Benutzer:Simon Rinderknecht/Spielwiese

The Density Ratio Class is a collection or family of probability distributions.

Definition

For continuous random variables, the Density Ratio Class is defined as the set of probability density functions (PDFs),

$\Gamma _{l,u}^{DR}$

where $l$ and $l$ are two bounded non-negative functions (non-normalized densities) such that $l(\theta )\leq u(\theta )$ for all $\theta$ in the domain of the random variable and $\int u(\theta )d\theta <\infty$.

\backslash\mbox{PDFs\ } f : \exists c : l(\theta) \le cf(\theta) \le u(\theta) \sim\ \forall \theta