Libraries.Compute.Statistics.Distributions.NormalDistribution Documentation

This represents a normal (guassian) distribution. More information can be found at: http://en.wikipedia.org/wiki/Normal_distribution This is a port of Apache Commons.

Example Code

use Libraries.Compute.Statistics.Distributions.NormalDistribution
NormalDistribution distribution

//should output approximately
//0.0000002866515719
output distribution:CumulativeDistribution(-5)

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)

For a random variable {@code X} whose values are distributed according to this distribution, this method returns P(X <= x). In other words, this method represents the (cumulative) distribution function (CDF) for this distribution.

Parameters

  • number x: the point at which the CDF is evaluated

Return

number: the probability that a random variable with this distribution takes a value less than or equal to x

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)

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()

Return

number

GetMean()

Return

number

GetSolverAbsoluteAccuracy()

For a random variable {@code X} whose values are distributed according to this distribution, this method returns P(X <= x). In other words, this method represents the (cumulative) distribution function (CDF) for this distribution.

Return

number: the probability that a random variable with this distribution takes a value less than or equal to x

GetUpperBound()

Return

number

GetVariance()

Return

number

InverseCumulativeDistribution(number p)

This action overrides the standard Inverse Cumulative Distribution action to one specifically for normal distributions. To do this it uses the inverse calculation from http://people.maths.ox.ac.uk/gilesm/files/gems_erfinv.pdf Approximating the erfinv function by Mike Giles, Oxford-Man Institute of Quantitative Finance, which was published in GPU Computing Gems, volume 2, 2010.

Parameters

  • number p: the p-value to approximate from.

Return

number: an estimate of the number that would return the probability.

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()

This action overrides the standard Inverse Cumulative Distribution action to one specifically for normal distributions. To do this it uses the inverse calculation from http://people.maths.ox.ac.uk/gilesm/files/gems_erfinv.pdf Approximating the erfinv function by Mike Giles, Oxford-Man Institute of Quantitative Finance, which was published in GPU Computing Gems, volume 2, 2010.

Return

boolean: an estimate of the number that would return the probability.

Setup(number mean, number standardDeviation)

Parameters

  • number mean
  • number standardDeviation

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