Convolution of Scale Invariant Continuous Ranked Probability Scores for Testing Experts' Statistical Accuracy

Computable solutions for expectations of Continuous Ranked Probability Scores are presented. After deriving a scale invariant version of these scores, a closed form for the convolutions of scores is presented. This closed form enables the testing experts' statistical accuracy. Results are compared with tests using a familiar Chi-square goodness of fit test using a recent data set of 6,761 expert probabilistic forecasts for which true values are known.