com.numericalmethod.suanshu.stats.descriptive.rank
Class Quantile

java.lang.Object
  com.numericalmethod.suanshu.stats.descriptive.rank.Quantile

All Implemented Interfaces:

Statistic

public class Quantile
extends java.lang.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.

See Also:

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

Nested Class Summary

static class

Quantile.Type the quantile definitions available For details, please refer to Sample quantiles in statistical packages by Hyndman, R.

Field Summary

Quantile.Type

type the quantile definition

Constructor Summary

Quantile(double[] data)
Construct a Quantile instance using the default type: APPROXIMATELY_MEDIAN_UNBIASED.

Quantile(double[] data, Quantile.Type type)
Construct a Quantile instance.

Method Summary

void	addData(double... data) Recompute the statistic, 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 probability.

Methods inherited from class java.lang.Object

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

Field Detail

type

public final Quantile.Type type

the quantile definition

Constructor Detail

Quantile

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

Construct a Quantile instance.

Parameters:

data - the data

type - the algorithm to compute Q(q)

Quantile

public Quantile(double[] data)

Construct a Quantile instance using the default type: APPROXIMATELY_MEDIAN_UNBIASED.

Parameters:

data - the data

Method Detail

addData

public void addData(double... data)

Description copied from interface: Statistic

Recompute the statistic, 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

value

public double value(double q)

Compute the sample value corresponding to a probability.

Parameters:

q - a quantile

Returns:

the value for the q quantile

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