Template:Loglogistic standard deviation

The Standard Deviation

The standard deviation of the loglogistic distribution, [math]\displaystyle{ {{\sigma }_{T}} }[/math] , is given by:

[math]\displaystyle{ {{\sigma }_{T}}={{e}^{\mu }}\sqrt{\Gamma (1+2\sigma )\Gamma (1-2\sigma )-{{(\Gamma (1+\sigma )\Gamma (1-\sigma ))}^{2}}} }[/math]

Note that for [math]\displaystyle{ \sigma \ge 0.5, }[/math] the standard deviation does not exist.