“…with Grimit et al (2006) p i=1 ω i = 1, ω i=1,..., p > 0 Generalized extreme value: Y ∼ G E V (μ, σ, ξ ) Friederichs and Thorarinsdottir (2012) Generalized Pareto: Y ∼ G P D(μ, σ, ξ ) Friederichs and Thorarinsdottir (2012) Log-normal: ln(Y ) ∼ N (μ, σ ) Baran and Lerch (2015) Normal: Y ∼ N (μ, σ ) Gneiting et al (2005) Square-root truncated normal: √ Y ∼ N 0 (μ, σ ) Hemri et al (2014) Truncated normal: Y ∼ N 0 (μ, σ ) Thorarinsdottir and Gneiting (2010) The reference of the original article where to find the formula is also given. Taillardat et al (2016) gathers the closed form expression of the CRPS for these and other distributions in Appendix A, this score for an ensemble is minimized if all the members x i equal the median of F, which is obviously not the purpose of an ensemble.…”