smile.stat.distribution

Class EmpiricalDistribution

java.lang.Object

smile.stat.distribution.AbstractDistribution

smile.stat.distribution.DiscreteDistribution

smile.stat.distribution.EmpiricalDistribution

All Implemented Interfaces:

Distribution

public class EmpiricalDistribution
extends DiscreteDistribution

An empirical distribution function or empirical cdf, is a cumulative probability distribution function that concentrates probability 1/n at each of the n numbers in a sample. As n grows the empirical distribution will getting closer to the true distribution. Empirical distribution is a very important estimator in Statistics. In particular, the Bootstrap method rely heavily on the empirical distribution.

Author:

Haifeng Li

Constructor Summary

Constructors

Constructor and Description
EmpiricalDistribution(double[] prob) Constructor.
EmpiricalDistribution(int[] data) Constructor.

Method Summary

Methods

Modifier and Type	Method and Description
double	cdf(double k) Cumulative distribution function.
double	entropy() Shannon entropy of the distribution.
double	logp(int k) The probability mass function in log scale.
double	mean() The mean of distribution.
int	npara() The number of parameters of the distribution.
double	p(int k) The probability mass function.
double	quantile(double p) The quantile, the probability to the left of quantile is p.
double	rand() Generates a random number following this distribution.
int[]	rand(int n)
double	sd() The standard deviation of distribution.
String	toString()
double	var() The variance of distribution.

Methods inherited from class smile.stat.distribution.DiscreteDistribution

likelihood, logLikelihood, logp, p, quantile

Methods inherited from class smile.stat.distribution.AbstractDistribution

inverseTransformSampling, likelihood, logLikelihood, quantile, quantile, rejection

Methods inherited from class java.lang.Object

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

Constructor Detail

EmpiricalDistribution

public EmpiricalDistribution(double[] prob)

Constructor.

EmpiricalDistribution

public EmpiricalDistribution(int[] data)

Constructor. CDF will be estimated from the data.

Method Detail

npara

public int npara()

Description copied from interface: Distribution

The number of parameters of the distribution.

mean

public double mean()

Description copied from interface: Distribution

The mean of distribution.

var

public double var()

Description copied from interface: Distribution

The variance of distribution.

sd

public double sd()

Description copied from interface: Distribution

The standard deviation of distribution.

entropy

public double entropy()

Description copied from interface: Distribution

Shannon entropy of the distribution.

toString

public String toString()

Overrides:

toString in class Object

rand

public double rand()

Description copied from interface: Distribution

Generates a random number following this distribution.

rand

public int[] rand(int n)

p

public double p(int k)

Description copied from class: DiscreteDistribution

The probability mass function.

Specified by:

p in class DiscreteDistribution

logp

public double logp(int k)

Description copied from class: DiscreteDistribution

The probability mass function in log scale.

Specified by:

logp in class DiscreteDistribution

cdf

public double cdf(double k)

Description copied from interface: Distribution

Cumulative distribution function. That is the probability to the left of x.

quantile

public double quantile(double p)

Description copied from interface: Distribution

The quantile, the probability to the left of quantile is p. It is actually the inverse of cdf.