.. _continuous-mielke:

Mielke's Beta-Kappa Distribution

A generalized F distribution. Two shape parameters :math:\kappa and :math:\theta, with support :math:x\geq0. The :math:\beta in the DATAPLOT reference is a scale parameter.

.. math:: :nowrap:

\begin{eqnarray*} f\left(x;\kappa,\theta\right) & = & \frac{\kappa x^{\kappa-1}}{\left(1+x^{\theta}\right)^{1+\frac{\kappa}{\theta}}}\\ F\left(x;\kappa,\theta\right) & = & \frac{x^{\kappa}}{\left(1+x^{\theta}\right)^{\kappa/\theta}}\\ G\left(q;\kappa,\theta\right) & = & \left(\frac{q^{\theta/\kappa}}{1-q^{\theta/\kappa}}\right)^{1/\theta}\end{eqnarray*}

Implementation: scipy.stats.mielke