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<br>where 0 <math><t<\infty </math> , <math>-\infty <\mu <\infty </math> and <span class="texhtml">''k'' > 0</span>. | <br>where 0 <math><t<\infty </math> , <math>-\infty <\mu <\infty </math> and <span class="texhtml">''k'' > 0</span>. | ||
The gamma distribution and its characteristics are presented in | The gamma distribution and its characteristics are presented in detail in the chapter [[The Gamma Distribution]]. <br> | ||
Revision as of 16:18, 12 March 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, the gamma distribution has applications in Bayesian analysis as a prior distribution, and it is also commonly used in queuing theory. The pdf 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 k > 0.
The gamma distribution and its characteristics are presented in detail in the chapter The Gamma Distribution.