Template:Logistic probability density function: Difference between revisions
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::<math>\begin{matrix} | ::<math>\begin{matrix} | ||
f( | f(t)=\tfrac{{{e}^{z}}}{\sigma {{(1+{{e}^{z}})}^{2}}} \\ | ||
z=\tfrac{t-\mu }{\sigma } \\ | z=\tfrac{t-\mu }{\sigma } \\ | ||
-\infty < | |||
-\infty <t<\infty ,\ \ -\infty <\mu <\infty ,\sigma >0 \\ | |||
\end{matrix}</math> | \end{matrix}</math> | ||
where: | |||
::<math>\begin{align} | ::<math>\begin{align} | ||
\mu = & \text{location parameter (also denoted as }\overline{T) | \mu = & \text{location parameter (also denoted as }\overline{T}) \\ | ||
\sigma = & \text{scale parameter} | \sigma = & \text{scale parameter} | ||
\end{align}</math> | \end{align}</math> | ||
Revision as of 22:58, 14 February 2012
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]