getCrps: Calculate the continuous ranked probability score
In hydro-giub/hydroBE: Miscellaneous Functions of the Group of Hydrology Bern

Description Usage Arguments Details Value Note Author(s) References Examples

The continuous ranked probability score (CRPS) is intended to verify a probabilistic prediction, i.e. a prediction in the form of a probability distribution. Informally, it judges how close this distribution envelops the verifying observation.

1	getCrps(cdfx, cdfy, obs)

`cdfx`	numeric vector. The quantiles belonging to the probabilities defined in `cdfy`.
`cdfy`	numeric vector. The probabilities belonging to the quantiles defined in `cdfx`.
`obs`	real number. The value of the observation corresponding to the probabilistic prediction.

cdfx can have a variable step width.

Real number, i.e. the CRPS value.

The step width in cdfx should be small enough such that a linear approximation between the points is reasonable.
Step functions (i.e. deterministic predictions with the entire probability mass at a single value) should be avoided since the numerical integration fails (see the 'Examples' below).

Simon S

Hersbach, H. (2000). "Decomposition of the continuous ranked probability score for ensemble prediction systems". Weather and Forecasting.

## normal distribution
obs <- 0
cdfx <- seq(from=-5,to=5,by=0.01)
cdfy <- pnorm(q=cdfx)
getCrps(cdfx=cdfx,cdfy=cdfy,obs=obs)

## 'deterministic' prediction:
## in theory we should end up with the mean absolute error
## however, the numerical integration of the step function fails
obs <- 0
cdfx <- c(-3,-1,-1,2)
cdfy <- c(0,0,1,1)
getCrps(cdfx=cdfx,cdfy=cdfy,obs=obs)