org.apache.commons.math.stat.descriptive.rank

## Class Percentile

• All Implemented Interfaces:
java.io.Serializable, UnivariateStatistic
Direct Known Subclasses:
Median

```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 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.`

``` Since 2.2, Percentile implementation uses only selection instead of complete sorting and caches selection algorithm state between calls to the various evaluate methods when several percentiles are to be computed on the same data. This greatly improves efficiency, both for single percentile and multiple percentiles computations. However, it also induces a need to be sure the data at one call to evaluate is the same as the data with the cached algorithm state from the previous calls. Percentile does this by checking the array reference itself and a checksum of its content by default. If the user already knows he calls evaluate on an immutable array, he can save the checking time by calling the evaluate methods that do not 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 ```
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``` Constructor Summary Constructors  Constructor and Description Percentile() Constructs a Percentile with a default quantile value of 50.0. Percentile(double p) Constructs a Percentile with the specific quantile value. Percentile(Percentile original) Copy constructor, creates a new Percentile identical to the original Method Summary All Methods Static Methods Instance Methods Concrete 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) Copies source to dest. 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 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 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). Methods inherited from class org.apache.commons.math.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 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 Percentile public Percentile(Percentile original) Copy constructor, creates a new Percentile identical to the original Parameters: original - the Percentile instance to copy 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) Set the data array. 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 See Also: AbstractUnivariateStatistic.evaluate() evaluate public double evaluate(double p) Returns the result of evaluating the statistic over the stored data. The stored array is the one which was set by previous calls to Parameters: p - the percentile value to compute Returns: the value of the statistic applied to the stored data 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 interface UnivariateStatistic 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 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 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 public static void copy(Percentile source, Percentile dest) Copies source to dest. Neither source nor dest can be null. Parameters: source - Percentile to copy dest - Percentile to copy to Throws: java.lang.NullPointerException - if either source or dest is null ```
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