程序包 org.hipparchus.stat.descriptive.rank

枚举类 Percentile.EstimationType

java.lang.Object
java.lang.Enum<Percentile.EstimationType>
org.hipparchus.stat.descriptive.rank.Percentile.EstimationType
所有已实现的接口:
Serializable, Comparable<Percentile.EstimationType>, Constable
封闭类:
Percentile
public static enum Percentile.EstimationType extends Enum<Percentile.EstimationType>
An enum for various estimation strategies of a percentile referred in wikipedia on quantile with the names of enum matching those of types mentioned in wikipedia.

Each enum corresponding to the specific type of estimation in wikipedia implements the respective formulae that specializes in the below aspects

  • An index method to calculate approximate index of the estimate
  • An estimate method to estimate a value found at the earlier computed index
  • A minLimit on the quantile for which first element of sorted input is returned as an estimate
  • A maxLimit on the quantile for which last element of sorted input is returned as an estimate

Users can now create Percentile by explicitly passing this enum; such as by invoking Percentile.withEstimationType(EstimationType)

References:

  1. Wikipedia on quantile
  2. Hyndman, R. J. and Fan, Y. (1996) Sample quantiles in statistical packages, American Statistician 50, 361–365
  3. R-Manual

  • 嵌套类概要

    从类继承的嵌套类/接口 java.lang.Enum

    Enum.EnumDesc<E extends Enum<E>>

  • 枚举常量概要

    枚举常量
    枚举常量
    说明
    LEGACY
    This is the default type used in the Percentile.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
    \( \begin{align} &index = (N + 1/4)p + 3/8\\ &estimate = x_{\lfloor h \rfloor} + (h - \lfloor h \rfloor) (x_{\lfloor h \rfloor + 1} - x_{\lfloor h \rfloor}) \\ &minLimit = (5/8)/(N+1/4) \\ &maxLimit = (N-3/8)/(N+1/4) \\ \end{align}\)

  • 方法概要

    修饰符和类型
    方法
    说明
    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 Percentile.EstimationType
    valueOf(String name)
    返回带有指定名称的该类的枚举常量。
    static Percentile.EstimationType[]
    values()
    返回包含该枚举类的常量的数组， 顺序与声明这些常量的顺序相同

    从类继承的方法 java.lang.Enum

    clone, compareTo, describeConstable, equals, finalize, getDeclaringClass, hashCode, name, ordinal, toString, valueOf

    从类继承的方法 java.lang.Object

    getClass, notify, notifyAll, wait, wait, wait

  • 枚举常量详细资料

    • LEGACY

      public static final Percentile.EstimationType LEGACY
      This is the default type used in the Percentile.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 Percentile.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 Percentile.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 Percentile.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 Percentile.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 Percentile.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 Percentile.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 Hipparchus 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 Percentile.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 Percentile.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 Percentile.EstimationType R_9
      The method R_9 has the following formulae for index and estimates
      \( \begin{align} &index = (N + 1/4)p + 3/8\\ &estimate = x_{\lfloor h \rfloor} + (h - \lfloor h \rfloor) (x_{\lfloor h \rfloor + 1} - x_{\lfloor h \rfloor}) \\ &minLimit = (5/8)/(N+1/4) \\ &maxLimit = (N-3/8)/(N+1/4) \\ \end{align}\)

  • 方法详细资料

    • values

      public static Percentile.EstimationType[] values()
      返回包含该枚举类的常量的数组， 顺序与声明这些常量的顺序相同
      返回:
      包含该枚举类的常量的数组，顺序与声明这些常量的顺序相同

    • valueOf

      public static Percentile.EstimationType valueOf(String name)
      返回带有指定名称的该类的枚举常量。 字符串必须与用于声明该类的枚举常量的 标识符完全匹配。（不允许有多余 的空格字符。）
      参数:
      name - 要返回的枚举常量的名称。
      返回:
      返回带有指定名称的枚举常量
      抛出:
      IllegalArgumentException - 如果该枚举类没有带有指定名称的常量
      NullPointerException - 如果参数为空值

    • 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 Percentile.EstimationType.
      参数:
      p - the pth quantile
      length - the total number of array elements in the work array
      返回:
      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.
      参数:
      work - array of numbers to be used for finding the percentile
      pivotsHeap - an earlier populated cache if exists; will be used
      pos - indicated positional index prior computed from calling index(double, int)
      length - size of array considered
      selector - a KthSelector used for pivoting during search
      返回:
      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.
      参数:
      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
      返回:
      estimated percentile
      抛出:
      MathIllegalArgumentException - 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.
      参数:
      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
      返回:
      estimated percentile
      抛出:
      MathIllegalArgumentException - if length or p is out of range
      NullArgumentException - if work array is null