smile.stat.distribution

Class TDistribution

java.lang.Object

smile.stat.distribution.AbstractDistribution

smile.stat.distribution.TDistribution

All Implemented Interfaces:

Distribution

public class TDistribution
extends AbstractDistribution

Student's t-distribution (or simply the t-distribution) is a probability distribution that arises in the problem of estimating the mean of a normally distributed population when the sample size is small. Student's t-distribution arises when (as in nearly all practical statistical work) the population standard deviation is unknown and has to be estimated from the data. It is the basis of the popular Student's t-tests for the statistical significance of the difference between two sample means, and for confidence intervals for the difference between two population means. The Student's t-distribution is a special case of the generalised hyperbolic distribution.

Constructor Summary

Constructors

Constructor and Description
TDistribution(int nu) Constructor.

Method Summary

Modifier and Type	Method and Description
double	cdf(double x) Cumulative distribution function.
double	cdf2tiled(double x) Two-tailed cdf.
double	entropy() Shannon entropy of the distribution.
double	logp(double x) The density at x in log scale, which may prevents the underflow problem.
double	mean() The mean of distribution.
int	npara() The number of parameters of the distribution.
double	p(double x) The probability density function for continuous distribution or probability mass function for discrete distribution at x.
double	quantile(double p) The quantile, the probability to the left of quantile is p.
double	quantile2tiled(double p) Two-tailed quantile.
double	rand() Generates a random number following this distribution.
double	sd() The standard deviation of distribution.
java.lang.String	toString()
double	var() The variance of distribution.

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

TDistribution

public TDistribution(int nu)

Constructor.

Parameters:

nu - degree of freedom.

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 java.lang.String toString()

Overrides:

toString in class java.lang.Object

rand

public double rand()

Description copied from interface: Distribution

Generates a random number following this distribution.

p

public double p(double x)

Description copied from interface: Distribution

The probability density function for continuous distribution or probability mass function for discrete distribution at x.

logp

public double logp(double x)

Description copied from interface: Distribution

The density at x in log scale, which may prevents the underflow problem.

cdf

public double cdf(double x)

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.

cdf2tiled

public double cdf2tiled(double x)

Two-tailed cdf.

quantile2tiled

public double quantile2tiled(double p)

Two-tailed quantile.