com.numericalmethod.suanshu.stats.distribution.univariate

Class EmpiricalDistribution

java.lang.Object

com.numericalmethod.suanshu.stats.distribution.univariate.EmpiricalDistribution

All Implemented Interfaces:

ProbabilityDistribution, java.io.Serializable

Direct Known Subclasses:

ADFAsymptoticDistribution, ADFAsymptoticDistribution1, ADFDistribution, ADFFiniteSampleDistribution, FisherExactDistribution, JarqueBeraDistribution, JohansenAsymptoticDistribution

public class EmpiricalDistribution
extends java.lang.Object
implements ProbabilityDistribution

An empirical cumulative probability distribution function is a cumulative probability distribution function that assigns probability 1/n at each of the n numbers in a sample.

The R equivalent function is ecdf.

See Also:

Wikipedia: EmpiricalDistribution distribution function, Serialized Form

Constructor Summary

Constructors

Constructor and Description
EmpiricalDistribution(double[] data) Construct an empirical distribution from a sample using the default quantile type Quantile.QuantileType.APPROXIMATELY_MEDIAN_UNBIASED.
EmpiricalDistribution(double[] data, Quantile.QuantileType quantileType) Construct an empirical distribution from a sample.

Method Summary

Modifier and Type	Method and Description
double	cdf(double x) Get the cumulative probability F(x) = Pr(X ≤ x).
double	density(double x) This is the probability mass function for the discrete sample.
double	entropy() Deprecated. Not supported yet.
double	kurtosis() Get the excess kurtosis of this distribution.
double	mean() Get the mean of this distribution.
double	median() Get the median of this distribution.
double	moment(double x) Deprecated. Not supported yet.
int	nSamples() Get the number of samples in the empirical distribution.
double	quantile(double u) Get the quantile, the inverse of the cumulative distribution function.
double	skew() Get the skewness of this distribution.
double[]	toArray() Get the sorted sample.
double	variance() Get the variance of this distribution.

Methods inherited from class java.lang.Object

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

Constructor Detail

EmpiricalDistribution

public EmpiricalDistribution(double[] data,
                             Quantile.QuantileType quantileType)

Construct an empirical distribution from a sample.

Parameters:

data - a sample

quantileType - specify how the quantile function is computed

EmpiricalDistribution

public EmpiricalDistribution(double[] data)

Construct an empirical distribution from a sample using the default quantile type Quantile.QuantileType.APPROXIMATELY_MEDIAN_UNBIASED.

Parameters:

data - a sample

Method Detail

nSamples

public int nSamples()

Get the number of samples in the empirical distribution.

Returns:

the number of samples

toArray

public double[] toArray()

Get the sorted sample.

Returns:

the sorted sample

mean

public double mean()

Description copied from interface: ProbabilityDistribution

Get the mean of this distribution.

Specified by:

mean in interface ProbabilityDistribution

Returns:

the mean

See Also:

Wikipedia: Expected value

median

public double median()

Description copied from interface: ProbabilityDistribution

Get the median of this distribution.

Specified by:

median in interface ProbabilityDistribution

Returns:

the median

See Also:

Wikipedia: Median

variance

public double variance()

Description copied from interface: ProbabilityDistribution

Get the variance of this distribution.

Specified by:

variance in interface ProbabilityDistribution

Returns:

the variance

See Also:

Wikipedia: Variance

skew

public double skew()

Description copied from interface: ProbabilityDistribution

Get the skewness of this distribution.

Specified by:

skew in interface ProbabilityDistribution

Returns:

the skewness

See Also:

Wikipedia: Skewness

kurtosis

public double kurtosis()

Description copied from interface: ProbabilityDistribution

Get the excess kurtosis of this distribution.

Specified by:

kurtosis in interface ProbabilityDistribution

Returns:

the excess kurtosis

See Also:

Wikipedia: Kurtosis

entropy

@Deprecated
public double entropy()

Deprecated. Not supported yet.

Description copied from interface: ProbabilityDistribution

Get the entropy of this distribution.

Specified by:

entropy in interface ProbabilityDistribution

Returns:

the entropy

See Also:

Wikipedia: Entropy (information theory)

cdf

public double cdf(double x)

Description copied from interface: ProbabilityDistribution

Get the cumulative probability F(x) = Pr(X ≤ x).

Specified by:

cdf in interface ProbabilityDistribution

Parameters:

x - x

Returns:

F(x) = Pr(X ≤ x)

See Also:

Wikipedia: Cumulative distribution function

quantile

public double quantile(double u)

Get the quantile, the inverse of the cumulative distribution function. It is the value below which random draws from the distribution would fall u×100 percent of the time.

 F-1(u) = x, such that
 Pr(X ≤ x) = u
 

This may not always exist.

For an empirical distribution, this implementation assumes the following.

 F-1(0) = the minimum x value
 F-1(1) = the maximum x value
 

Specified by:

quantile in interface ProbabilityDistribution

Parameters:

u - u, a quantile

Returns:

F^-1(u)

See Also:

Wikipedia: Quantile function

density

public double density(double x)

This is the probability mass function for the discrete sample.

Specified by:

density in interface ProbabilityDistribution

Parameters:

x - an observation

Returns:

pmf(x)

See Also:

• Wikipedia: Probability density function
• Wikipedia: Probability mass function

moment

@Deprecated
public double moment(double x)

Deprecated. Not supported yet.

Description copied from interface: ProbabilityDistribution

The moment generating function is the expected value of e^tX. That is,

E(e^tX)

This may not always exist.

Specified by:

moment in interface ProbabilityDistribution

Parameters:

x - x

Returns:

E(exp(tX))

See Also:

Wikipedia: Moment-generating function