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