Percentile

java.lang.Object
- org.apache.commons.math3.stat.descriptive.AbstractUnivariateStatistic
- - org.apache.commons.math3.stat.descriptive.rank.Percentile

All Implemented Interfaces:

Serializable, UnivariateStatistic, MathArrays.Function

Direct Known Subclasses:

Median
```
public class Percentile
extends AbstractUnivariateStatistic
implements Serializable
```
Provides percentile computation.
There are several commonly used methods for estimating percentiles (a.k.a. quantiles) based on sample data. For large samples, the different methods agree closely, but when sample sizes are small, different methods will give significantly different results. The algorithm implemented here works as follows:
1. Let n be the length of the (sorted) array and 0 < p <= 100 be the desired percentile.
2. If n = 1 return the unique array element (regardless of the value of p); otherwise
3. Compute the estimated percentile position pos = p * (n + 1) / 100 and the difference, d between pos and floor(pos) (i.e. the fractional part of pos).
4. If pos < 1 return the smallest element in the array.
5. Else if pos >= n return the largest element in the array.
6. Else let lower be the element in position floor(pos) in the array and let upper be the next element in the array. Return lower + d * (upper - lower)
To compute percentiles, the data must be at least partially ordered. Input arrays are copied and recursively partitioned using an ordering definition. The ordering used by Arrays.sort(double[]) is the one determined by Double.compareTo(Double). This ordering makes Double.NaN larger than any other value (including Double.POSITIVE_INFINITY). Therefore, for example, the median (50th percentile) of {0, 1, 2, 3, 4, Double.NaN} evaluates to 2.5.

Since percentile estimation usually involves interpolation between array elements, arrays containing NaN or infinite values will often result in NaN or infinite values returned.

Further, to include different estimation types such as R1, R2 as mentioned in Quantile page(wikipedia), a type specific NaN handling strategy is used to closely match with the typically observed results from popular tools like R(R1-R9), Excel(R7).

Since 2.2, Percentile uses only selection instead of complete sorting and caches selection algorithm state between calls to the various evaluate methods. This greatly improves efficiency, both for a single percentile and multiple percentile computations. To maximize performance when multiple percentiles are computed based on the same data, users should set the data array once using either one of the evaluate(double[], double) or setData(double[]) methods and thereafter evaluate(double) with just the percentile provided.

Note that this implementation is not synchronized. If multiple threads access an instance of this class concurrently, and at least one of the threads invokes the increment() or clear() method, it must be synchronized externally.
See Also:

Serialized Form

Nested Class Summary

Nested Classes
Modifier and Type	Class and Description
`static class`	`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.

Constructor Summary

Constructors
Constructor and Description
`Percentile()` Constructs a Percentile with the following defaults.
`Percentile(double quantile)` Constructs a Percentile with the specific quantile value and the following default method type: `Percentile.EstimationType.LEGACY` default NaN strategy: `NaNStrategy.REMOVED` a Kth Selector : `KthSelector`
`Percentile(Percentile original)` Copy constructor, creates a new `Percentile` identical to the `original`

