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

java.lang.Object
  com.numericalmethod.suanshu.stats.distribution.univariate.EmpiricalDistribution

All Implemented Interfaces:

UnivariateDistribution

Direct Known Subclasses:

AdfAsymptoticDistribution, AdfAsymptoticDistribution1, AdfDistribution, AdfFiniteSampleDistribution, FisherExactDistribution, JarqueBeraDistribution, JohansenAsymptoticDistribution

public class EmpiricalDistribution
extends java.lang.Object
implements UnivariateDistribution

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

Constructor Summary

EmpiricalDistribution(double[] data)
Construct an empirical distribution from a sample.

EmpiricalDistribution(double[] data, Quantile.Type quantileType)
Construct an empirical distribution from a sample.

Method Summary

double	cdf(double x) The cumulative distribution function.
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.
double	quantile(double u) The inverse of the cumulative distribution function.
double	skew() Get the skewness of this distribution.
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.Type 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.

Parameters:

data - a sample

Method Detail

mean

public double mean()

Description copied from interface: UnivariateDistribution

Get the mean of this distribution.

Specified by:

mean in interface UnivariateDistribution

Returns:

the mean

See Also:

Wikipedia: Expected value

median

public double median()

Description copied from interface: UnivariateDistribution

Get the median of this distribution.

Specified by:

median in interface UnivariateDistribution

Returns:

the median

See Also:

Wikipedia: Median

variance

public double variance()

Description copied from interface: UnivariateDistribution

Get the variance of this distribution.

Specified by:

variance in interface UnivariateDistribution

Returns:

the variance

See Also:

Wikipedia: Variance

skew

public double skew()

Description copied from interface: UnivariateDistribution

Get the skewness of this distribution.

Specified by:

skew in interface UnivariateDistribution

Returns:

the skewness

See Also:

Wikipedia: Skewness

kurtosis

public double kurtosis()

Description copied from interface: UnivariateDistribution

Get the excess kurtosis of this distribution.

Specified by:

kurtosis in interface UnivariateDistribution

Returns:

the excess kurtosis

See Also:

Wikipedia: Kurtosis

entropy

@Deprecated
public double entropy()

Deprecated. Not supported yet.

Description copied from interface: UnivariateDistribution

Get the entropy of this distribution.

Specified by:

entropy in interface UnivariateDistribution

Returns:

the entropy

See Also:

Wikipedia: Entropy (information theory)

cdf

public double cdf(double x)

Description copied from interface: UnivariateDistribution

The cumulative distribution function.

F(x) = Pr(X <= x)

Specified by:

cdf in interface UnivariateDistribution

Parameters:

x - x

Returns:

F(x) = Pr(X <= x)

See Also:

Wikipedia: Cumulative distribution function

quantile

public double quantile(double u)

Description copied from interface: UnivariateDistribution

The inverse of the cumulative distribution function. It returns the value below which random draws from the given distribution would fall, u×100 percent of the time.

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

This may not always exist.

Specified by:

quantile in interface UnivariateDistribution

Parameters:

u - u

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 UnivariateDistribution

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: UnivariateDistribution

The moment generating function, which is the expected value of

etX

This may not always exist.

Specified by:

moment in interface UnivariateDistribution

Parameters:

x - x

Returns:

E(exp(tX))

See Also:

Wikipedia: Moment-generating function