## 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

## Summary

### Actions Summary Table

Actions | Description |
---|---|

Compare(Libraries.Language.Object object) | This action compares two object hash codes and returns an integer. |

CumulativeDistribution(number x) | For a random variable {@code X} whose values are distributed according to this distribution, this method returns P(X <= x). |

Equals(Libraries.Language.Object object) | This action determines if two objects are equal based on their hash code values. |

GetHashCode() | This action gets the hash code for an object. |

GetLowerBound() | |

GetMean() | |

GetSolverAbsoluteAccuracy() | For a random variable {@code X} whose values are distributed according to this distribution, this method returns P(X <= x). |

GetUpperBound() | |

GetVariance() | |

InverseCumulativeDistribution(number p) | This action overrides the standard Inverse Cumulative Distribution action to one specifically for normal distributions. |

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() | This action overrides the standard Inverse Cumulative Distribution action to one specifically for normal distributions. |

Setup(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. |

## 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 (smaller)
```

#### Parameters

- Libraries.Language.Object: The object to compare to.

#### Return

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

### 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.

**Example Code**

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

#### Parameters

- Libraries.Language.Object: The to be compared.

#### Return

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

### 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()

#### 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

#### 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

### 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 function