Method Summary

All Methods Static Methods Instance Methods Concrete Methods Deprecated Methods
Modifier and Type	Method and Description
`Percentile`	`copy()` Returns a copy of the statistic with the same internal state.
`static void`	`copy(Percentile source, Percentile dest)` Deprecated. as of 3.4 this method does not work anymore, as it fails to copy internal states between instances configured with different `estimation type`, `NaN handling strategies` and `kthSelector`, it therefore always throw `MathUnsupportedOperationException`
`double`	`evaluate(double p)` Returns the result of evaluating the statistic over the stored data.
`double`	`evaluate(double[] values, double p)` Returns an estimate of the `p`th percentile of the values in the `values` array.
`double`	`evaluate(double[] values, int start, int length)` Returns an estimate of the `quantile`th percentile of the designated values in the `values` array.
`double`	`evaluate(double[] values, int begin, int length, double p)` Returns an estimate of the `p`th percentile of the values in the `values` array, starting with the element in (0-based) position `begin` in the array and including `length` values.
`Percentile.EstimationType`	`getEstimationType()` Get the estimation `type` used for computation.
`KthSelector`	`getKthSelector()` Get the `kthSelector` used for computation.
`NaNStrategy`	`getNaNStrategy()` Get the `NaN Handling` strategy used for computation.
`PivotingStrategyInterface`	`getPivotingStrategy()` Get the `PivotingStrategyInterface` used in KthSelector for computation.
`double`	`getQuantile()` Returns the value of the quantile field (determines what percentile is computed when evaluate() is called with no quantile argument).
`void`	`setData(double[] values)` Set the data array.
`void`	`setData(double[] values, int begin, int length)` Set the data array.
`void`	`setQuantile(double p)` Sets the value of the quantile field (determines what percentile is computed when evaluate() is called with no quantile argument).
`Percentile`	`withEstimationType(Percentile.EstimationType newEstimationType)` Build a new instance similar to the current one except for the `estimation type`.
`Percentile`	`withKthSelector(KthSelector newKthSelector)` Build a new instance similar to the current one except for the `kthSelector` instance specifically set.
`Percentile`	`withNaNStrategy(NaNStrategy newNaNStrategy)` Build a new instance similar to the current one except for the `NaN handling` strategy.

Methods inherited from class org.apache.commons.math3.stat.descriptive.AbstractUnivariateStatistic
evaluate, evaluate, getData

Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Constructor Detail
  - Percentile
```
public Percentile()
```
    Constructs a Percentile with the following defaults.
    - default quantile: 50.0, can be reset with setQuantile(double)
    - default estimation type: Percentile.EstimationType.LEGACY, can be reset with withEstimationType(EstimationType)
    - default NaN strategy: NaNStrategy.REMOVED, can be reset with withNaNStrategy(NaNStrategy)
    - a KthSelector that makes use of MedianOf3PivotingStrategy, can be reset with withKthSelector(KthSelector)
  - Percentile
```
public Percentile(double quantile)
           throws MathIllegalArgumentException
```
    Constructs a Percentile with the specific quantile value and the following
    - default method type: Percentile.EstimationType.LEGACY
    - default NaN strategy: NaNStrategy.REMOVED
    - a Kth Selector : KthSelector
    Parameters:
    
    quantile - the quantile
    
    Throws:
    
    MathIllegalArgumentException - if p is not greater than 0 and less than or equal to 100
  - Percentile
```
public Percentile(Percentile original)
           throws NullArgumentException
```
    Copy constructor, creates a new Percentile identical to the original
    
    Parameters:
    
    original - the Percentile instance to copy
    
    Throws:
    
    NullArgumentException - if original is null
- Method Detail
  - setData
```
public void setData(double[] values)
```
    Set the data array.
    The stored value is a copy of the parameter array, not the array itself.
    
    Overrides:
    
    setData in class AbstractUnivariateStatistic
    
    Parameters:
    
    values - data array to store (may be null to remove stored data)
    
    See Also:
    
    AbstractUnivariateStatistic.evaluate()
  - setData
```
public void setData(double[] values,
                    int begin,
                    int length)
             throws MathIllegalArgumentException
```
    Set the data array. The input array is copied, not referenced.
    
    Overrides:
    
    setData in class AbstractUnivariateStatistic
    
    Parameters:
    
    values - data array to store
    
    begin - the index of the first element to include
    
    length - the number of elements to include
    
    Throws:
    
    MathIllegalArgumentException - if values is null or the indices are not valid
    
    See Also:
    
    AbstractUnivariateStatistic.evaluate()
  - evaluate
```
public double evaluate(double p)
                throws MathIllegalArgumentException
```
    Returns the result of evaluating the statistic over the stored data.
    The stored array is the one which was set by previous calls to setData(double[])
    
