STK_DISTRIB_NORMAL_CRPS computes the CRPS for Gaussian predictive distributions CALL: CRPS = stk_distrib_normal_crps (Z, MU, SIGMA) computes the Continuous Ranked Probability Score (CRPS) of Z with respect to a Gaussian predictive distribution with mean MU and standard deviation SIGMA. The CRPS is defined as the integral of the Brier score for the event {Z <= z}, when z ranges from -inf to +inf: CRPS = int_{-inf}^{+inf} [Phi((z - MU)/SIGMA) - u(z - Z)]^2 dz, where Phi is the normal cdf and u the Heaviside step function. The CRPS is equal to zero if, and only if, the predictive distribution is a Dirac distribution (SIGMA = 0) and the observed value is equal to the predicted value (Z = MU). REFERENCE [1] Tilmann Gneiting and Adrian E. Raftery, "Strictly proper scoring rules, prediction, and estimation", Journal of the American Statistical Association, 102(477):359-378, 2007. See also: stk_distrib_normal_cdf, stk_predict_leaveoneout
Package: stk