scoringrules.crps_laplace

Contents

scoringrules.crps_laplace#

scoringrules.crps_laplace(obs: ArrayLike, location: ArrayLike = 0.0, scale: ArrayLike = 1.0, *, backend: Backend = None) → ArrayLike#

Compute the closed form of the CRPS for the laplace distribution.

It is based on the following formulation from [1]:

\[\mathrm{CRPS}(F, y) = |y - \mu| + \sigma \exp ( -| y - \mu| / \sigma) - \frac{3\sigma}{4},\]

where \(\mu\) and \(\sigma > 0\) are the location and scale parameters of the Laplace distribution.

Parameters:
obsarray_like

Observed values.

locationarray_like

Location parameter of the forecast laplace distribution.

scalearray_like

Scale parameter of the forecast laplace distribution.

backendstr, optional

The name of the backend used for computations. Defaults to numba if available, else numpy.

Returns:
crps:

The CRPS between obs and Laplace(location, scale).

References

[1]

Jordan, A., Krüger, F., & Lerch, S. (2019). Evaluating Probabilistic Forecasts with scoringRules. Journal of Statistical Software, 90(12), 1-37. https://doi.org/10.18637/jss.v090.i12

Examples

>>> import scoringrules as sr
>>> sr.crps_laplace(0.3, 0.1, 0.2)
0.12357588823428847
Contents