Can someone point me to an example of how to do randomized response with a continuous outcome $Y \in [ 0,\infty ]$, rather than a binary one? I am interested in the mean and variance of this outcome or the entire distribution if possible. The true distribution is expected to have a mass at zero and a long right tail, similar to expenditures on hospitalization in the US.
Poole (1974)* developed an approach where the interviewee multiplies his true response $Y$ by a random number $X$ and only tells the interviewer the product $Z=X \cdot Y$. Unfortunately, I am finding the notation and the example very hard to follow.
*The reference in the link above is gated, but the full citation is:
Poole, W. Kenneth (1974) "Estimation of the Distribution Function of a Continuous Type Random Variable through Randomized Response," Journal of the American Statistical Association, Vol. 69, Iss. 348, pp. 1002-1005.
