damar-wicaksono / uqtestfuns

A Python3 library of test functions from the uncertainty quantification community with a common interface for validation and benchmarking purposes.
https://uqtestfuns.readthedocs.io/en/latest/
MIT License
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Add support for the Weibull distribution #268

Open damar-wicaksono opened 1 year ago

damar-wicaksono commented 1 year ago

To include several test functions relevant in reliability analysis exercises (see for example Issue #267), the Weibull distribution should be added to the code base. The density function of the distribution reads:

$$ f_X(x; \alpha, \beta) = \frac{\beta}{\alpha} \left( \frac{x}{\alpha} \right)^{\beta-1} \exp{\left( - \frac{x}{\alpha} \right)^\beta}, x > 0; $$

where $\alpha >0$ and $\beta > 0$ are the parameters of the distribution.