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:  
where:  


::<math>z=\ln (t)-\mu </math>
::<math>z=\ln (t)-\mu </math>


:and:  
and:  


::<math>\begin{align}
::<math>\begin{align}
   & {{e}^{\mu }}= & \text{scale parameter} \\  
   & {{e}^{\mu }}= \text{scale parameter} \\  
  & k= & \text{shape parameter}   
  & 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] .