java.lang.Object
- org.apache.commons.statistics.descriptive.Quantile

```
public final class Quantile
extends Object
```
Provides quantile computation.
For values of length n:
- The result is NaN if n = 0.
- The result is values[0] if n = 1.
- Otherwise the result is computed using the Quantile.EstimationMethod.
Computation of multiple quantiles will handle duplicate and unordered probabilities. Passing ordered probabilities is recommended if the order is already known as this can improve efficiency; for example using uniform spacing through the array data, or to identify extreme values from the data such as [0.001, 0.999].
This implementation respects the ordering imposed by Double.compare(double, double) for NaN values. If a NaN occurs in the selected positions in the fully sorted values then the result is NaN.
The NaNPolicy can be used to change the behaviour on NaN values.
Instances of this class are immutable and thread-safe.
Support for long arrays
The result on long values can be returned as a double or a long using a StatisticResult.
The double result is computed within 1 ULP of the exact result. In some cases this may be outside the range defined by the minimum and maximum of the input array following rounding to a 53-bit floating point representation. For example a quantile of an array containing only Long.MAX_VALUE as a double is 2⁶³, which is the closest representation of 2⁶³ - 1.
The long result is returned using the nearest whole number. In the event of ties the result is rounded towards positive infinity. This value will always be within the range defined by the minimum and maximum of the input array. Due to interpolation it may be a value not observed in the input values.
Interpolation between two long values requires extended precision floating-point arithmetic. This can be avoided using a discontinuous Quantile.EstimationMethod. In this case the long quantile will be a value observed in the input values.
If the array length n is zero the result as a double is NaN and the result as a long will raise an ArithmeticException.
Multiple quantile results required as only one of the primitive values can be converted to a primitive array using a stream, for example:
```
 long[] values = ...
 double[] p = Quantile.probabilities(10);
 Quantile q = Quantile.withDefaults();
 long[] result = Arrays.stream(q.evaluate(values, p))
                       .mapToLong(StatisticResult::getAsLong)
                       .toArray();
 
```
Since:

1.1

See Also:

with(NaNPolicy), Quantile (Wikipedia)

Nested Class Summary

Nested Classes
Modifier and Type Class Description

static class Quantile.EstimationMethod
Enumerates estimation methods for a quantile.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`double`	`evaluate(double[] values, double p)`	Evaluate the `p`-th quantile of the values.
`double[]`	`evaluate(double[] values, double... p)`	Evaluate the `p`-th quantiles of the values.
`double`	`evaluate(int[] values, double p)`	Evaluate the `p`-th quantile of the values.
`double[]`	`evaluate(int[] values, double... p)`	Evaluate the `p`-th quantiles of the values.
`double`	`evaluate(int n, IntToDoubleFunction values, double p)`	Evaluate the `p`-th quantile of the sorted values provided as a `double`.
`double[]`	`evaluate(int n, IntToDoubleFunction values, double... p)`	Evaluate the `p`-th quantiles of the sorted values provided as a `double`.
`StatisticResult`	`evaluate(long[] values, double p)`	Evaluate the `p`-th quantile of the values.
`StatisticResult[]`	`evaluate(long[] values, double... p)`	Evaluate the `p`-th quantiles of the values.
`StatisticResult`	`evaluateAsLong(int n, IntToLongFunction values, double p)`	Evaluate the `p`-th quantile of the sorted values provided as a `long`.
`StatisticResult[]`	`evaluateAsLong(int n, IntToLongFunction values, double... p)`	Evaluate the `p`-th quantiles of the sorted values provided as a `long`.
`double`	`evaluateRange(double[] values, int from, int to, double p)`	Evaluate the `p`-th quantile of the specified range of values.
`double[]`	`evaluateRange(double[] values, int from, int to, double... p)`	Evaluate the `p`-th quantiles of the specified range of values.
`double`	`evaluateRange(int[] values, int from, int to, double p)`	Evaluate the `p`-th quantile of the specified range of values.
`double[]`	`evaluateRange(int[] values, int from, int to, double... p)`	Evaluate the `p`-th quantiles of the specified range of values..
`StatisticResult`	`evaluateRange(long[] values, int from, int to, double p)`	Evaluate the `p`-th quantile of the specified range of values.
`StatisticResult[]`	`evaluateRange(long[] values, int from, int to, double... p)`	Evaluate the `p`-th quantiles of the specified range of values..
`static double[]`	`probabilities(int n)`	Generate `n` evenly spaced probabilities in the range `[0, 1]`.
`static double[]`	`probabilities(int n, double p1, double p2)`	Generate `n` evenly spaced probabilities in the range `[p1, p2]`.
`Quantile`	`with(NaNPolicy v)`	Return an instance with the configured `NaNPolicy`.
`Quantile`	`with(Quantile.EstimationMethod v)`	Return an instance with the configured `Quantile.EstimationMethod`.
`Quantile`	`withCopy(boolean v)`	Return an instance with the configured copy behaviour.
`static Quantile`	`withDefaults()`	Return a new instance with the default options.

