Template:Loglogistic mean median and mode

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{ \overline{T}={{e}^{{\mu+\sigma}ln(\frac{1-\sigma}{1+\sigma})} }[/math]