Template:Loglogistic mean median and mode

Mean, Median and Mode
The mean of the loglogistic distribution, $$\overline{T}$$, is given by:


 * $$\overline{T}={{e}^{\mu }}\Gamma (1+\sigma )\Gamma (1-\sigma )$$

Note that for $$\sigma \ge 1,$$   $$\overline{T}$$  does not exist.

The median of the loglogistic distribution, $$\breve{T}$$, is given by:


 * $$\widehat{T}={{e}^{\mu }}$$

The mode of the loglogistic distribution, $$\tilde{T}$$, if  $$\sigma <1,$$  is given by:


 * $$\tilde{T} = e^{\mu+\sigma ln(\frac{1-\sigma}{1+\sigma})}$$