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

- Method Detail
  - withDefaults
```
public static Quantile withDefaults()
```
    Return a new instance with the default options.
    
    Copy = false
    
    NaN policy = include
    
    Estimation method = HF8
    
    Note: The default options configure for processing in-place and including NaN values in the data. This is the most efficient mode and has the smallest memory consumption.
    Returns:
    
    the quantile implementation
    
    See Also:
    
    withCopy(boolean), with(NaNPolicy), with(EstimationMethod)
  - withCopy
```
public Quantile withCopy(boolean v)
```
    Return an instance with the configured copy behaviour. If false then the input array will be modified by the call to evaluate the quantiles; otherwise the computation uses a copy of the data.
    
    Parameters:
    
    v - Value.
    
    Returns:
    
    an instance
  - with
```
public Quantile with(NaNPolicy v)
```
    Return an instance with the configured NaNPolicy.
    Note: This implementation respects the ordering imposed by Double.compare(double, double) for NaN values: NaN is considered greater than all other values, and all NaN values are equal. The NaNPolicy changes the computation of the statistic in the presence of NaN values.
    
    NaNPolicy.INCLUDE: NaN values are moved to the end of the data; the size of the data includes the NaN values and the quantile will be NaN if any value used for quantile interpolation is NaN.
    
    NaNPolicy.EXCLUDE: NaN values are moved to the end of the data; the size of the data excludes the NaN values and the quantile will never be NaN for non-zero size. If all data are NaN then the size is zero and the result is NaN.
    
    NaNPolicy.ERROR: An exception is raised if the data contains NaN values.
    
    Note that the result is identical for all policies if no NaN values are present.
    Parameters:
    
    v - Value.
    
    Returns:
    
    an instance
  - with
```
public Quantile with(Quantile.EstimationMethod v)
```
    Return an instance with the configured Quantile.EstimationMethod.
    
    Parameters:
    
    v - Value.
    
    Returns:
    
    an instance
  - probabilities
```
public static double[] probabilities(int n)
```
    Generate n evenly spaced probabilities in the range [0, 1].
    1/(n + 1), 2/(n + 1), ..., n/(n + 1)
    Parameters:
    
    n - Number of probabilities.
    
    Returns:
    
    the probabilities
    
    Throws:
    
    IllegalArgumentException - if n < 1
  - probabilities
```
public static double[] probabilities(int n,
                                     double p1,
                                     double p2)
```
    Generate n evenly spaced probabilities in the range [p1, p2].
    w = p2 - p1 p1 + w/(n + 1), p1 + 2w/(n + 1), ..., p1 + nw/(n + 1)
    Parameters:
    
    n - Number of probabilities.
    
    p1 - Lower probability.
    
    p2 - Upper probability.
    
    Returns:
    
    the probabilities
    
    Throws:
    
    IllegalArgumentException - if n < 1; if the probabilities are not in the range [0, 1]; or p2 <= p1.
  - evaluate
```
public double evaluate(double[] values,
                       double p)
```
    Evaluate the p-th quantile of the values.
    Note: This method may partially sort the input values if not configured to copy the input data.
    Performance
    It is not recommended to use this method for repeat calls for different quantiles within the same values. The evaluate(double[], double...) method should be used which provides better performance.
    
    Parameters:
    
    values - Values.
    
    p - Probability for the quantile to compute.
    
