Template:Loglogistic probability density function: Difference between revisions
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::<math>f(t)=\frac{{{e}^{z}}}{\sigma {t}{{(1+{{e}^{z}})}^{2}}}</math> | ::<math>f(t)=\frac{{{e}^{z}}}{\sigma {t}{{(1+{{e}^{z}})}^{2}}}</math> | ||
where: | |||
::<math>z=\frac{{t}'-\mu }{\sigma }</math> | ::<math>z=\frac{{t}'-\mu }{\sigma }</math> | ||
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::<math>{t}'=\ln (t)</math> | ::<math>{t}'=\ln (t)</math> | ||
and: | |||
::<math>\begin{align} | ::<math>\begin{align} | ||
Revision as of 01:47, 15 February 2012
Loglogistic Probability Density Function
The loglogistic distribution is a two-parameter distribution with parameters [math]\displaystyle{ \mu }[/math] and [math]\displaystyle{ \sigma }[/math] . The [math]\displaystyle{ pdf }[/math] for this distribution is given by:
- [math]\displaystyle{ f(t)=\frac{{{e}^{z}}}{\sigma {t}{{(1+{{e}^{z}})}^{2}}} }[/math]
where:
- [math]\displaystyle{ z=\frac{{t}'-\mu }{\sigma } }[/math]
- [math]\displaystyle{ {t}'=\ln (t) }[/math]
and:
- [math]\displaystyle{ \begin{align} & \mu = & \text{scale parameter} \\ & \sigma = & \text{shape parameter} \end{align} }[/math]
where [math]\displaystyle{ 0\lt t\lt \infty }[/math] , [math]\displaystyle{ -\infty \lt \mu \lt \infty }[/math] and [math]\displaystyle{ 0\lt \sigma \lt \infty }[/math] .