Template:Logistic probability density function

Logistic Probability Density Function

The logistic [math]\displaystyle{ pdf }[/math] is given by:

[math]\displaystyle{ \begin{matrix} f(t)=\tfrac{{{e}^{z}}}{\sigma {{(1+{{e}^{z}})}^{2}}} \\ \\ z=\tfrac{t-\mu }{\sigma } \\ -\infty \lt t\lt \infty ,\ \ -\infty \lt \mu \lt \infty ,\sigma \gt 0 \\ \\ \end{matrix} }[/math]

where:

[math]\displaystyle{ \begin{align} \mu = & \text{location parameter (also denoted as }\overline{T}) \\ \sigma = & \text{scale parameter} \end{align} }[/math]