1Blurb:: 2Aleatory uncertain variable - gamma 3 4Description:: 5The gamma distribution is sometimes used to model time to complete a task, such as a repair or service task. It is a very flexible distribution with its shape governed by alpha and beta. 6 7The density function for the gamma distribution is given by: 8\f[ f(x) = \frac{ {x}^{\alpha-1} \exp \left( \frac{-x}{\beta} \right) } 9 { \beta^{\alpha}\Gamma(\alpha) }, 10\f] 11\f$\mu = \alpha\beta,\f$ and \f$\sigma^2 = \alpha\beta^2\f$. 12Note that the exponential distribution is a special 13case of this distribution for parameter \f$\alpha = 1\f$. 14 15Topics:: continuous_variables, aleatory_uncertain_variables 16Examples:: 17 18Theory:: 19When used with some methods such as design of experiments and 20multidimensional parameter studies, distribution bounds are inferred 21to be [0, \f$\mu + 3 \sigma\f$]. 22 23For some methods, including vector and centered parameter studies, an 24initial point is needed for the uncertain variables. When not given 25explicitly, these variables are initialized to their means. 26 27Faq:: 28See_Also:: 29