Enum UnivariateStatistics.EstimationType

    • Enum Constant Summary

      Enum Constants 
      Enum Constant Description
      LEGACY
      This is the default type used in the percentile estimation.This method has the following formulae for index and estimates
      \( \begin{align} &index = (N+1)p\ \\ &estimate = x_{\lceil h\,-\,1/2 \rceil} \\ &minLimit = 0 \\ &maxLimit = 1 \\ \end{align}\)
      R_1
      The method R_1 has the following formulae for index and estimates
      \( \begin{align} &index= Np + 1/2\, \\ &estimate= x_{\lceil h\,-\,1/2 \rceil} \\ &minLimit = 0 \\ \end{align}\)
      R_2
      The method R_2 has the following formulae for index and estimates
      \( \begin{align} &index= Np + 1/2\, \\ &estimate=\frac{x_{\lceil h\,-\,1/2 \rceil} + x_{\lfloor h\,+\,1/2 \rfloor}}{2} \\ &minLimit = 0 \\ &maxLimit = 1 \\ \end{align}\)
      R_3
      The method R_3 has the following formulae for index and estimates
      \( \begin{align} &index= Np \\ &estimate= x_{\lfloor h \rceil}\, \\ &minLimit = 0.5/N \\ \end{align}\)
      R_4
      The method R_4 has the following formulae for index and estimates
      \( \begin{align} &index= Np\, \\ &estimate= x_{\lfloor h \rfloor} + (h - \lfloor h \rfloor) (x_{\lfloor h \rfloor + 1} - x_{\lfloor h \rfloor}) \\ &minLimit = 1/N \\ &maxLimit = 1 \\ \end{align}\)
      R_5
      The method R_5 has the following formulae for index and estimates
      \( \begin{align} &index= Np + 1/2\\ &estimate= x_{\lfloor h \rfloor} + (h - \lfloor h \rfloor) (x_{\lfloor h \rfloor + 1} - x_{\lfloor h \rfloor}) \\ &minLimit = 0.5/N \\ &maxLimit = (N-0.5)/N \end{align}\)
      R_6
      The method R_6 has the following formulae for index and estimates
      \( \begin{align} &index= (N + 1)p \\ &estimate= x_{\lfloor h \rfloor} + (h - \lfloor h \rfloor) (x_{\lfloor h \rfloor + 1} - x_{\lfloor h \rfloor}) \\ &minLimit = 1/(N+1) \\ &maxLimit = N/(N+1) \\ \end{align}\)
      R_7
      The method R_7 implements Microsoft Excel style computation has the following formulae for index and estimates.
      \( \begin{align} &index = (N-1)p + 1 \\ &estimate = x_{\lfloor h \rfloor} + (h - \lfloor h \rfloor) (x_{\lfloor h \rfloor + 1} - x_{\lfloor h \rfloor}) \\ &minLimit = 0 \\ &maxLimit = 1 \\ \end{align}\)
      R_8
      The method R_8 has the following formulae for index and estimates
      \( \begin{align} &index = (N + 1/3)p + 1/3 \\ &estimate = x_{\lfloor h \rfloor} + (h - \lfloor h \rfloor) (x_{\lfloor h \rfloor + 1} - x_{\lfloor h \rfloor}) \\ &minLimit = (2/3)/(N+1/3) \\ &maxLimit = (N-1/3)/(N+1/3) \\ \end{align}\)
      R_9
      The method R_9 has the following formulae for index and estimates
      \( \begin{align} &index = (N + 1/4)p + 3/8\\ &estimate = x_{\lfloor h \rfloor} + (h - \lfloor h \rfloor) (x_{\lfloor h \rfloor + 1} - x_{\lfloor h \rfloor}) \\ &minLimit = (5/8)/(N+1/4) \\ &maxLimit = (N-3/8)/(N+1/4) \\ \end{align}\)
    • Method Summary

