Suppose rv's $X_1, X_2, ..., X_n$ are continuous iid, and let $Z$ be some continuous rv independent from the $X_i$'s. Construct rv's $Y_1, Y_2, ..., Y_n$ as following:
$Y_i$ is sampled from the interval $[X_i - 1, X_i + 1]$ using the distribution of $Z$ restricted to this interval (i.e. normalized so that $P(Y_i \in [X_i - 1, X_i + 1] = 1$).
Question: Do these types of constructed rv's $Y_i$ have a term/name?
My goal is to estimate the "underlying distribution" of $Z$ using data samples $(X_i, Y_i)$ (perhaps using something similar to kernel density estimation), but I'm struggling what to search for in the litterature.