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

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