dev.nm.stat.descriptive.rank

Class Quantile

java.lang.Object

dev.nm.stat.descriptive.rank.Quantile

All Implemented Interfaces:

Statistic

public class Quantile
extends Object
implements Statistic

Quantiles are points taken at regular intervals from the cumulative distribution function (CDF) of a random variable. Dividing ordered data into q essentially equal-sized data subsets is the motivation for q-quantiles; the quantiles are the data values marking the boundaries between consecutive subsets. Put another way, the k-th q-quantile for a random variable is the value x such that the probability that the random variable will be less than x is at most k/q and the probability that the random variable will be more than x is at most (q - k)/q. There are q-1 q-quantiles, with k an integer satisfying 0 < k < q. The smallest observation corresponds to probability 0 and the largest probability 1. This class implements the 9 different quantile definitions in Hyndman 1996.

The R equivalent function is quantile.

Choose a quantile convention explicitly

Different interpolation conventions can return different quartiles for the same sample. The S convention matches R type 7 and linearly interpolates between ordered observations.

 import dev.nm.stat.descriptive.rank.Quantile;
 Quantile quantiles = new Quantile(new double[]{4, 1, 3, 2}, Quantile.QuantileType.S);
 assert Math.abs(quantiles.value(0.25) - 1.75) < 1e-12;
 assert Math.abs(quantiles.value(0.5) - 2.5) < 1e-12;
 assert quantiles.value(0) == 1.0;
 assert quantiles.value(1) == 4.0;
 

See Also:

• "R. J. Hyndman, and Y. Fan, "Sample quantiles in statistical packages," American Statistician, 50, 361-365, 1996."
• Wikipedia: Quantile

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	Quantile.QuantileType the available quantile definitions

Constructor Summary

Constructors

Constructor and Description
Quantile() Construct a Quantile calculator using the default type: Quantile.QuantileType.APPROXIMATELY_MEDIAN_UNBIASED, without initial data.
Quantile(double[] data) Construct a Quantile calculator using the default type: Quantile.QuantileType.APPROXIMATELY_MEDIAN_UNBIASED.
Quantile(double[] data, Quantile.QuantileType type) Construct a Quantile calculator.

Method Summary

Modifier and Type	Method and Description
void	addData(double... data) Recompute the statistic with more data, incrementally if possible.
long	N() Get the size of the sample.
double	value() Get the value of the statistic.
double	value(double q) Compute the sample value corresponding to a quantile.

Methods inherited from class java.lang.Object

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

Constructor Detail

Quantile

public Quantile(double[] data,
                Quantile.QuantileType type)

Construct a Quantile calculator.

Parameters:

data - the data

type - the algorithm to compute Q(q)

Quantile

public Quantile(double[] data)

Construct a Quantile calculator using the default type: Quantile.QuantileType.APPROXIMATELY_MEDIAN_UNBIASED.

Parameters:

data - the data

Quantile

public Quantile()

Construct a Quantile calculator using the default type: Quantile.QuantileType.APPROXIMATELY_MEDIAN_UNBIASED, without initial data.

Method Detail

value

public double value(double q)

Compute the sample value corresponding to a quantile.

Parameters:

q - a quantile

Returns:

the value for the q quantile

addData

public void addData(double... data)

Description copied from interface: Statistic

Recompute the statistic with more data, incrementally if possible.

Specified by:

addData in interface Statistic

Parameters:

data - an array of new items

value

public double value()

Description copied from interface: Statistic

Get the value of the statistic.

Specified by:

value in interface Statistic

Returns:

the statistic

N

public long N()

Description copied from interface: Statistic

Get the size of the sample.

Specified by:

N in interface Statistic

Returns:

the sample size