com.itemanalysis.psychometrics.kernel

Class KernelDensity

java.lang.Object

com.itemanalysis.psychometrics.kernel.KernelDensity

All Implemented Interfaces:

DistributionApproximation

public class KernelDensity
extends java.lang.Object
implements DistributionApproximation

Field Summary

Fields

Modifier and Type	Field and Description
protected boolean	interpolatorUpdateNeeded

Constructor Summary

Constructors

Constructor and Description
KernelDensity(KernelFunction kernel, Bandwidth h, UniformDistributionApproximation uniform)

Method Summary

Modifier and Type	Method and Description
double[]	evaluate() Call this method when using the incremental update to the density estimator.
double[]	evaluate(double[] x) Call tihs method when not using the incremental update.
double[]	evaluate(double[] x, int index) Leave one out kernel evaluate estimate.
Bandwidth	getBandwidth() Bandwith
double	getDensityAt(int index) Gets an elements from the array of density values.
org.apache.commons.math3.analysis.UnivariateFunction	getInterpolater()
org.apache.commons.math3.analysis.UnivariateFunction	getInterpolater2() Returns interpolator for squared evaluate
double	getMaximum()
double	getMean()
double	getMinimum()
int	getNumberOfPoints() Number of evaluation points (and corresponding number of density values) in this approximation.
double	getPointAt(int index) Gets an element from the array of evaluation points.
double[]	getPoints() Gets an array of evaluation points.
double	getStandardDeviation()
void	increment(double x) Incremental computation of the density.
void	setDensityAt(int index, double value)
void	setPointAt(int index, double value)
double[]	standardize(boolean keepPoints) Uses current quadrature points and weights to compute the mean and standard deviation of the density, and tehn standardizes the distribution to have a mean of zero and a standard deviation of one.

Methods inherited from class java.lang.Object

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

Field Detail

interpolatorUpdateNeeded

protected boolean interpolatorUpdateNeeded

Constructor Detail

KernelDensity

public KernelDensity(KernelFunction kernel,
                     Bandwidth h,
                     UniformDistributionApproximation uniform)

Method Detail

increment

public void increment(double x)

Incremental computation of the density. This method is called for each data point.

Parameters:

x - a data point

evaluate

public double[] evaluate()

Call this method when using the incremental update to the density estimator.

Specified by:

evaluate in interface DistributionApproximation

Returns:

an array representing the density (y-axis) at the evaluation points.

evaluate

public double[] evaluate(double[] x)

Call tihs method when not using the incremental update. It will compute the density from an array of data points.

Parameters:

x - an array of data points

Returns:

density of the points

evaluate

public double[] evaluate(double[] x,
                         int index)

Leave one out kernel evaluate estimate. Omitted data point is given by index. This method is primarily used by the least squares cross validation method of choosing the smoothing parameter.

Parameters:

x -

index -

Returns:

getPoints

public double[] getPoints()

Description copied from interface: DistributionApproximation

Gets an array of evaluation points.

Specified by:

getPoints in interface DistributionApproximation

Returns:

evaluation points.

getNumberOfPoints

public int getNumberOfPoints()

Description copied from interface: DistributionApproximation

Number of evaluation points (and corresponding number of density values) in this approximation.

Specified by:

getNumberOfPoints in interface DistributionApproximation

Returns:

number of points.

getBandwidth

public Bandwidth getBandwidth()

Bandwith

Returns:

bandwith used for the kernel estimator

getInterpolater

public org.apache.commons.math3.analysis.UnivariateFunction getInterpolater()

getInterpolater2

public org.apache.commons.math3.analysis.UnivariateFunction getInterpolater2()

Returns interpolator for squared evaluate

Returns:

getPointAt

public double getPointAt(int index)

Description copied from interface: DistributionApproximation

Gets an element from the array of evaluation points.

Specified by:

getPointAt in interface DistributionApproximation

Parameters:

index - array index of evaluation points.

Returns:

evaluation point at index.

getDensityAt

public double getDensityAt(int index)

Description copied from interface: DistributionApproximation

Gets an elements from the array of density values.

Specified by:

getDensityAt in interface DistributionApproximation

Parameters:

index - array index of density value.

Returns:

density value at index.

setDensityAt

public void setDensityAt(int index,
                         double value)

Specified by:

setDensityAt in interface DistributionApproximation

setPointAt

public void setPointAt(int index,
                       double value)

Specified by:

setPointAt in interface DistributionApproximation

getMinimum

public double getMinimum()

Specified by:

getMinimum in interface DistributionApproximation

getMaximum

public double getMaximum()

Specified by:

getMaximum in interface DistributionApproximation

getMean

public double getMean()

Specified by:

getMean in interface DistributionApproximation

getStandardDeviation

public double getStandardDeviation()

Specified by:

getStandardDeviation in interface DistributionApproximation

standardize

public double[] standardize(boolean keepPoints)

Uses current quadrature points and weights to compute the mean and standard deviation of the density, and tehn standardizes the distribution to have a mean of zero and a standard deviation of one. It achieves standardization in one of two possible ways. If keepPoints is true, the original points are retained and linear interpolation of the empiricial cumulative distribution is used to obtain the new weights. That is, the points are never changed, but the distribution is standardized. If keepPoints is false, the original weights are retained, but the points are transformed to standardize the distribution.

Specified by:

standardize in interface DistributionApproximation

Parameters:

keepPoints - if true original points are retained and weights are computed at these points using linear interpolation of the empirical cumulative distribution. If false, original weights are retained and standardization is achieved by linearly transforming the original points.

Returns:

transformation coefficients as a double array with two values used for the linear transformation of the points. The first value is the slope and the second value is the intercept.