Template:Generalized gamma probability density function: Difference between revisions

Latest revision as of 09:36, 9 August 2012

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-====Generalized Gamma Probability Density Function====
+#REDIRECT [[The_Generalized_Gamma_Distribution]]
-The generalized gamma function is a three-parameter distribution. One version of the generalized gamma distribution uses the parameters  ,  , and  . The   for this form of the generalized gamma distribution is given by:
-where   is a scale parameter,   and   are shape parameters and   is the gamma function of  , which is defined by:
-With this version of the distribution, however, convergence problems arise that severely limit its usefulness. Even with data sets containing 200 or more data points, the MLE methods may fail to converge. Further adding to the confusion is the fact that distributions with widely different values of , , and  may appear almost identical [21]. In order to overcome these difficulties, Weibull++ uses a reparameterization with parameters   ,   , and   [21] where:
-where   and   While this makes the distribution converge much more easily in computations, it does not facilitate manual manipulation of the equation. By allowing   to become negative, the   of the reparameterized distribution is given by: