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| ===The Gamma Distribution===
| | #REDIRECT [[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.
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| The <math>pdf</math> of the gamma distribution is given by:
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| <br>
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| ::<math>\begin{align}
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| f(t)= & \frac{e^{kz-{e^{z}}}}{t\Gamma(k)} \\
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| z= & \ln{t}-\mu
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| \end{align}</math>
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| <br>
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| where:
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| <br>
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| ::<math>\begin{align}
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| \mu = & \text{scale parameter} \\
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| k= & \text{shape parameter}
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| \end{align}</math>
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| <br>
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| where 0 <math><t<\infty </math> , <math>-\infty <\mu <\infty </math> and <math>k>0</math>.
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| The gamma distribution and its characteristics are presented in more detail in Chapter [[The Gamma Distribution]].
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| <br>
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