scores_moments {scoringRules}

Scoring Rules for a Vector of Moments

Description

Calculate scores (DSS, ESS) given observations and moments of the predictive distributions.

Usage

dss_moments(y, mean = 0, var = 1)

ess_moments(y, mean = 0, var = 1, skew = 0)

Arguments

y

vector of realized values.

mean

vector of mean values.

var

vector of variance values.

skew

vector of skewness values.

Details

The skewness of a random variable X is the third standardized moment

E[(\frac{X-\textnormal{mean}}{\sqrt{\textnormal{var}}})^3].

Value

Value of the score. A lower score indicates a better forecast.

Author(s)

Alexander Jordan, Sebastian Lerch

References

Dawid-Sebastiani score:

Dawid, A.P. and P. Sebastiani (1999): 'Coherent dispersion criteria for optimal experimental design' The Annals of Statistics, 27, 65-81. 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. doi:10.1002/qj.2375