scoringrules.crps_uniform

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scoringrules.crps_uniform#

scoringrules.crps_uniform(obs: ArrayLike, min: ArrayLike, max: ArrayLike, lmass: ArrayLike = 0.0, umass: ArrayLike = 0.0, *, backend: Backend = None) → ArrayLike#

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

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

\[\mathrm{CRPS}(\mathcal{U}_{L}^{U}(l, u), y) = (u - l) \left\{ | \frac{y - l}{u - l} - F \left( \frac{y - l}{u - l} \right) | + F \left( \frac{y - l}{u - l} \right)^{2} (1 - L - U) - F \left( \frac{y - l}{u - l} \right) (1 - 2L) + \frac{(1 - L - U)^{2}}{3} + (1 - L)U \right\}\]

where \(\mathcal{U}_{L}^{U}(l, u)\) is the uniform distribution with lower bound \(l\), upper bound \(u > l\), point mass \(L\) on the lower bound, and point mass \(U\) on the upper bound. We must have that \(L, U \ge 0, L + U < 1\).

Parameters:
obsarray_like

The observed values.

min: array_like

Lower bound of the forecast uniform distribution.

max: array_like

Upper bound of the forecast uniform distribution.

lmassarray_like

Point mass on the lower bound of the forecast uniform distribution.

umassarray_like

Point mass on the upper bound of the forecast uniform distribution.

Returns:
crpsarray_like

The CRPS between U(min, max, lmass, umass) 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
>>> sr.crps_uniform(0.4, 0.0, 1.0, 0.0, 0.0)
0.09333333333333332
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