## Libraries.Compute.Statistics.Distributions.HeavyTailNormalDistribution Documentation

This class, ported from Apache Commons, is an implementation of the T-Distribution. More information can be found here: https://en.wikipedia.org/wiki/Student%27s_t-distributi

## Summary

### Actions Summary Table

ActionsDescription
Compare(Libraries.Language.Object object)This action compares two object hash codes and returns an integer.
CumulativeDistribution(number x)* {@inheritDo
Density(number x)* {@inheritDo
Equals(Libraries.Language.Object object)This action determines if two objects are equal based on their hash code values.
GetDegreesOfFreedom()discussed in https://issues.
GetHashCode()This action gets the hash code for an object.
GetLowerBound()* * {@inheritDoc} * * For degrees of freedom parameter {@code df}, the variance is *
*
• if {@code df > 2} then {@code df / (df - 2)},
• *
• if {@code 1 < df <= 2} then positive infinity * ({@code Double.
GetMean()@Overri
GetNumericalMean()* * {@inheritDoc} * * For degrees of freedom parameter {@code df}, the mean is *
*
• if {@code df > 1} then {@code 0},
• *
• else undefined ({@code Double.
GetNumericalVariance()* * {@inheritDoc} * * For degrees of freedom parameter {@code df}, the variance is *
*
• if {@code df > 2} then {@code df / (df - 2)},
• *
• if {@code 1 < df <= 2} then positive infinity * ({@code Double.
GetSolverAbsoluteAccuracy()@Overri
GetSupportLowerBound()* * {@inheritDoc} * * The lower bound of the support is always negative infinity no matter the * parameters.
GetSupportUpperBound()* * {@inheritDoc} * * The upper bound of the support is always positive infinity no matter the * parameters.
GetUpperBound()* * {@inheritDoc} * * For degrees of freedom parameter {@code df}, the mean is *
*
• if {@code df > 1} then {@code 0},
• *
• else undefined ({@code Double.
GetVariance()* * {@inheritDoc} * * The support of this distribution is connected.
InverseCumulativeDistribution(number p)This action is an implementation of the Inverse Cumulative Distribution, which is also called the Percent Point Function.
InverseSurvival(number p)This action is an implementation of the inverse survival function, as described by NIST/SEMATECH e-Handbook of Statistical Methods, http://www.
IsSupportConnected()* * {@inheritDoc} * * The support of this distribution is connected.
IsSupportLowerBoundInclusive()* {@inheritDo
IsSupportUpperBoundInclusive()* {@inheritDo
LogDensity(number x)* {@inheritDo
Setup(number degreesOfFreedom)
Survival(number p)This action is an implementation of the survival function, as described by NIST/SEMATECH e-Handbook of Statistical Methods, http://www.

## Actions Documentation

### Compare(Libraries.Language.Object object)

This action compares two object hash codes and returns an integer. The result is larger if this hash code is larger than the object passed as a parameter, smaller, or equal. In this case, -1 means smaller, 0 means equal, and 1 means larger. This action was changed in Quorum 7 to return an integer, instead of a CompareResult object, because the previous implementation was causing efficiency issues.

Example Code

``````Object o
Object t
integer result = o:Compare(t) //1 (larger), 0 (equal), or -1 (smalle``````

#### Return

integer: The Compare result, Smaller, Equal, or Larger.

* {@inheritDo

number:

### Density(number x)

* {@inheritDo

number:

### Equals(Libraries.Language.Object object)

This action determines if two objects are equal based on their hash code values.

Example Code

``````use Libraries.Language.Object
use Libraries.Language.Types.Text
Object o
Text t
boolean result = o:Equals(``````

#### Return

boolean: True if the hash codes are equal and false if they are not equal.

### GetDegreesOfFreedom()

discussed in https://issues.apache.org/jira/browse/STATISTICS-

number:

### GetHashCode()

This action gets the hash code for an object.

Example Code

``````Object o
integer hash = o:GetHashCode``````

#### Return

integer: The integer hash code of the object.

### GetLowerBound()

* * {@inheritDoc} * * For degrees of freedom parameter {@code df}, the variance is *

*
• if {@code df > 2} then {@code df / (df - 2)},
• *
• if {@code 1 < df <= 2} then positive infinity * ({@code Double.POSITIVE_INFINITY}),
• *
• else undefined ({@code Double.NaN}).
• *

number:

@Overri

number:

### GetNumericalMean()

* * {@inheritDoc} * * For degrees of freedom parameter {@code df}, the mean is *

*
• if {@code df > 1} then {@code 0},
• *
• else undefined ({@code Double.NaN}).
• *

number:

### GetNumericalVariance()

* * {@inheritDoc} * * For degrees of freedom parameter {@code df}, the variance is *

*
• if {@code df > 2} then {@code df / (df - 2)},
• *
• if {@code 1 < df <= 2} then positive infinity * ({@code Double.POSITIVE_INFINITY}),
• *
• else undefined ({@code Double.NaN}).
• *

number:

@Overri

number:

### GetSupportLowerBound()

* * {@inheritDoc} * * The lower bound of the support is always negative infinity no matter the * parameters. * * @return lower bound of the support (always * {@code Double.NEGATIVE_INFINITY

number:

### GetSupportUpperBound()

* * {@inheritDoc} * * The upper bound of the support is always positive infinity no matter the * parameters. * * @return upper bound of the support (always * {@code Double.POSITIVE_INFINITY

number:

### GetUpperBound()

* * {@inheritDoc} * * For degrees of freedom parameter {@code df}, the mean is *

*
• if {@code df > 1} then {@code 0},
• *
• else undefined ({@code Double.NaN}).
• *

number:

### GetVariance()

* * {@inheritDoc} * * The support of this distribution is connected. * * @return {@code tru

number:

### InverseCumulativeDistribution(number p)

This action is an implementation of the Inverse Cumulative Distribution, which is also called the Percent Point Function. NIST describes this as NIST/SEMATECH e-Handbook of Statistical Methods, http://www.itl.nist.gov/div898/handbook/, date. https://www.itl.nist.gov/div898/handbook/eda/section3/eda362.htm

#### Return

number: the result of the acti

### InverseSurvival(number p)

This action is an implementation of the inverse survival function, as described by NIST/SEMATECH e-Handbook of Statistical Methods, http://www.itl.nist.gov/div898/handbook/, date. This action is equivalent to InverseCumulativeDistribution(1 - p) https://www.itl.nist.gov/div898/handbook/eda/section3/eda362.htm

#### Return

number: the result of the survival functi

### IsSupportConnected()

* * {@inheritDoc} * * The support of this distribution is connected. * * @return {@code tru

#### Return

boolean:

### IsSupportLowerBoundInclusive()

* {@inheritDo

#### Return

boolean:

### IsSupportUpperBoundInclusive()

* {@inheritDo

#### Return

boolean:

### LogDensity(number x)

* {@inheritDo

#### Return

number:

### Survival(number p)

This action is an implementation of the survival function, as described by NIST/SEMATECH e-Handbook of Statistical Methods, http://www.itl.nist.gov/div898/handbook/, date. This action is equivalent to CumulativeDistribution(1 - p) https://www.itl.nist.gov/div898/handbook/eda/section3/eda362.htm

#### Return

number: the result of the survival functi