Calculate scores (DSS, ESS) given observations and moments of the predictive distributions.
dss_moments(y, mean = 0, var = 1)ess_moments(y, mean = 0, var = 1, skew = 0)
Value of the score. A lower score indicates a better forecast.
vector of realized values.
vector of mean values.
vector of variance values.
vector of skewness values.
Alexander Jordan, Sebastian Lerch
The skewness of a random variable \(X\) is the third standardized moment $$E[(\frac{X-\textnormal{mean}}{\sqrt{\textnormal{var}}})^3].$$
Dawid-Sebastiani score:
Dawid, A.P. and P. Sebastiani (1999): 'Coherent dispersion criteria for optimal experimental design' The Annals of Statistics, 27, 65-81. tools:::Rd_expr_doi("10.1214/aos/1018031101")
Error-spread score:
Christensen, H.M., I.M. Moroz, and T.N. Palmer (2015): `Evaluation of ensemble forecast uncertainty using a new proper score: Application to medium-range and seasonal forecasts', Quarterly Journal of the Royal Meteorological Society, 141, 538-549. tools:::Rd_expr_doi("10.1002/qj.2375")