1Blurb:: 2Aleatory uncertain variable - Frechet 3Description:: 4The Frechet distribution is also referred to as the Type II Largest Extreme Value distribution. 5The distribution of maxima in sample sets from a population with a lognormal distribution will asymptotically converge to this distribution. It is commonly used to model non-negative demand variables. 6 7The density function for the frechet distribution is: 8\f[f(x) = \frac{\alpha}{\beta} 9 \left( \frac{\beta}{x} \right)^{\alpha+1} 10 \exp \left( -\left(\frac{\beta}{x}\right)^\alpha \right), 11\f] 12\f$\mu = \beta\Gamma(1-\frac{1}{\alpha}),\f$ and 13\f$\sigma^2 = \beta^2[\Gamma(1-\frac{2}{\alpha})-\Gamma^2(1-\frac{1}{\alpha})]\f$ 14 15Topics:: continuous_variables, aleatory_uncertain_variables 16Examples:: 17Theory:: 18When used with some methods such as design of experiments and 19multidimensional parameter studies, distribution bounds are inferred 20to be [0, \f$\mu + 3 \sigma\f$]. 21 22For some methods, including vector and centered parameter studies, an 23initial point is needed for the uncertain variables. When not given 24explicitly, these variables are initialized to their means. 25 26Faq:: 27See_Also:: 28