org.apache.commons.math.stat
Class Percentile

java.lang.Object
  org.apache.commons.math.stat.AbstractUnivariateStatistic
      org.apache.commons.math.stat.Percentile

All Implemented Interfaces:

java.io.Serializable

public class Percentile
extends AbstractUnivariateStatistic
implements java.io.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). If pos >= n return the largest element in the array; otherwise
4. 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 (totally) ordered. Input arrays are copied and then sorted using Arrays.sort(double[]). 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.

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.

Version:

$Revision$ $Date$

See Also:

Serialized Form

Constructor Summary

Percentile()
Constructs a Percentile with a default quantile value of 50.0.

Percentile(double p)
Constructs a Percentile with the specific quantile value.

Method Summary

double	evaluate(double[] values, double p) Returns an estimate of the pth percentile of the values in the values array.
double	evaluate(double[] values, int start, int length) Returns an estimate of the quantileth percentile of the designated values in the values array.
double	evaluate(double[] values, int begin, int length, double p) 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.
double	getQuantile() Returns the value of the quantile field (determines what percentile is computed when evaluate() is called with no quantile argument).
void	setQuantile(double p) Sets the value of the quantile field (determines what percentile is computed when evaluate() is called with no quantile argument).

Methods inherited from class org.apache.commons.math.stat.AbstractUnivariateStatistic

evaluate, test

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

Percentile

public Percentile()

Constructs a Percentile with a default quantile value of 50.0.

Percentile

public Percentile(double p)

Constructs a Percentile with the specific quantile value.

Parameters:

p - the quantile

Throws:

java.lang.IllegalArgumentException - if p is not greater than 0 and less than or equal to 100

Method Detail

evaluate

public double evaluate(double[] values,
                       double p)

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 IllegalArgumentException 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:

java.lang.IllegalArgumentException - if values is null or p is invalid

evaluate

public double evaluate(double[] values,
                       int start,
                       int length)

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 IllegalArgumentException 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 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:

java.lang.IllegalArgumentException - if the parameters are not valid

See Also:

org.apache.commons.math.stat.descriptive.UnivariateStatistic#evaluate(double[], int, int)

evaluate

public double evaluate(double[] values,
                       int begin,
                       int length,
                       double p)

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 IllegalArgumentException 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:

java.lang.IllegalArgumentException - 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

setQuantile

public void setQuantile(double p)

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:

java.lang.IllegalArgumentException - if p is not greater than 0 and less than or equal to 100