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 \leq t), \mathbb{P}(T \geq 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.