    Parameters:
    
    p - the percentile value to compute
    
    Returns:
    
    the value of the statistic applied to the stored data
    
    Throws:
    
    MathIllegalArgumentException - if p is not a valid quantile value (p must be greater than 0 and less than or equal to 100)
  - evaluate
```
public double evaluate(double[] values,
                       double p)
                throws MathIllegalArgumentException
```
    Returns an estimate of the pth percentile of the values in the values array.
    Calls to this method do not modify the internal quantile state of this statistic.
    - Returns Double.NaN if values has length 0
    - Returns (for any value of p) values[0] if values has length 1
    - Throws MathIllegalArgumentException if values is null or p is not a valid quantile value (p must be greater than 0 and less than or equal to 100)
    See Percentile for a description of the percentile estimation algorithm used.
    Parameters:
    
    values - input array of values
    
    p - the percentile value to compute
    
    Returns:
    
    the percentile value or Double.NaN if the array is empty
    
    Throws:
    
    MathIllegalArgumentException - if values is null or p is invalid
  - evaluate
```
public double evaluate(double[] values,
                       int start,
                       int length)
                throws MathIllegalArgumentException
```
    Returns an estimate of the quantileth percentile of the designated values in the values array. The quantile estimated is determined by the quantile property.
    - Returns Double.NaN if length = 0
    - Returns (for any value of quantile) values[begin] if length = 1
    - Throws MathIllegalArgumentException if values is null, or start or length is invalid
    See Percentile for a description of the percentile estimation algorithm used.
    Specified by:
    
    evaluate in interface UnivariateStatistic
    
    Specified by:
    
    evaluate in interface MathArrays.Function
    
    Specified by:
    
    evaluate in class AbstractUnivariateStatistic
    
    Parameters:
    
    values - the input array
    
    start - index of the first array element to include
    
    length - the number of elements to include
    
    Returns:
    
    the percentile value
    
    Throws:
    
    MathIllegalArgumentException - if the parameters are not valid
  - evaluate
```
public double evaluate(double[] values,
                       int begin,
                       int length,
                       double p)
                throws MathIllegalArgumentException
```
    Returns an estimate of the pth percentile of the values in the values array, starting with the element in (0-based) position begin in the array and including length values.
    Calls to this method do not modify the internal quantile state of this statistic.
    - Returns Double.NaN if length = 0
    - Returns (for any value of p) values[begin] if length = 1
    - Throws MathIllegalArgumentException if values is null , begin or length is invalid, or p is not a valid quantile value (p must be greater than 0 and less than or equal to 100)
    See Percentile for a description of the percentile estimation algorithm used.
    Parameters:
    
    values - array of input values
    
    p - the percentile to compute
    
    begin - the first (0-based) element to include in the computation
    
    length - the number of array elements to include
    
    Returns:
    
    the percentile value
    
    Throws:
    
    MathIllegalArgumentException - if the parameters are not valid or the input array is null
  - getQuantile
```
public double getQuantile()
```
    Returns the value of the quantile field (determines what percentile is computed when evaluate() is called with no quantile argument).
    
    Returns:
    
    quantile set while construction or setQuantile(double)
  - setQuantile
```
public void setQuantile(double p)
                 throws MathIllegalArgumentException
```
    Sets the value of the quantile field (determines what percentile is computed when evaluate() is called with no quantile argument).
    
    Parameters:
    
    p - a value between 0 < p <= 100
    
    Throws:
    
    MathIllegalArgumentException - if p is not greater than 0 and less than or equal to 100
  - copy
```
public Percentile copy()
```
    Returns a copy of the statistic with the same internal state.
    
    Specified by:
    
    copy in interface UnivariateStatistic
    
    Specified by:
    
    copy in class AbstractUnivariateStatistic
    
    Returns:
    
    a copy of the statistic
  - copy
```
@Deprecated
public static void copy(Percentile source,
                                    Percentile dest)
                             throws MathUnsupportedOperationException
```
    Deprecated. as of 3.4 this method does not work anymore, as it fails to copy internal states between instances configured with different estimation type, NaN handling strategies and kthSelector, it therefore always throw MathUnsupportedOperationException
    
    Copies source to dest.
    
