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title: "Parameters of an uncertainty distribution"
canonical: "https://modelassist.epixanalytics.com/space/EA/26574966/Parameters%20of%20an%20uncertainty%20distribution"
format: markdown
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Descriptive parameters can be calculated for an uncertainty distribution providing one knows the [density function](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26574888/) (or [mass function](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26574887/)) f(x) and the inverse F<sup>-1</sup>(x) of the distribution function F(x).  We will use the uncertainty about the height of a selected person (i.e. a [continuous quantity](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575199/)) as our parameter in the examples below:

  


| Continuous variable |
| --- |
| Parameter | Description | Definition |
| Percentiles x<sub>P</sub> | P% confidence the person is shorter than x<sub>P</sub> | F<sup>-1</sup>(P) |
| Location |  |  |
| Mode | Our 'best guess' of the height | Value x s.t. f(x) = max |
| Median x<sub>50</sub> | 50% confidence the person will be shorter than x<sub>50</sub> | F<sup>-1</sup>(0.5) |
| Mean estimate *m* | The center of gravity of the uncertainty distribution | ![image](media://9656d137-1d55-4d18-9408-39ac17e4036d)<br>> Macro (mathinline) |
| Spread |  |  |
| Standard deviation *s* | The square root of the distribution's variance | > Macro (mathinline) |
| Variance V | The confidence-weighted squared deviation of height from the mean estimate | ![image](media://8b1e60c7-e232-496b-b577-d45094736f9a)<br>> Macro (mathinline) |
| Mean absolute deviation | The confidence-weighted average difference in height from the mean estimate | ![image](media://da50b9e2-448f-4acb-9a0a-eda27ee0b3fd)<br>> Macro (mathinline) |

  


  


  


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