.. _continuous-truncweibull_min:

Truncated Weibull Minimum Extreme Value Distribution

A doubly truncated version of Weibull minimum extreme value distribution. Defined for :math:a<x<=b and :math:c>0.

.. math:: :nowrap:

\begin{eqnarray*}
    f\left(x;c,a,b\right) & = & \frac{cx^{c-1}\exp\left(-x^{c}\right)}{\exp\left(-a^{c}\right) - \exp\left(-b^{c}\right)} \\
    F\left(x;c,a,b\right) & = & \frac{\exp\left(-a^{c}\right) - \exp\left(-x^{c}\right)}{\exp\left(-a^{c}\right) - \exp\left(-b^{c}\right)} \\
    G\left(q;c,a,b\right) & = & \left[-\log\left(\left(1-q\right)\exp\left(-a^{c}\right)+q\exp\left(-b^{c}\right)\right)\right]^{1/c}
\end{eqnarray*}

.. math::

 \mu_{n}^{\prime}=\frac{\exp\left(a^{c}\right)}{1-\exp\left(-b^{c}\right)}\left[\gamma\left(\frac{n}{c}+1,b^{c}\right)-\gamma\left(\frac{n}{c}+1,a^{c}\right)\right]

where :math:\gamma\left(\right) is the lower incomplete gamma function.

Implementation: scipy.stats.truncweibull_min