Transformation model
= Transformation model
{title2=$gY\sim P_{g\theta}\quad\text{when }Y\sim P_\theta$}
A <group action> on the sample space induces a compatible action on the parameter space, preserving the family of <probability laws>. In a transitive model every law arises by transforming a fixed reference law. A <location-scale model> is generated by $y\mapsto a+by$, $b>0$, with parameter action $(\mu,\sigma)\mapsto(a+b\mu,b\sigma)$.