# Class TDistribution

java.lang.Object
smile.stat.distribution.AbstractDistribution
smile.stat.distribution.TDistribution
All Implemented Interfaces:
`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.
• ## Field Summary

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

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

Modifier and Type
Method
Description
`double`
`cdf(double x)`
Cumulative distribution function.
`double`
`cdf2tailed(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`
`quantile2tailed(double p)`
Two-tailed quantile.
`double`
`rand()`
Generates a random number following this distribution.
`double`
`sd()`
The standard deviation of distribution.
`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 Details

• ### nu

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

• ### TDistribution

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

• ### 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.
Returns:
The number of parameters.
• ### mean

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

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

public double sd()
Description copied from interface: `Distribution`
The standard deviation of distribution.
Returns:
The standard deviation.
• ### entropy

public double entropy()
Description copied from interface: `Distribution`
Shannon entropy of the distribution.
Returns:
Shannon entropy.
• ### 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.
Returns:
a random number.
• ### 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.
Parameters:
`x` - a real number.
Returns:
the density.
• ### logp

public double logp(double x)
Description copied from interface: `Distribution`
The density at x in log scale, which may prevents the underflow problem.
Parameters:
`x` - a real number.
Returns:
the log density.
• ### cdf

public double cdf(double x)
Description copied from interface: `Distribution`
Cumulative distribution function. That is the probability to the left of x.
Parameters:
`x` - a real number.
Returns:
the probability.
• ### 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.
Parameters:
`p` - the probability.
Returns:
the quantile.
• ### cdf2tailed

public double cdf2tailed(double x)
Two-tailed cdf.
Parameters:
`x` - a real number.
Returns:
the two-tailed cdf.
• ### quantile2tailed

public double quantile2tailed(double p)
Two-tailed quantile.
Parameters:
`p` - a probability.
Returns:
the two-tailed quantile.