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-distribution

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

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.

Parameters

Return

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

Example

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

CumulativeDistribution(number x)

* {@inheritDoc}

Parameters

  • number x

Return

number:

Density(number x)

* {@inheritDoc}

Parameters

  • number x

Return

number:

Equals(Libraries.Language.Object object)

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

Parameters

Return

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

Example

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

GetDegreesOfFreedom()

discussed in https://issues.apache.org/jira/browse/STATISTICS-25

Return

number:

GetHashCode()

This action gets the hash code for an object.

Return

integer: The integer hash code of the object.

Example

Object o
integer hash = o:GetHashCode()

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()

@Override

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()

@Override

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 true}

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

  • number p

Return

number: the result of the action

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

  • number p

Return

number: the result of the survival function

IsSupportConnected()

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

Return

boolean:

IsSupportLowerBoundInclusive()

* {@inheritDoc}

Return

boolean:

IsSupportUpperBoundInclusive()

* {@inheritDoc}

Return

boolean:

LogDensity(number x)

* {@inheritDoc}

Parameters

  • number x

Return

number:

Setup(number degreesOfFreedom)

Parameters

  • 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.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

  • number p

Return

number: the result of the survival function