Class Quantiles
 java.lang.Object

 com.google.common.math.Quantiles

@GwtIncompatible public final class Quantiles extends java.lang.Object
Provides a fluent API for calculating quantiles.Examples
To compute the median:
wheredouble myMedian = median().compute(myDataset);
median()
has been statically imported.To compute the 99th percentile:
wheredouble myPercentile99 = percentiles().index(99).compute(myDataset);
percentiles()
has been statically imported.To compute median and the 90th and 99th percentiles:
whereMap<Integer, Double> myPercentiles = percentiles().indexes(50, 90, 99).compute(myDataset);
percentiles()
has been statically imported:myPercentiles
maps the keys 50, 90, and 99, to their corresponding quantile values.To compute quartiles, use
quartiles()
instead ofpercentiles()
. To compute arbitrary qquantiles, usescale(q)
.These examples all take a copy of your dataset. If you have a double array, you are okay with it being arbitrarily reordered, and you want to avoid that copy, you can use
computeInPlace
instead ofcompute
.Definition and notes on interpolation
The definition of the kth qquantile of N values is as follows: define x = k * (N  1) / q; if x is an integer, the result is the value which would appear at index x in the sorted dataset (unless there are
NaN
values, see below); otherwise, the result is the average of the values which would appear at the indexes floor(x) and ceil(x) weighted by (1frac(x)) and frac(x) respectively. This is the same definition as used by Excel and by S, it is the Type 7 definition in R, and it is described by wikipedia as providing "Linear interpolation of the modes for the order statistics for the uniform distribution on [0,1]."Handling of nonfinite values
If any values in the input are
NaN
then all values returned areNaN
. (This is the one occasion when the behaviour is not the same as you'd get from sorting withArrays.sort(double[])
orCollections.sort(List<Double>)
and selecting the required value(s). Those methods would sortNaN
as if it is greater than any other value and place them at the end of the dataset, even afterPOSITIVE_INFINITY
.)Otherwise,
NEGATIVE_INFINITY
andPOSITIVE_INFINITY
sort to the beginning and the end of the dataset, as you would expect.If required to do a weighted average between an infinity and a finite value, or between an infinite value and itself, the infinite value is returned. If required to do a weighted average between
NEGATIVE_INFINITY
andPOSITIVE_INFINITY
,NaN
is returned (note that this will only happen if the dataset contains no finite values).Performance
The average time complexity of the computation is O(N) in the size of the dataset. There is a worst case time complexity of O(N^2). You are extremely unlikely to hit this quadratic case on randomly ordered data (the probability decreases faster than exponentially in N), but if you are passing in unsanitized user data then a malicious user could force it. A light shuffle of the data using an unpredictable seed should normally be enough to thwart this attack.
The time taken to compute multiple quantiles on the same dataset using
indexes
is generally less than the total time taken to compute each of them separately, and sometimes much less. For example, on a large enough dataset, computing the 90th and 99th percentiles together takes about 55% as long as computing them separately.When calling
Quantiles.ScaleAndIndex.compute(java.util.Collection<? extends java.lang.Number>)
(in either form), the memory requirement is 8*N bytes for the copy of the dataset plus an overhead which is independent of N (but depends on the quantiles being computed). When callingcomputeInPlace
(in either form), only the overhead is required. The number of object allocations is independent of N in both cases. Since:
 20.0
 Author:
 Pete Gillin


Nested Class Summary
Nested Classes Modifier and Type Class Description static class
Quantiles.Scale
Describes the point in a fluent API chain where only the scale (i.e.static class
Quantiles.ScaleAndIndex
Describes the point in a fluent API chain where the scale and a single quantile index (i.e.static class
Quantiles.ScaleAndIndexes
Describes the point in a fluent API chain where the scale and a multiple quantile indexes (i.e.

Constructor Summary
Constructors Constructor Description Quantiles()

Method Summary
All Methods Static Methods Concrete Methods Modifier and Type Method Description static Quantiles.ScaleAndIndex
median()
Specifies the computation of a median (i.e.static Quantiles.Scale
percentiles()
Specifies the computation of percentiles (i.e.static Quantiles.Scale
quartiles()
Specifies the computation of quartiles (i.e.static Quantiles.Scale
scale(int scale)
Specifies the computation of qquantiles.



Constructor Detail

Quantiles
public Quantiles()


Method Detail

median
public static Quantiles.ScaleAndIndex median()
Specifies the computation of a median (i.e. the 1st 2quantile).

quartiles
public static Quantiles.Scale quartiles()
Specifies the computation of quartiles (i.e. 4quantiles).

percentiles
public static Quantiles.Scale percentiles()
Specifies the computation of percentiles (i.e. 100quantiles).

scale
public static Quantiles.Scale scale(int scale)
Specifies the computation of qquantiles. Parameters:
scale
 the scale for the quantiles to be calculated, i.e. the q of the qquantiles, which must be positive

