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

Inherits from: Libraries.Language.Object, Libraries.Compute.Statistics.Distributions.NumberDistribution

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

Parameters

Return

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

CumulativeDistribution(number x)

* {@inheritDo

Parameters

Return

number:

Density(number x)

* {@inheritDo

Parameters

Return

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(

Parameters

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-

Return

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}).
  • *

Return

number:

GetMean()

@Overri

Return

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}).
  • *

Return

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}).
  • *

Return

number:

GetSolverAbsoluteAccuracy()

@Overri

Return

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

Return

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

Return

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}).
  • *

Return

number:

GetVariance()

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

Return

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

Parameters

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

Parameters

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

Parameters

Return

number:

Setup(number degreesOfFreedom)

Parameters

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

Parameters

Return

number: the result of the survival functi