scoringrules.crps_logistic

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scoringrules.crps_logistic#

scoringrules.crps_logistic(obs: ArrayLike, mu: ArrayLike, sigma: ArrayLike, *, backend: Backend = None) → ArrayLike#

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

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

\[\mathrm{CRPS}(\mathcal{L}(\mu, \sigma), y) = \sigma \left\{ \omega - 2 \log F(\omega) - 1 \right\},\]

where \(F(\omega)\) is the CDF of the standard logistic distribution at the normalized prediction error \(\omega = \frac{y - \mu}{\sigma}\).

Parameters:
obsarray_like

Observed values.

mu: array_like

Location parameter of the forecast logistic distribution.

sigma: array_like

Scale parameter of the forecast logistic distribution.

Returns:
crpsarray_like

The CRPS for the Logistic(mu, sigma) forecasts given the observations.

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_logistic(0.0, 0.4, 0.1)
0.3036299855835619
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