crps

crps, function

def pure crps(r: ranvar, n: number): number
def pure crps(r1: ranvar, r2: ranvar): number

Calculates the Continuous Ranked Probability Score (CRPS) for probabilistic predictions. When called as crps(r, n), it computes the score between the predictive distribution r and the observed value n. When called as crps(r1, r2), it computes the extended CRPS between two predictive distributions r1 and r2.

Examples

Example: CRPS between a ranvar and an observation

r = poisson(3)
show scalar "" with crps(r, 4)

Example: Extended CRPS between two ranvars

r1 = poisson(3)
r2 = poisson(7)
show scalar "" with crps(r1, r2)

Remarks

Let $X_1$ and $X_2$ be two random variables. Let $F_1$ and $F_2$ be the cumulative distribution functions (CDF) of $X_1$ and $X_2$ respectively. We define the CRPS between $X_1$ and $X_2$ as:

$$CRPS(X_1, X_2) = \int_{-\infty}^{+\infty} (F_1(x) - F_2(x))^2 dx$$