Template:Gamma probability density function: Difference between revisions
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::<math>f(t)=\frac{{{e}^{kz-{{e}^{z}}}}}{t\Gamma (k)}</math> | ::<math>f(t)=\frac{{{e}^{kz-{{e}^{z}}}}}{t\Gamma (k)}</math> | ||
where: | |||
::<math>z=\ln (t)-\mu </math> | ::<math>z=\ln (t)-\mu </math> | ||
and: | |||
::<math>\begin{align} | ::<math>\begin{align} | ||
& {{e}^{\mu }}= | & {{e}^{\mu }}= \text{scale parameter} \\ | ||
& k= | & k= \text{shape parameter} | ||
\end{align}</math> | \end{align}</math> | ||
where <math>0<t<\infty </math> , <math>-\infty <\mu <\infty </math> and <math>k>0</math> . | where <math>0<t<\infty </math> , <math>-\infty <\mu <\infty </math> and <math>k>0</math> . | ||
Revision as of 22:14, 14 February 2012
Gamma Probability Density Function
The [math]\displaystyle{ pdf }[/math] of the gamma distribution is given by:
- [math]\displaystyle{ f(t)=\frac{{{e}^{kz-{{e}^{z}}}}}{t\Gamma (k)} }[/math]
where:
- [math]\displaystyle{ z=\ln (t)-\mu }[/math]
and:
- [math]\displaystyle{ \begin{align} & {{e}^{\mu }}= \text{scale parameter} \\ & k= \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{ k\gt 0 }[/math] .