      All Methods Static Methods Instance Methods Abstract Methods Concrete Methods 
      Modifier and Type Method Description
      protected double estimate​(double[] work, int[] pivotsHeap, double pos, int length, KthSelector selector)
      Estimation based on Kth selection.
      double evaluate​(double[] work, double p, KthSelector selector)
      Evaluate method to compute the percentile for a given bounded array.
      protected double evaluate​(double[] work, int[] pivotsHeap, double p, KthSelector selector)
      Evaluate method to compute the percentile for a given bounded array using earlier computed pivots heap.
      This basically calls the index and then estimate functions to return the estimated percentile value.
      protected abstract double index​(double p, int length)
      Finds the index of array that can be used as starting index to estimate percentile.
      static UnivariateStatistics.EstimationType valueOf​(java.lang.String name)
      Returns the enum constant of this type with the specified name.
      static UnivariateStatistics.EstimationType[] values()
      Returns an array containing the constants of this enum type, in the order they are declared.
      • Methods inherited from class java.lang.Enum

        clone, compareTo, equals, finalize, getDeclaringClass, hashCode, name, ordinal, toString, valueOf
      • Methods inherited from class java.lang.Object

        getClass, notify, notifyAll, wait, wait, wait
    • Enum Constant Detail

      • LEGACY

        public static final UnivariateStatistics.EstimationType LEGACY
        This is the default type used in the percentile estimation.This method has the following formulae for index and estimates
        \( \begin{align} &index = (N+1)p\ \\ &estimate = x_{\lceil h\,-\,1/2 \rceil} \\ &minLimit = 0 \\ &maxLimit = 1 \\ \end{align}\)
      • R_1

        public static final UnivariateStatistics.EstimationType R_1
        The method R_1 has the following formulae for index and estimates
        \( \begin{align} &index= Np + 1/2\, \\ &estimate= x_{\lceil h\,-\,1/2 \rceil} \\ &minLimit = 0 \\ \end{align}\)
      • R_2

        public static final UnivariateStatistics.EstimationType R_2
        The method R_2 has the following formulae for index and estimates
        \( \begin{align} &index= Np + 1/2\, \\ &estimate=\frac{x_{\lceil h\,-\,1/2 \rceil} + x_{\lfloor h\,+\,1/2 \rfloor}}{2} \\ &minLimit = 0 \\ &maxLimit = 1 \\ \end{align}\)
      • R_3

        public static final UnivariateStatistics.EstimationType R_3
        The method R_3 has the following formulae for index and estimates
        \( \begin{align} &index= Np \\ &estimate= x_{\lfloor h \rceil}\, \\ &minLimit = 0.5/N \\ \end{align}\)
      • R_4

        public static final UnivariateStatistics.EstimationType R_4
        The method R_4 has the following formulae for index and estimates
        \( \begin{align} &index= Np\, \\ &estimate= x_{\lfloor h \rfloor} + (h - \lfloor h \rfloor) (x_{\lfloor h \rfloor + 1} - x_{\lfloor h \rfloor}) \\ &minLimit = 1/N \\ &maxLimit = 1 \\ \end{align}\)
      • R_5

        public static final UnivariateStatistics.EstimationType R_5
        The method R_5 has the following formulae for index and estimates
        \( \begin{align} &index= Np + 1/2\\ &estimate= x_{\lfloor h \rfloor} + (h - \lfloor h \rfloor) (x_{\lfloor h \rfloor + 1} - x_{\lfloor h \rfloor}) \\ &minLimit = 0.5/N \\ &maxLimit = (N-0.5)/N \end{align}\)
      • R_6

        public static final UnivariateStatistics.EstimationType R_6
        The method R_6 has the following formulae for index and estimates
        \( \begin{align} &index= (N + 1)p \\ &estimate= x_{\lfloor h \rfloor} + (h - \lfloor h \rfloor) (x_{\lfloor h \rfloor + 1} - x_{\lfloor h \rfloor}) \\ &minLimit = 1/(N+1) \\ &maxLimit = N/(N+1) \\ \end{align}\)

        Note: This method computes the index in a manner very close to the default Commons Math Percentile existing implementation. However the difference to be noted is in picking up the limits with which first element (p<1(N+1)) and last elements (p>N/(N+1))are done. While in default case; these are done with p=0 and p=1 respectively.

