scoringrules.crps_binomial

scoringrules.crps_binomial(obs: ArrayLike, n: ArrayLike, prob: ArrayLike, *, backend: Backend = None) → ArrayLike

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

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

\[\mathrm{CRPS}(F_{n, p}, y) = 2 \sum_{x = 0}^{n} f_{n,p}(x) (1\{y < x\} - F_{n,p}(x) + f_{n,p}(x)/2) (x - y),\]

where \(f_{n, p}\) and \(F_{n, p}\) are the PDF and CDF of the binomial distribution with size parameter \(n = 0, 1, 2, ...\) and probability parameter \(p \in [0, 1]\).

Parameters:

obsarray_like

The observed values as an integer or array of integers.

n: array_like

Size parameter of the forecast binomial distribution as an integer or array of integers.

probarray_like

Probability parameter of the forecast binomial distribution as a float or array of floats.

backendstr, optional

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

Returns:

crps:

The CRPS between Binomial(n, prob) 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_binomial(4, 10, 0.5)
0.5955772399902344