    Returns:
    
    the quantile
    
    Throws:
    
    IllegalArgumentException - if the probability p is not in the range [0, 1]; or if the values contain NaN and the configuration is NaNPolicy.ERROR
    
    See Also:
    
    evaluate(double[], double...), with(NaNPolicy)
  - evaluateRange
```
public double evaluateRange(double[] values,
                            int from,
                            int to,
                            double p)
```
    Evaluate the p-th quantile of the specified range of values.
    Note: This method may partially sort the input values if not configured to copy the input data.
    Performance
    It is not recommended to use this method for repeat calls for different quantiles within the same values. The evaluateRange(double[], int, int, double...) method should be used which provides better performance.
    
    Parameters:
    
    values - Values.
    
    from - Inclusive start of the range.
    
    to - Exclusive end of the range.
    
    p - Probability for the quantile to compute.
    
    Returns:
    
    the quantile
    
    Throws:
    
    IllegalArgumentException - if the probability p is not in the range [0, 1]; or if the values contain NaN and the configuration is NaNPolicy.ERROR
    
    IndexOutOfBoundsException - if the sub-range is out of bounds
    
    Since:
    
    1.2
    
    See Also:
    
    evaluateRange(double[], int, int, double...), with(NaNPolicy)
  - evaluate
```
public double[] evaluate(double[] values,
                         double... p)
```
    Evaluate the p-th quantiles of the values.
    Note: This method may partially sort the input values if not configured to copy the input data.
    
    Parameters:
    
    values - Values.
    
    p - Probabilities for the quantiles to compute.
    
    Returns:
    
    the quantiles
    
    Throws:
    
    IllegalArgumentException - if any probability p is not in the range [0, 1]; no probabilities are specified; or if the values contain NaN and the configuration is NaNPolicy.ERROR
    
    See Also:
    
    with(NaNPolicy)
  - evaluateRange
```
public double[] evaluateRange(double[] values,
                              int from,
                              int to,
                              double... p)
```
    Evaluate the p-th quantiles of the specified range of values.
    Note: This method may partially sort the input values if not configured to copy the input data.
    
    Parameters:
    
    values - Values.
    
    from - Inclusive start of the range.
    
    to - Exclusive end of the range.
    
    p - Probabilities for the quantiles to compute.
    
    Returns:
    
    the quantiles
    
    Throws:
    
    IllegalArgumentException - if any probability p is not in the range [0, 1]; no probabilities are specified; or if the values contain NaN and the configuration is NaNPolicy.ERROR
    
    IndexOutOfBoundsException - if the sub-range is out of bounds
    
    Since:
    
    1.2
    
    See Also:
    
    with(NaNPolicy)
  - evaluate
```
public double evaluate(int[] values,
                       double p)
```
    Evaluate the p-th quantile of the values.
    Note: This method may partially sort the input values if not configured to copy the input data.
    Performance
    It is not recommended to use this method for repeat calls for different quantiles within the same values. The evaluate(int[], double...) method should be used which provides better performance.
    
    Parameters:
    
    values - Values.
    
    p - Probability for the quantile to compute.
    
    Returns:
    
    the quantile
    
    Throws:
    
    IllegalArgumentException - if the probability p is not in the range [0, 1]
    
    See Also:
    
    evaluate(int[], double...)
  - evaluateRange
```
public double evaluateRange(int[] values,
                            int from,
                            int to,
                            double p)
```
    Evaluate the p-th quantile of the specified range of values.
    Note: This method may partially sort the input values if not configured to copy the input data.
    Performance
    It is not recommended to use this method for repeat calls for different quantiles within the same values. The evaluateRange(int[], int, int, double...) method should be used which provides better performance.
    
    Parameters:
    
    values - Values.
    
    from - Inclusive start of the range.
    
    to - Exclusive end of the range.
    
    p - Probability for the quantile to compute.
    
    Returns:
    
    the quantile
    
    Throws:
    
    IllegalArgumentException - if the probability p is not in the range [0, 1]
    
    IndexOutOfBoundsException - if the sub-range is out of bounds
    
    Since:
    
    1.2
    
    See Also:
    
    evaluateRange(int[], int, int, double...)
  - evaluate
```
public double[] evaluate(int[] values,
                         double... p)
```
    Evaluate the p-th quantiles of the values.
    Note: This method may partially sort the input values if not configured to copy the input data.
    
