scoringrules.crps_exponential

scoringrules.crps_exponential(obs: ArrayLike, rate: ArrayLike, *, backend: Backend = None) → ArrayLike

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

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

\[\mathrm{CRPS}(F_{\lambda}, y) = |y| - \frac{2F_{\lambda}(y)}{\lambda} + \frac{1}{2 \lambda},\]

where \(F_{\lambda}\) is exponential distribution function with rate parameter \(\lambda > 0\).

Parameters:

obsarray_like

The observed values.

ratearray_like

Rate parameter of the forecast exponential distribution.

backendstr, optional

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

Returns:

crps:

The CRPS between Exp(rate) and obs.

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
>>> import numpy as np
>>> sr.crps_exponential(0.8, 3.0)
0.360478635526275
>>> sr.crps_exponential(np.array([0.8, 0.9]), np.array([3.0, 2.0]))
array([0.36047864, 0.31529889])