This week, we tackle the probability distribution inference.
Why do we care? As a start, no matter how good a stochastic model you have, you will always end up with an error term (aka shock or innovation) and the uncertainty (e.g., risk, forecast error) of the model is solely determined by this random variable. Second, uncertainty is commonly expressed as a probability distribution, so there is no escape!
In this issue, we attempt to derive an approximate of the underlying density probability using a sample data histogram and the (cumulative) empirical density function, but the histogram suffers from major drawbacks.