## Class TDistributionImpl

• All Implemented Interfaces:
`java.io.Serializable`, `ContinuousDistribution`, `Distribution`, `TDistribution`

```public class TDistributionImpl
extends AbstractContinuousDistribution
implements TDistribution, java.io.Serializable```
Default implementation of `TDistribution`.
Serialized Form
• ### Field Summary

Fields
Modifier and Type Field Description
`static double` `DEFAULT_INVERSE_ABSOLUTE_ACCURACY`
Default inverse cumulative probability accuracy
• ### Constructor Summary

Constructors
Constructor Description
`TDistributionImpl​(double degreesOfFreedom)`
Create a t distribution using the given degrees of freedom.
```TDistributionImpl​(double degreesOfFreedom, double inverseCumAccuracy)```
Create a t distribution using the given degrees of freedom and the specified inverse cumulative probability absolute accuracy.
• ### Method Summary

All Methods
Modifier and Type Method Description
`double` `cumulativeProbability​(double x)`
For this distribution, X, this method returns P(X < `x`).
`double` `density​(double x)`
Returns the probability density for a particular point.
`double` `getDegreesOfFreedom()`
Access the degrees of freedom.
`double` `getNumericalMean()`
Returns the mean.
`double` `getNumericalVariance()`
Returns the variance.
`double` `getSupportLowerBound()`
Returns the lower bound of the support for the distribution.
`double` `getSupportUpperBound()`
Returns the upper bound of the support for the distribution.
`double` `inverseCumulativeProbability​(double p)`
For this distribution, X, this method returns the critical point x, such that P(X < x) = `p`.
`void` `setDegreesOfFreedom​(double degreesOfFreedom)`
Deprecated.
as of 2.1 (class will become immutable in 3.0)
• ### Methods inherited from class org.apache.commons.math.distribution.AbstractContinuousDistribution

`reseedRandomGenerator, sample, sample`
• ### Methods inherited from class org.apache.commons.math.distribution.AbstractDistribution

`cumulativeProbability`
• ### Methods inherited from class java.lang.Object

`equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`
• ### Methods inherited from interface org.apache.commons.math.distribution.Distribution

`cumulativeProbability`
• ### Field Detail

• #### DEFAULT_INVERSE_ABSOLUTE_ACCURACY

`public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY`
Default inverse cumulative probability accuracy
Since:
2.1
Constant Field Values
• ### Constructor Detail

• #### TDistributionImpl

```public TDistributionImpl​(double degreesOfFreedom,
double inverseCumAccuracy)```
Create a t distribution using the given degrees of freedom and the specified inverse cumulative probability absolute accuracy.
Parameters:
`degreesOfFreedom` - the degrees of freedom.
`inverseCumAccuracy` - the maximum absolute error in inverse cumulative probability estimates (defaults to `DEFAULT_INVERSE_ABSOLUTE_ACCURACY`)
Since:
2.1
• #### TDistributionImpl

`public TDistributionImpl​(double degreesOfFreedom)`
Create a t distribution using the given degrees of freedom.
Parameters:
`degreesOfFreedom` - the degrees of freedom.
• ### Method Detail

• #### setDegreesOfFreedom

```@Deprecated
public void setDegreesOfFreedom​(double degreesOfFreedom)```
Deprecated.
as of 2.1 (class will become immutable in 3.0)
Modify the degrees of freedom.
Specified by:
`setDegreesOfFreedom` in interface `TDistribution`
Parameters:
`degreesOfFreedom` - the new degrees of freedom.
• #### getDegreesOfFreedom

`public double getDegreesOfFreedom()`
Access the degrees of freedom.
Specified by:
`getDegreesOfFreedom` in interface `TDistribution`
Returns:
the degrees of freedom.
• #### density

`public double density​(double x)`
Returns the probability density for a particular point.
Overrides:
`density` in class `AbstractContinuousDistribution`
Parameters:
`x` - The point at which the density should be computed.
Returns:
The pdf at point x.
Since:
2.1
• #### cumulativeProbability

```public double cumulativeProbability​(double x)
throws MathException```
For this distribution, X, this method returns P(X < `x`).
Specified by:
`cumulativeProbability` in interface `Distribution`
Parameters:
`x` - the value at which the CDF is evaluated.
Returns:
CDF evaluated at `x`.
Throws:
`MathException` - if the cumulative probability can not be computed due to convergence or other numerical errors.
• #### inverseCumulativeProbability

```public double inverseCumulativeProbability​(double p)
throws MathException```
For this distribution, X, this method returns the critical point x, such that P(X < x) = `p`.

Returns `Double.NEGATIVE_INFINITY` for p=0 and `Double.POSITIVE_INFINITY` for p=1.

Specified by:
`inverseCumulativeProbability` in interface `ContinuousDistribution`
Overrides:
`inverseCumulativeProbability` in class `AbstractContinuousDistribution`
Parameters:
`p` - the desired probability
Returns:
x, such that P(X < x) = `p`
Throws:
`MathException` - if the inverse cumulative probability can not be computed due to convergence or other numerical errors.
`java.lang.IllegalArgumentException` - if `p` is not a valid probability.
• #### getSupportLowerBound

`public double getSupportLowerBound()`
Returns the lower bound of the support for the distribution. The lower bound of the support is always negative infinity no matter the parameters.
Returns:
lower bound of the support (always Double.NEGATIVE_INFINITY)
Since:
2.2
• #### getSupportUpperBound

`public double getSupportUpperBound()`
Returns the upper bound of the support for the distribution. The upper bound of the support is always positive infinity no matter the parameters.
Returns:
upper bound of the support (always Double.POSITIVE_INFINITY)
Since:
2.2
• #### getNumericalMean

`public double getNumericalMean()`
Returns the mean. For degrees of freedom parameter df, the mean is
• if `df > 1` then `0`
• else `undefined`
Returns:
the mean
Since:
2.2
• #### getNumericalVariance

`public double getNumericalVariance()`
Returns the variance. For degrees of freedom parameter df, the variance is
• if `df > 2` then `df / (df - 2)`
• if `1 < df <= 2` then `positive infinity`
• else `undefined`
Returns:
the variance
Since:
2.2