com.imsl.stat

Class EmpiricalQuantiles

java.lang.Object

com.imsl.stat.EmpiricalQuantiles

All Implemented Interfaces:

Serializable, Cloneable

public class EmpiricalQuantiles
extends Object
implements Serializable, Cloneable

Computes empirical quantiles.

The class EmpiricalQuantiles determines the empirical quantiles, as indicated in the array qProp, from the data in x. The algorithm first checks to see if x is sorted; if x is not sorted, the algorithm does either a complete or partial sort, depending on how many order statistics are required to compute the quantiles requested. The algorithm returns the empirical quantiles and, for each quantile, the two order statistics from the sample that are at least as large and at least as small as the quantile. For a sample of size n, the quantile corresponding to the proportion p is defined as $$Q(p) = (1 - f)x_{(j)} + fx_{(j+1)} $$ where \(j = \lfloor p(n+1) \rfloor \), \(f = p(n+1) - j\), and \(x_{(j)}\), is the j-th order statistic, if \(1 \leq j \le n\); otherwise, the empirical quantile is the smallest or largest order statistic.

See Also:

Example 1, Serialized Form

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	EmpiricalQuantiles.ScaleFactorZeroException The computations cannot continue because a scale factor is zero.

Constructor Summary

Constructors

Constructor and Description
EmpiricalQuantiles(double[] x, double[] qProp) Constructor for EmpiricalQuantiles.

Method Summary

Modifier and Type	Method and Description
double[]	getQ() Returns the empirical quantiles.
int	getTotalMissing() Returns the total number of missing values.
double[]	getXHi() Returns the smallest element of x greater than or equal to the desired quantile.
double[]	getXLo() Returns the largest element of x less than or equal to the desired quantile.

Methods inherited from class java.lang.Object

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

Constructor Detail

EmpiricalQuantiles

public EmpiricalQuantiles(double[] x,
                          double[] qProp)

Constructor for EmpiricalQuantiles.

Parameters:

x - A double array containing the data.

qProp - A double array containing the quantile proportions.

Method Detail

getTotalMissing

public int getTotalMissing()

Returns the total number of missing values.

Returns:

an int scalar value representing the total number of missing values (NaN) in input x.

getQ

public final double[] getQ()

Returns the empirical quantiles.

Returns:

A double array containing the empirical quantiles. Q[i] corresponds to the empirical quantile at proportion qProp[i]. The quantiles are determined by linear interpolation between adjacent ordered sample values.

getXLo

public final double[] getXLo()

Returns the largest element of x less than or equal to the desired quantile.

Returns:

A double array containing the largest element of x less than or equal to the desired quantile.

getXHi

public final double[] getXHi()

Returns the smallest element of x greater than or equal to the desired quantile.

Returns:

A double array containing the smallest element of x greater than or equal to the desired quantile.