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===The Gamma Distribution=== | === 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 < | 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 <span class="texhtml">''pdf ''</span>of the gamma distribution is given by: <br> | ||
<br> | |||
::<math>\begin{align} | ::<math>\begin{align} | ||
f(t)= & \frac{e^{kz-{e^{z}}}}{t\Gamma(k)} \\ | f(t)= & \frac{e^{kz-{e^{z}}}}{t\Gamma(k)} \\ | ||
z= & \ln{t}-\mu | z= & \ln{t}-\mu | ||
\end{align}</math> | \end{align}</math> | ||
<br> | |||
where: | <br>where: <br> | ||
<br> | |||
::<math>\begin{align} | ::<math>\begin{align} | ||
\mu = & \text{scale parameter} \\ | \mu = & \text{scale parameter} \\ | ||
k= & \text{shape parameter} | k= & \text{shape parameter} | ||
\end{align}</math> | \end{align}</math> | ||
The gamma distribution and its characteristics are presented in more detail in | <br>where 0 <math><t<\infty </math> , <math>-\infty <\mu <\infty </math> and <span class="texhtml">''k'' > 0</span>. | ||
<br> | |||
The gamma distribution and its characteristics are presented in more detail in the chapter [[The Gamma Distribution]]. <br> | |||
Revision as of 16:04, 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 more detail in the chapter The Gamma Distribution.