I have a dataset with several observed view rates per unit for products. I want to use this rates as proxies for the demand for a certain product.
Product Items Views Rate(Views/Item) a 50 800 16 b 2 80 40 c 100 1200 12
However, for example, in the case of product "b" only few data was observed. Hence, the observed rate is very unreliable compared to other products that have much more observations.
Therefore, I specifically need a procedure to adjust the rates for products with few items to account for the fact, that the observed rates are not very certain, but are probably more like some average rate.
My idea: using a prior rate (or distribution to be more concise) that stems from all products (i.e., average rate of 13.68 in this case), I want to calculate a posterior rate for every single product using bayesian statistics.
Nonetheless, because the rates do not lie within [0..1] as for binomial distributions (and also a binomial distribution does not fit in this case), updating by estimating Alpha/Beta-parameters of a Beta-Distribution and calculating posterior rates by (alpha + x) / (alpha + beta + n) does not work.
What is a suitable way to tackle this issue? What prior distribution to use and what method to use to obtain posterior rates for each product that adjust the cases with few observations to be closer to an average?