Say you have a binomial distribution with $p$ very small ($\approx 0.001$). You are asked to predict the conditional success rate $SR=S/T$ with $S$ successes out of $T$ trials given a set of conditions $X$.One would expect (correct me if I'm wrong, though I ran simulations and am quite confident) $SR$ to have a downward with increasing $T$ when $T$ is still small, and to approach $p$ when $T$ is large.The distribution of trials and successes is not uniform across $X$, so the train set tends to give higher $SR$ to conditions with smaller $T$ values.How would you treat this data skew when constructing a model?
Skewed binomial data for small p
predictive modeling;feature engineering