Template:Characteristics of the generalized gamma distribution: Difference between revisions

Latest revision as of 09:35, 9 August 2012

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-===Characteristics of the Generalized Gamma Distribution===
+#REDIRECT [[The_Generalized_Gamma_Distribution]]
-As mentioned previously, the generalized gamma distribution includes other distributions as special cases based on the values of the parameters.
-[[Image:ldagamma10.1.gif|thumb|center|500px| ]]
-:•	The Weibull distribution is a special case when  <math>\lambda =1</math>  and:
-::<math>\begin{align}
-  & \beta = \frac{1}{\sigma } \\
- & \eta = \ln (\mu )
-\end{align}</math>
-:•	 In this case, the generalized distribution has the same behavior as the Weibull for  <math>\sigma >1,</math>   <math>\sigma =1,</math>  and  <math>\sigma <1</math>  ( <math>\beta
-<1,</math>   <math>\beta =1,</math>  and  <math>\beta >1</math>  respectively).
-:•	The exponential distribution is a special case when  <math>\lambda =1</math>  and  <math>\sigma =1</math>.
-:•	The lognormal distribution is a special case when  <math>\lambda =0</math>.
-:•	The gamma distribution is a special case when  <math>\lambda =\sigma </math>.
-By allowing  <math>\lambda </math>  to take negative values, the generalized gamma distribution can be further extended to include additional distributions as special cases. For example, the Fréchet distribution of maxima (also known as a reciprocal Weibull) is a special case when  <math>\lambda =-1</math>.