Template:GammaDistribution: Difference between revisions
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where 0 <math><t<\infty </math> , <math>-\infty <\mu <\infty </math> and <math>k>0</math>. | where 0 <math><t<\infty </math> , <math>-\infty <\mu <\infty </math> and <math>k>0</math>. | ||
The gamma distribution and its characteristics are presented in more detail in [[The Gamma Distribution | The gamma distribution and its characteristics are presented in more detail in Chapter [[The Gamma Distribution]]. | ||
<br> | <br> | ||
Revision as of 23:59, 10 February 2012
The Gamma Distribution
The gamma distribution is a flexible distribution that may offer a good fit to some sets of life data. Sometimes called the Erlang distribution, gamma distribution has applications in Bayesian analysis as a prior distribution and is also commonly used in queuing theory.
The [math]\displaystyle{ pdf }[/math] of the gamma distribution is given by:
- [math]\displaystyle{ \begin{align} f(t)= & \frac{e^{kz-{e^{z}}}}{t\Gamma(k)} \\ z= & \ln{t}-\mu \end{align} }[/math]
where:
- [math]\displaystyle{ \begin{align} \mu = & \text{scale parameter} \\ k= & \text{shape parameter} \end{align} }[/math]
where 0 [math]\displaystyle{ \lt t\lt \infty }[/math] , [math]\displaystyle{ -\infty \lt \mu \lt \infty }[/math] and [math]\displaystyle{ k\gt 0 }[/math].
The gamma distribution and its characteristics are presented in more detail in Chapter The Gamma Distribution.