Continuous rank probability score

Calculates continuous rank probability score (CRPS) for probabilistic and ensemble forecasts

The CRPS measures the closeness of forecast distribution (fcst) and corresponding observation (obs). This score is widely used in forecast verification.

[mean_CRPS] = crps(fcst,obs);
[mean_CRPS] = crps(fcst,obs,plot_pos);
[mean_CRPS,crps_values,num] = crps(fcst,obs);

INPUT
obs: Vector of observations
fcst: Matrix of Ensemble forecast of size N x M. NB: N must equal length(obs), M equals the number of ensemble members
plot_pos: plotting positions that determine cumulative distribution function

OUTPUT
mean_CRPS: Mean of non missing CRPS values
crps_values: A vector (length n) of CRPS values
num: number of non missing CRPS values used to compute mean_CRPS

EXAMPLES:
fcst = rand(1000,1000);
obs = rand(1000,1);
[meanCRPS] = crps(fcst,obs);