Percentile.EstimationType (Apache Commons Math 4.0-SNAPSHOT API)

java.lang.Object
- java.lang.Enum<Percentile.EstimationType>
- - org.apache.commons.math4.stat.descriptive.rank.Percentile.EstimationType

All Implemented Interfaces:

Serializable, Comparable<Percentile.EstimationType>

Enclosing class:

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:

Enum Constant Summary

Enum Constants
Enum Constant and Description
`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 \( \begin{align} &index = (N + 1/4)p + 3/8\\ &estimate = x_{\lfloor h \rfloor} + (h - \lfloor h \rfloor) (x_{\lfloor h \rfloor + 1} - x_{\lfloor h \rfloor}) \\ &minLimit = (5/8)/(N+1/4) \\ &maxLimit = (N-3/8)/(N+1/4) \\ \end{align}\)

Method Summary

Methods
Modifier and Type	Method and Description
`protected double`	`estimate(double[] work, int[] pivotsHeap, double pos, int length, KthSelector kthSelector)` Estimation based on K^th selection.
`double`	`evaluate(double[] work, double p, KthSelector kthSelector)` Evaluate method to compute the percentile for a given bounded array.
`protected double`	`evaluate(double[] work, int[] pivotsHeap, double p, KthSelector kthSelector)` 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)` Returns the enum constant of this type with the specified name.
`static Percentile.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 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 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 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
    \( \begin{align} &index = (N + 1/4)p + 3/8\\ &estimate = x_{\lfloor h \rfloor} + (h - \lfloor h \rfloor) (x_{\lfloor h \rfloor + 1} - x_{\lfloor h \rfloor}) \\ &minLimit = (5/8)/(N+1/4) \\ &maxLimit = (N-3/8)/(N+1/4) \\ \end{align}\)
- Method Detail
  - values
```
public static Percentile.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 (Percentile.EstimationType c : Percentile.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 Percentile.EstimationType valueOf(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:
    
    IllegalArgumentException - if this enum type has no constant with the specified name
    
    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 Percentile.EstimationType.
    
    Parameters:
    p - the p^th 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 kthSelector)
```
    Estimation based on K^th 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
    kthSelector - a KthSelector used for pivoting during search
    
    Returns:
    estimated percentile
  - evaluate
```
protected double evaluate(double[] work,
              int[] pivotsHeap,
              double p,
              KthSelector kthSelector)
```
    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 p^th quantile to be computed
    kthSelector - 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 kthSelector)
```
    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 p^th quantile to be computed
    kthSelector - 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

Enum Percentile.EstimationType

Enum Constant Summary

Method Summary

Methods inherited from class java.lang.Enum

Methods inherited from class java.lang.Object

Enum Constant Detail

LEGACY

R_1

R_2

R_3

R_4

R_5

R_6

R_7

R_8

R_9

Method Detail

values

valueOf

index

estimate

evaluate

evaluate