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 and 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.

Since:

1.1

See Also:

Nested Class Summary

Nested Classes

Modifier and Type

Class

Description

static enum

Quantile.EstimationMethod

Estimation methods for a quantile.
Method Summary

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 values.

double[]

evaluate(int n, IntToDoubleFunction values, double... p)

Evaluate the p-th quantiles of the values.

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..

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 Details
- 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 double evaluate(int n, IntToDoubleFunction values, double p)
  Evaluate the p-th quantile of the values.
  This method can be used when the values of known size are already sorted.
  short[] x = ... Arrays.sort(x); double q = Quantile.withDefaults().evaluate(x.length, i -> x[i], 0.05);
  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].
- evaluate
  
  public double[] evaluate(int n, IntToDoubleFunction values, double... p)
  Evaluate the p-th quantiles of the values.
  This method can be used when the values of known size are already sorted.
  short[] x = ... Arrays.sort(x); double[] q = Quantile.withDefaults().evaluate(x.length, i -> x[i], 0.25, 0.5, 0.75);
  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.

Class Quantile

Nested Class Summary

Method Summary

Methods inherited from class java.lang.Object

Method Details

withDefaults

withCopy

with

with

probabilities

probabilities

evaluate

evaluateRange

evaluate

evaluateRange

evaluate

evaluateRange

evaluate

evaluateRange

evaluate

evaluate