Multiple-threshold informational predictability applied to rainfall intensities

Predictability, in its informational sense, has been defined as the expected value of the logarithm of conditional probability of the predicted variable, conditioned on its predictors (Fernández Méndez et al., SERRA 37, pp.2651–2656, 2023). While the formulation in the cited work allows for assigning a normalized predictability value between 0 and 1 for any conditional probability distribution whose essential range has finite cardinality, the application therein only deals with Bernoulli-type distributions (i.e., 2 feasible states, in the case of rainfall, rain / no rain). The present study extends the scope of the application of informational predictability to multiply-thresholded rainfall intensity time series, and analyses the resulting conclusions.