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| === The Generalized Gamma Distribution ===
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| Compared to the other distributions previously discussed, the generalized gamma distribution is not as frequently used for modeling life data; however, it has the the ability to mimic the attributes of other distributions, such as the Weibull or lognormal, based on the values of the distribution’s parameters. This offers a compromise between two lifetime distributions. The generalized gamma function is a three-parameter distribution with parameters <span class="texhtml">μ</span> , <span class="texhtml">σ</span> and <span class="texhtml">λ</span> . The ''pdf ''of the distribution is given by,
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| ::<math>
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| f(x)=\begin{cases}
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| \frac{|\lambda|}{\sigma \cdot t}\cdot \tfrac{1}{\Gamma( \tfrac{1}{\lambda}^2)}\cdot
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| {e^{\tfrac{\lambda \cdot{\tfrac{\ln(t)-\mu}{\sigma}}+\ln( \tfrac{1}{{\lambda}^2})-e^{\lambda \cdot {\tfrac{\ln(t)-\mu}{\sigma}}}}{{\lambda}^2}}}, & \text{if} \ \lambda \ne 0 \\
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| \frac{1}{t\cdot \sigma \sqrt{2\pi }} e^{-\tfrac{1}{2}{(\tfrac{\ln(t)-\mu}{\sigma })^2}}, & \text{if} \ \lambda =0
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| \end{cases}
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| </math>
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| <br>where <span class="texhtml">Γ(''x'')</span> is the gamma function, defined by: <br>
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| ::<math>\Gamma (x)=\int_{0}^{\infty}{s}^{x-1}{e^{-s}}ds</math>
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| <br>
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| This distribution behaves as do other distributions based on the values of the parameters. For example, if <span class="texhtml">λ = 1</span>, then the distribution is identical to the Weibull distribution. If both <span class="texhtml">λ = 1</span> and <span class="texhtml">σ = 1</span>, then the distribution is identical to the exponential distribution, and for <span class="texhtml">λ = 0,</span> it is identical to the lognormal distribution. While the generalized gamma distribution is not often used to model life data by itself, its ability to behave like other more commonly-used life distributions is sometimes used to determine which of those life distributions should be used to model a particular set of data.
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| The Generalized Gamma distribution and its characteristics are presented in [[The Generalized Gamma Distribution]].
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| <br>
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