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# ems:NormalDistribution

Probability distributions: ems:PointEstimate, ems:UniformDistribution, ems:TriangularDistribution, ems:NormalDistribution, ems:PoissonDistribution, ems:QuantileFunction, ems:CumulativeDistributionFunction

## Description

The normal distribution naturally occurs in many situations. When a measure is affected by many random factors, the result is a normal distribution under very general conditions (see the Central Limit Theorem). For example, the total duration of a project depends on the durations of all the tasks. If there are many tasks and they their estimated durations are described by well-behaved probability distributions, then the estimated total duration is described by a normal distribution.

An ems:NormalDistribution resource represents a normal distribution.

## Properties

An ems:NormalDistribution has the following properties

Property Range Type Occurrence Edits Description
ems:mu datatype xsd:double exactly-one read-write The mean of the distribution.
ems:sigma datatype xsd:double exactly-one read-write The scale of the distribution.

### ems:mu

This required property is the mean of the distribution, traditionally denoted by the Greek letter mu.

### ems:scale

This required property is the scale of the distribution, traditionally denoted by the Greek letter sigma. Its square is the variance of the distribution. This property MUST be positive.

## Examples

### Normal Distribution 1

The following resource represents a normal distribution with a mu value of 42 and a sigma value of 7:

###### Listing of Normal Distribution 1
<?xml version="1.0"?>
<ems:NormalDistribution xmlns:ems="http://open-services.net/ns/ems#"
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<ems:mu rdf:datatype="http://www.w3.org/2001/XMLSchema#double">42</ems:mu>
<ems:sigma rdf:datatype="http://www.w3.org/2001/XMLSchema#double">7</ems:sigma>
</ems:NormalDistribution>