## Libraries.Compute.Statistics.Distributions.NumberDistribution Documentation

This is a parent class of distributions that use real numbers as part of their distribution. It contains some default actions to assist in calculating probabilities and distributions. This is adapted from Apache Commons and NIST: https://www.itl.nist.gov/div898/handbook/eda/section3/eda362.htm

*Inherits from: *Libraries.Language.Object

## Summary

### Actions Summary Table

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

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

CumulativeDistribution(number p) | 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() | Access the lower bound of the support. |

GetMean() | Returns the mean for this distribution. |

GetSolverAbsoluteAccuracy() | This action returns the current accuracy of the solving calculations. |

GetUpperBound() | Access the lower bound of the support. |

GetVariance() | Returns the variance for this distribution. |

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() | If this action returns true, then all values between the lower and upper bound are supported by this distribution. |

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 p)

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

#### 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()

Access the lower bound of the support. This method must return the same value as InverseCumulativeProbability(0). In other words, this method must return

#### Return

number: lower bound of the support

### GetMean()

Returns the mean for this distribution.

#### Return

number: the mean

### GetSolverAbsoluteAccuracy()

This action returns the current accuracy of the solving calculations. These are used typically for the inverse calculations.

#### Return

number: the accuracy

### GetUpperBound()

Access the lower bound of the support. This method must return the same value as InverseCumulativeProbability(1). In other words, this method must return

#### Return

number: upper bound of the support

### GetVariance()

Returns the variance for this distribution.

#### Return

number: the variance

### 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 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

#### Return

number: the result of the survival function

### IsSupportConnected()

If this action returns true, then all values between the lower and upper bound are supported by this distribution.

#### Return

boolean: whether or not all values are supported

### 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