# skfolio.metrics.exceedance_rate ### skfolio.metrics.exceedance_rate(squared_distances, n_features, confidence_level) Exceedance rate for chi-squared calibration statistics. Computes the fraction of squared distances exceeding the upper `confidence_level` chi-squared quantile. The reference threshold assumes Gaussian standardized returns. In practice, the rate is sensitive not only to covariance misspecification but also to heavy tails, regime shifts, and non-Gaussian standardized returns. It is best used as a comparative metric across estimators rather than as an absolute calibration test. * **Parameters:** **squared_distances** *array-like of shape (n_observations,)* : Squared Mahalanobis distances or similar chi-squared statistics. **n_features** *int* : Degrees of freedom (number of features/assets). **confidence_level** *float* : Coverage confidence level used to define the upper chi-squared threshold. For example, `0.95` corresponds to an expected exceedance rate of `0.05` under calibration. * **Returns:** float : Observed exceedance rate. It should be close to $1 - \text{confidence\_level}$ when the reference chi-squared approximation is appropriate. #### SEE ALSO [`mahalanobis_calibration_ratio`](https://skfolio.org/generated/skfolio.metrics.mahalanobis_calibration_ratio.html.md#skfolio.metrics.mahalanobis_calibration_ratio) : Calibration ratio based on squared Mahalanobis distances. ### Notes Under correct calibration and Gaussian standardized returns, $d^2 \sim \chi^2(n_{\text{features}})$, so $P(d^2 > \chi^2_{\text{confidence\_level}}) = 1 - \text{confidence\_level}$.