qq GOF Test for Particular Distribution

Test if some data comes from a particular continous distribution $G$. $H_0:F=G$ We know that given $H_0$ the qq-Plot wil approximately resemble a straight diagonal line which is why we can use the slope of the regression line $T$ as Test Statistic.

The simulated distribution of $T$ on $H_0$ can be used to calculate the p-Value and Acceptance Domain: $p(t)=2\cdot \min \{\mathbb{P}(T\le t),\mathbb{P}(T\ge t)\}$ $t\in \left[z_{\alpha /2},z_{1-\alpha /2}\right]$

This is basically the same as a two Two-Sided Gauß Test.

If we need to accept the Null Hypothesis the Type 2 Error cant be quantified without further assumptions for the other hypothesis.