smile.stat.distribution

## Class TDistribution

• All Implemented Interfaces:
java.io.Serializable, 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.
Serialized Form
• ### Field Summary

Fields
Modifier and Type Field and Description
`int` `nu`
The degree of freedom.
• ### Constructor Summary

Constructors
Constructor and Description
`TDistribution(int nu)`
Constructor.
• ### Method Summary

All Methods
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.
`int` `length()`
The number of parameters 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.
`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` `variance()`
The variance of distribution.
• ### Methods inherited from class smile.stat.distribution.AbstractDistribution

`inverseTransformSampling, quantile, quantile, rejection`
• ### Methods inherited from class java.lang.Object

`clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait`
• ### Methods inherited from interface smile.stat.distribution.Distribution

`likelihood, logLikelihood, rand`
• ### Field Detail

• #### nu

`public final int nu`
The degree of freedom.
• ### Constructor Detail

• #### TDistribution

`public TDistribution(int nu)`
Constructor.
Parameters:
`nu` - degree of freedom.
• ### Method Detail

• #### length

`public int length()`
Description copied from interface: `Distribution`
The number of parameters of the distribution. The "length" is in the sense of the minimum description length principle.
• #### mean

`public double mean()`
Description copied from interface: `Distribution`
The mean of distribution.
• #### variance

`public double variance()`
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.