    Parameters:
    
    values - Values.
    
    p - Probabilities for the quantiles to compute.
    
    Returns:
    
    the quantiles
    
    Throws:
    
    IllegalArgumentException - if any probability p is not in the range [0, 1]; or no probabilities are specified.
  - evaluateRange
```
public double[] evaluateRange(int[] values,
                              int from,
                              int to,
                              double... p)
```
    Evaluate the p-th quantiles of the specified range of values..
    Note: This method may partially sort the input values if not configured to copy the input data.
    
    Parameters:
    
    values - Values.
    
    from - Inclusive start of the range.
    
    to - Exclusive end of the range.
    
    p - Probabilities for the quantiles to compute.
    
    Returns:
    
    the quantiles
    
    Throws:
    
    IllegalArgumentException - if any probability p is not in the range [0, 1]; or no probabilities are specified.
    
    IndexOutOfBoundsException - if the sub-range is out of bounds
    
    Since:
    
    1.2
  - evaluate
```
public StatisticResult evaluate(long[] values,
                                double p)
```
    Evaluate the p-th quantile of the values.
    Note: This method may partially sort the input values if not configured to copy the input data.
    Performance
    It is not recommended to use this method for repeat calls for different quantiles within the same values. The evaluate(long[], double...) method should be used which provides better performance.
    
    Parameters:
    
    values - Values.
    
    p - Probability for the quantile to compute.
    
    Returns:
    
    the quantile
    
    Throws:
    
    IllegalArgumentException - if the probability p is not in the range [0, 1]
    
    Since:
    
    1.3
    
    See Also:
    
    evaluate(long[], double...)
  - evaluateRange
```
public StatisticResult evaluateRange(long[] values,
                                     int from,
                                     int to,
                                     double p)
```
    Evaluate the p-th quantile of the specified range of values.
    Note: This method may partially sort the input values if not configured to copy the input data.
    Performance
    It is not recommended to use this method for repeat calls for different quantiles within the same values. The evaluateRange(long[], int, int, double...) method should be used which provides better performance.
    
    Parameters:
    
    values - Values.
    
    from - Inclusive start of the range.
    
    to - Exclusive end of the range.
    
    p - Probability for the quantile to compute.
    
    Returns:
    
    the quantile
    
    Throws:
    
    IllegalArgumentException - if the probability p is not in the range [0, 1]
    
    IndexOutOfBoundsException - if the sub-range is out of bounds
    
    Since:
    
    1.3
    
    See Also:
    
    evaluateRange(long[], int, int, double...)
  - evaluate
```
public StatisticResult[] evaluate(long[] values,
                                  double... p)
```
    Evaluate the p-th quantiles of the values.
    Note: This method may partially sort the input values if not configured to copy the input data.
    
    Parameters:
    
    values - Values.
    
    p - Probabilities for the quantiles to compute.
    
    Returns:
    
    the quantiles
    
    Throws:
    
    IllegalArgumentException - if any probability p is not in the range [0, 1]; or no probabilities are specified.
    
    Since:
    
    1.3
  - evaluateRange
```
public StatisticResult[] evaluateRange(long[] values,
                                       int from,
                                       int to,
                                       double... p)
```
    Evaluate the p-th quantiles of the specified range of values..
    Note: This method may partially sort the input values if not configured to copy the input data.
    
    Parameters:
    
    values - Values.
    
    from - Inclusive start of the range.
    
    to - Exclusive end of the range.
    
    p - Probabilities for the quantiles to compute.
    
    Returns:
    
    the quantiles
    
    Throws:
    
    IllegalArgumentException - if any probability p is not in the range [0, 1]; or no probabilities are specified.
    
