Template:Loglogistic probability density function

Loglogistic Probability Density Function
The loglogistic distribution is a two-parameter distribution with parameters $$\mu $$  and  $$\sigma $$. The $$pdf$$  for this distribution is given by:


 * $$f(t)=\frac{\sigma {t}{{(1+{{e}^{z}})}^{2}}}$$


 * where:


 * $$z=\frac{{t}'-\mu }{\sigma }$$


 * $${t}'=\ln (t)$$


 * and:


 * $$\begin{align}

& \mu = & \text{scale parameter} \\ & \sigma = & \text{shape parameter} \end{align}$$

where $$0<t<\infty $$,  $$-\infty <\mu <\infty $$  and  $$0<\sigma <\infty $$.