      • R_7

        public static final UnivariateStatistics.EstimationType R_7
        The method R_7 implements Microsoft Excel style computation has the following formulae for index and estimates.
        \( \begin{align} &index = (N-1)p + 1 \\ &estimate = x_{\lfloor h \rfloor} + (h - \lfloor h \rfloor) (x_{\lfloor h \rfloor + 1} - x_{\lfloor h \rfloor}) \\ &minLimit = 0 \\ &maxLimit = 1 \\ \end{align}\)
      • R_8

        public static final UnivariateStatistics.EstimationType R_8
        The method R_8 has the following formulae for index and estimates
        \( \begin{align} &index = (N + 1/3)p + 1/3 \\ &estimate = x_{\lfloor h \rfloor} + (h - \lfloor h \rfloor) (x_{\lfloor h \rfloor + 1} - x_{\lfloor h \rfloor}) \\ &minLimit = (2/3)/(N+1/3) \\ &maxLimit = (N-1/3)/(N+1/3) \\ \end{align}\)

        As per Ref [2,3] this approach is most recommended as it provides an approximate median-unbiased estimate regardless of distribution.

      • R_9

        public static final UnivariateStatistics.EstimationType R_9
        The method R_9 has the following formulae for index and estimates
        \( \begin{align} &index = (N + 1/4)p + 3/8\\ &estimate = x_{\lfloor h \rfloor} + (h - \lfloor h \rfloor) (x_{\lfloor h \rfloor + 1} - x_{\lfloor h \rfloor}) \\ &minLimit = (5/8)/(N+1/4) \\ &maxLimit = (N-3/8)/(N+1/4) \\ \end{align}\)
    • Method Detail

      • values

        public static UnivariateStatistics.EstimationType[] values()
        Returns an array containing the constants of this enum type, in the order they are declared. This method may be used to iterate over the constants as follows:
        for (UnivariateStatistics.EstimationType c : UnivariateStatistics.EstimationType.values())
            System.out.println(c);
        
        Returns:
        an array containing the constants of this enum type, in the order they are declared
      • valueOf

        public static UnivariateStatistics.EstimationType valueOf​(java.lang.String name)
        Returns the enum constant of this type with the specified name. The string must match exactly an identifier used to declare an enum constant in this type. (Extraneous whitespace characters are not permitted.)
        Parameters:
        name - the name of the enum constant to be returned.
        Returns:
        the enum constant with the specified name
        Throws:
        java.lang.IllegalArgumentException - if this enum type has no constant with the specified name
        java.lang.NullPointerException - if the argument is null
      • index

        protected abstract double index​(double p,
                                        int length)
        Finds the index of array that can be used as starting index to estimate percentile. The calculation of index calculation is specific to each UnivariateStatistics.EstimationType.
        Parameters:
        p - the pth quantile
        length - the total number of array elements in the work array
        Returns:
        a computed real valued index as explained in the wikipedia
      • estimate

        protected double estimate​(double[] work,
                                  int[] pivotsHeap,
                                  double pos,
                                  int length,
                                  KthSelector selector)
        Estimation based on Kth selection. This may be overridden in specific enums to compute slightly different estimations.
        Parameters:
        work - array of numbers to be used for finding the percentile
        pos - indicated positional index prior computed from calling index(double, int)
        pivotsHeap - an earlier populated cache if exists; will be used
        length - size of array considered
        selector - a KthSelector used for pivoting during search
        Returns:
        estimated percentile
      • evaluate

        protected double evaluate​(double[] work,
                                  int[] pivotsHeap,
                                  double p,
                                  KthSelector selector)
        Evaluate method to compute the percentile for a given bounded array using earlier computed pivots heap.
        This basically calls the index and then estimate functions to return the estimated percentile value.
        Parameters:
        work - array of numbers to be used for finding the percentile
        pivotsHeap - a prior cached heap which can speed up estimation
        p - the pth quantile to be computed
        selector - a KthSelector used for pivoting during search
        Returns:
        estimated percentile
        Throws:
        OutOfRangeException - if p is out of range
        NullArgumentException - if work array is null
      • evaluate

        public double evaluate​(double[] work,
                               double p,
                               KthSelector selector)
        Evaluate method to compute the percentile for a given bounded array. This basically calls the index and then estimate functions to return the estimated percentile value. Please note that this method does not make use of cached pivots.
        Parameters:
        work - array of numbers to be used for finding the percentile
        p - the pth quantile to be computed
        selector - a KthSelector used for pivoting during search
        Returns:
        estimated percentile
        Throws:
        OutOfRangeException - if length or p is out of range
        NullArgumentException - if work array is null