    IndexOutOfBoundsException - if the sub-range is out of bounds
    
    Since:
    
    1.3
  - evaluate
```
public double evaluate(int n,
                       IntToDoubleFunction values,
                       double p)
```
    Evaluate the p-th quantile of the sorted values provided as a double.
    This method can be used when the values of known size are already sorted. It can be used for primitive types not supported by other evaluation methods. Numeric types byte, short and float can be converted to type double without loss of precision.
    short[] x = ... Arrays.sort(x); double q = Quantile.withDefaults().evaluate(x.length, i -> x[i], 0.05);
    
    If the sorted array is a long datatype this method can lose information about the precision of the quantiles due to primitive type conversion. Use the method evaluateAsLong(int, IntToLongFunction, double) to compute the long quantile result.
    Parameters:
    
    n - Size of the values.
    
    values - Values function.
    
    p - Probability for the quantile to compute.
    
    Returns:
    
    the quantile
    
    Throws:
    
    IllegalArgumentException - if size < 0; or if the probability p is not in the range [0, 1].
    
    See Also:
    
    evaluateAsLong(int, IntToLongFunction, double)
  - evaluate
```
public double[] evaluate(int n,
                         IntToDoubleFunction values,
                         double... p)
```
    Evaluate the p-th quantiles of the sorted values provided as a double.
    This method can be used when the values of known size are already sorted. It can be used for primitive types not supported by other evaluation methods. Numeric types byte, short and float can be converted to type double without loss of precision.
    short[] x = ... Arrays.sort(x); double[] q = Quantile.withDefaults().evaluate(x.length, i -> x[i], 0.25, 0.5, 0.75);
    
    If the sorted array is a long datatype this method can lose information about the precision of the quantiles due to primitive type conversion. Use the method evaluateAsLong(int, IntToLongFunction, double...) to compute the long quantile result.
    Parameters:
    
    n - Size of the values.
    
    values - Values function.
    
    p - Probabilities for the quantiles to compute.
    
    Returns:
    
    the quantiles
    
    Throws:
    
    IllegalArgumentException - if size < 0; if any probability p is not in the range [0, 1]; or no probabilities are specified.
    
    See Also:
    
    evaluateAsLong(int, IntToLongFunction, double...)
  - evaluateAsLong
```
public StatisticResult evaluateAsLong(int n,
                                      IntToLongFunction values,
                                      double p)
```
    Evaluate the p-th quantile of the sorted values provided as a long.
    This method can be used when the values of known size are already sorted.
    long[] x = ... Arrays.sort(x); StatisticResult q = Quantile.withDefaults() .evaluateAsLong(x.length, i -> x[i], 0.05);
    
    Note: It is not recommended to sort data for use only in the quantile computation. The evaluate(long[], double) method will partially sort the data as required and in most cases will be more efficient.
    Parameters:
    
    n - Size of the values.
    
    values - Values function.
    
    p - Probability for the quantile to compute.
    
    Returns:
    
    the quantile
    
    Throws:
    
    IllegalArgumentException - if size < 0; or if the probability p is not in the range [0, 1].
    
    Since:
    
    1.3
  - evaluateAsLong
```
public StatisticResult[] evaluateAsLong(int n,
                                        IntToLongFunction values,
                                        double... p)
```
    Evaluate the p-th quantiles of the sorted values provided as a long.
    This method can be used when the values of known size are already sorted.
    long[] x = ... Arrays.sort(x); StatisticResult[] q = Quantile.withDefaults() .evaluateAsLong(x.length, i -> x[i], 0.25, 0.5, 0.75);
    
    Note: It is not recommended to sort data for use only in the quantile computation. The evaluate(long[], double...) method will partially sort the data as required and in most cases will be more efficient.
    Parameters:
    
    n - Size of the values.
    
    values - Values function.
    
    p - Probabilities for the quantiles to compute.
    
    Returns:
    
    the quantiles
    
    Throws:
    
    IllegalArgumentException - if size < 0; if any probability p is not in the range [0, 1]; or no probabilities are specified.
    
    Since:
    
    1.3

Class Quantile

Nested Class Summary

Method Summary

Methods inherited from class java.lang.Object

Method Detail

withDefaults

withCopy

with

with

probabilities

probabilities

evaluate

evaluateRange

evaluate

evaluateRange

evaluate

evaluateRange

evaluate

evaluateRange

evaluate

evaluateRange

evaluate

evaluateRange

evaluate

evaluate

evaluateAsLong

evaluateAsLong