiles.
      double getMean()
      Computes the mean E[X] = ∑i=1npixi of the distribution.
      double getMedian()
      Returns the n/2th item of the sorted observations when the number of items is odd, and the mean of the n/2th and the (n/2 + 1)th items when the number of items is even.
      static double getMedian(double[] obs, int n)
      Returns the n/2th item of the array obs when the number of items is odd, and the mean of the n/2th and the (n/2 + 1)th items when the number of items is even.
      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()
      Computes the standard deviation of the distribution.
      double getVariance()
      Computes the variance Var[X] = ∑i=1npi(xi - E[X])2 of the distribution.
      double inverseF(double u)
      Returns the inverse distribution function F-1(u), defined in.
      double prob(int i)
      Returns pk, the probability of the k-th observation, for 0 <= k < n.
      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

      • EmpiricalDist

        public EmpiricalDist(double[] obs)
        Constructs a new empirical distribution using all the observations stored in obs, and which are assumed to have been sorted in increasing numerical order. 1 These observations are copied into an internal array.

      • EmpiricalDist

        public EmpiricalDist(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. One must be careful about lines starting with a blank. This format is the same as in UNURAN. The observations read are assumed to have been sorted in increasing numerical order.
        Throws:
        java.io.IOException

    • Method Detail

      • prob

        public double prob(int i)
        Description copied from class: DiscreteDistribution
        Returns pk, the probability of the k-th observation, for 0 <= k < n. The result should be a real number in the interval [0, 1].
        Overrides:
        prob in class DiscreteDistribution
        Parameters:
        i - observation number, 0 <= k < n
        Returns:
        the probability of observation k

      • cdf

        public double cdf(double x)
        Description copied from interface: Distribution
        Returns the distribution function F(x).
        Specified by:
        cdf in interface Distribution
        Overrides:
        cdf in class DiscreteDistribution
        Parameters:
        x - value at which the distribution function must be evaluated
        Returns:
        the distribution function evaluated at x

      • barF

        public double barF(double x)
        Description copied from interface: Distribution
        Returns bar(F)(x) = 1 - F(x).
        Specified by:
        barF in interface Distribution
        Overrides:
        barF in class DiscreteDistribution
        Parameters:
        x - value at which the complementary distribution function must be evaluated
        Returns:
        the complementary distribution function evaluated at x

      • inverseF

        public double inverseF(double u)
        Description copied from interface: Distribution
        Returns the inverse distribution function F-1(u), defined in.
        Specified by:
        inverseF in interface Distribution
        Overrides:
        inverseF in class DiscreteDistribution
        Parameters:
        u - value in the interval (0, 1) for which the inverse distribution function is evaluated
        Returns:
        the inverse distribution function evaluated at u

      • getMedian

        public double getMedian()
        Returns the n/2th item of the sorted observations when the number of items is odd, and the mean of the n/2th and the (n/2 + 1)th items when the number of items is even.

      • getMedian

        public static double getMedian(double[] obs,
                               int n)
        Returns the n/2th item of the array obs when the number of items is odd, and the mean of the n/2th and the (n/2 + 1)th items when the number of items is even. The array does not have to be sorted.
        Parameters:
        obs - the array of observations
        n - the number of observations
        Returns:
        return the median of the observations

      • 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.

      • getInterQuartileRange

        public double getInterQuartileRange()
        Returns the interquartile range of the observations, defined as the difference between the third and first quartiles.

      • toString

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