Template:Alta weibull distribution

The Weibull Distribution
The Weibull distribution is one of the most commonly used distributions in reliability engineering because of the many shapes it attains for various values of $$\beta $$  (slope). It can therefore model a great variety of data and life characteristics [18]. The 2-parameter Weibull $$pdf$$  is given by:
 * $$f(T)=\frac{\beta }{\eta }{{\left( \frac{T}{\eta } \right)}^{\beta -1}}{{e}^{-{{\left( \tfrac{T}{\eta } \right)}^{\beta }}}}$$


 * where:


 * $$f(T)\ge 0,\text{ }T\ge 0,\text{ }\beta >0,\text{ }\eta >0\text{ }$$


 * and:
 * •	 $$\eta =$$ scale parameter.
 * •	 $$\beta =$$ shape parameter (or slope).

Parameter Estimation
The estimates of the parameters of the Weibull distribution can be found graphically on probability plotting paper, or analytically using either least squares or maximum likelihood. (Parameter estimation methods are presented in detail in Appendix B.)