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TWiki> Main Web>PmHome>MetricsHome>MetricsWorkingDocuments>MetricsEMS10RestApi>MetricsEMS10RestApiDataModel>MetricsEmsCumulativeDistributionFunction (24 Sep 2010, ArthurRyman)

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

The cumulative distribution function may vary continuously, however, it can be approximated by giving its value a finite set of sample points. Values between the sample points can be approximated using simple linear interpolation.

In general, a probability distribution may have non-zero values for arbitrarily small or large values, i.e. the cumulative probability may only reach 0 at negative infinity and 1 at positive infinity. However, for software estimates, the range of possible values is finite in practice and it is useful to include these low and high values in the representation of the cumulative distribution function.

An ems:CumulativeDistributionFunction resource represents a cumulative distribution function.

Property | Range | Type | Occurrence | Edits | Description |
---|---|---|---|---|---|

ems:low | datatype | xsd:double | exactly-one | read-write | The low value. |

ems:cdfPoint | local inline resource | ems:CdfPoint | one-or-more | read-write | A cumulative distribution function data point. |

ems:high | datatype | xsd:double | exactly-one | read-write | The high value. |

It has the following properties:

Property | Range | Type | Occurrence | Edits | Description |
---|---|---|---|---|---|

ems:numericValue | datatype | xsd:double | exactly-one | read-write | The value of the random variable. |

ems:probability | datatype | xsd:double | exactly-one | read-write | The cumulative probability. |

This required property is the value for which the cumulative probability of this quantile is attained, i.e. the probability that a measurement gives a result less than or equal to this value is equal to the cumulative probability of this quantile.

This required property is the cumulative probability of this sample point.

Consider the following table of cumulative probabilities for duration of a project:

duration (months) | cumulative probability |
---|---|

4 | 0.00 |

6 | 0.10 |

8 | 0.50 |

10 | 0.80 |

12 | 0.95 |

14 | 1.00 |

This cumulative distribution function has the following representation as an ems:CumulativeDistributionFunction resource:

<?xml version="1.0"?> <ems:CumulativeDistributionFunction xmlns:ems="http://open-services.net/ns/ems#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"> <ems:low rdf:datatype="http://www.w3.org/2001/XMLSchema#double">4</ems:low> <ems:cdfPoint> <ems:CdfPoint> <ems:numericValue rdf:datatype="http://www.w3.org/2001/XMLSchema#double">6</ems:numericValue> <ems:probability rdf:datatype="http://www.w3.org/2001/XMLSchema#double">0.10</ems:probability> </ems:CdfPoint> </ems:cdfPoint> <ems:cdfPoint> <ems:CdfPoint> <ems:numericValue rdf:datatype="http://www.w3.org/2001/XMLSchema#double">8</ems:numericValue> <ems:probability rdf:datatype="http://www.w3.org/2001/XMLSchema#double">0.50</ems:probability> </ems:CdfPoint> </ems:cdfPoint> <ems:cdfPoint> <ems:CdfPoint> <ems:numericValue rdf:datatype="http://www.w3.org/2001/XMLSchema#double">10</ems:numericValue> <ems:probability rdf:datatype="http://www.w3.org/2001/XMLSchema#double">0.80</ems:probability> </ems:CdfPoint> </ems:cdfPoint> <ems:cdfPoint> <ems:CdfPoint> <ems:numericValue rdf:datatype="http://www.w3.org/2001/XMLSchema#double">12</ems:numericValue> <ems:probability rdf:datatype="http://www.w3.org/2001/XMLSchema#double">0.95</ems:probability> </ems:CdfPoint> </ems:cdfPoint> <ems:high rdf:datatype="http://www.w3.org/2001/XMLSchema#double">14</ems:high> </ems:CumulativeDistributionFunction>

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Topic revision: r6 - 24 Sep 2010 - 15:12:01 - ArthurRyman

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