pykelihood.metrics.

Brier_score

Brier_score(distribution, data, threshold=None)

Brier Score.

Represents the mean squared error between observed exceedance of a threshold \(u\) and the value of the fitted survival function at \(u\).

\[BS = \frac{1}{N}\sum_{i=1}^{N}(\bar{F}(u)-1_{y_i\geq u})^2,\]

where \(\bar{F}\) is the fitted survival function and \(1_{y_i\geq u}\) is the indicator function that the observed value is above threshold \(u\).

Parameters:

• distribution (Distribution) – pykelihood.Distribution object.

• data (Obs) – Data of type Obs.

• threshold (float, optional) – The tail we are interested in predicting correctly.

Raises:

ValueError – If threshold is None.