0
$\begingroup$

$X$ is a continuous and non-negative random valuable with CDF $F$, $b>0$, what is the generalized inverse function for $Y=\min(X, b)$

$\endgroup$
0
$\begingroup$

$$X: \Omega \rightarrow \mathbb R^+$$

$$Y = f \circ X$$ where for $b \in \mathbb R^+$ as a constant and $x \in \mathbb R$ $$f(x) = \min(x, b)$$

Then

$$Y^{-1} = X^{-1} \circ f^{-1}$$

Notice: $f^{-1}$ does not exist for $x = b$, but you could map it back to a set in $\Omega$, instead of a point in $\Omega$, i.e. the set $X^{-1}(\{x \ge b \}) \subset \Omega$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.