    Parameters:
    
    source - Percentile to copy
    
    dest - Percentile to copy to
    
    Throws:
    
    MathUnsupportedOperationException - always thrown since 3.4
  - getEstimationType
```
public Percentile.EstimationType getEstimationType()
```
    Get the estimation type used for computation.
    
    Returns:
    
    the estimationType set
  - withEstimationType
```
public Percentile withEstimationType(Percentile.EstimationType newEstimationType)
```
    Build a new instance similar to the current one except for the estimation type.
    This method is intended to be used as part of a fluent-type builder pattern. Building finely tune instances should be done as follows:
```
   Percentile customized = new Percentile(quantile).
                           withEstimationType(estimationType).
                           withNaNStrategy(nanStrategy).
                           withKthSelector(kthSelector);
 
```
    If any of the withXxx method is omitted, the default value for the corresponding customization parameter will be used.
    Parameters:
    
    newEstimationType - estimation type for the new instance
    
    Returns:
    
    a new instance, with changed estimation type
    
    Throws:
    
    NullArgumentException - when newEstimationType is null
  - getNaNStrategy
```
public NaNStrategy getNaNStrategy()
```
    Get the NaN Handling strategy used for computation.
    
    Returns:
    
    NaN Handling strategy set during construction
  - withNaNStrategy
```
public Percentile withNaNStrategy(NaNStrategy newNaNStrategy)
```
    Build a new instance similar to the current one except for the NaN handling strategy.
    This method is intended to be used as part of a fluent-type builder pattern. Building finely tune instances should be done as follows:
```
   Percentile customized = new Percentile(quantile).
                           withEstimationType(estimationType).
                           withNaNStrategy(nanStrategy).
                           withKthSelector(kthSelector);
 
```
    If any of the withXxx method is omitted, the default value for the corresponding customization parameter will be used.
    Parameters:
    
    newNaNStrategy - NaN strategy for the new instance
    
    Returns:
    
    a new instance, with changed NaN handling strategy
    
    Throws:
    
    NullArgumentException - when newNaNStrategy is null
  - getKthSelector
```
public KthSelector getKthSelector()
```
    Get the kthSelector used for computation.
    
    Returns:
    
    the kthSelector set
  - getPivotingStrategy
```
public PivotingStrategyInterface getPivotingStrategy()
```
    Get the PivotingStrategyInterface used in KthSelector for computation.
    
    Returns:
    
    the pivoting strategy set
  - withKthSelector
```
public Percentile withKthSelector(KthSelector newKthSelector)
```
    Build a new instance similar to the current one except for the kthSelector instance specifically set.
    This method is intended to be used as part of a fluent-type builder pattern. Building finely tune instances should be done as follows:
```
   Percentile customized = new Percentile(quantile).
                           withEstimationType(estimationType).
                           withNaNStrategy(nanStrategy).
                           withKthSelector(newKthSelector);
 
```
    If any of the withXxx method is omitted, the default value for the corresponding customization parameter will be used.
    Parameters:
    
    newKthSelector - KthSelector for the new instance
    
    Returns:
    
    a new instance, with changed KthSelector
    
    Throws:
    
    NullArgumentException - when newKthSelector is null

Class Percentile

Nested Class Summary

Constructor Summary

Method Summary

Methods inherited from class org.apache.commons.math3.stat.descriptive.AbstractUnivariateStatistic

Methods inherited from class java.lang.Object

Constructor Detail

Percentile

Percentile

Percentile

Method Detail

setData

setData

evaluate

evaluate

evaluate

evaluate

getQuantile

setQuantile

copy

copy

getEstimationType

withEstimationType

getNaNStrategy

withNaNStrategy

getKthSelector

getPivotingStrategy

withKthSelector