Template:Loglogistic mean median and mode: Difference between revisions
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==Mean, Median and Mode== | |||
The mean of the loglogistic distribution, <math>\overline{T}</math> , is given by: | The mean of the loglogistic distribution, <math>\overline{T}</math> , is given by: | ||
Revision as of 17:48, 20 February 2012
Mean, Median and Mode
The mean of the loglogistic distribution, [math]\displaystyle{ \overline{T} }[/math] , is given by:
- [math]\displaystyle{ \overline{T}={{e}^{\mu }}\Gamma (1+\sigma )\Gamma (1-\sigma ) }[/math]
Note that for [math]\displaystyle{ \sigma \ge 1, }[/math] [math]\displaystyle{ \overline{T} }[/math] does not exist.
The median of the loglogistic distribution, [math]\displaystyle{ \breve{T} }[/math] , is given by:
- [math]\displaystyle{ \widehat{T}={{e}^{\mu }} }[/math]
The mode of the loglogistic distribution, [math]\displaystyle{ \tilde{T} }[/math] , if [math]\displaystyle{ \sigma \lt 1, }[/math] is given by:
- [math]\displaystyle{ \tilde{T} = e^{\mu+\sigma ln(\frac{1-\sigma}{1+\sigma})} }[/math]