# skfolio.distribution.empirical_tail_concentration ### skfolio.distribution.empirical_tail_concentration(X, quantiles) Compute empirical tail concentration for the two variables in X. This function computes the concentration at each quantile provided. The tail concentration are estimated as: : - Lower tail: λ_L(q) = P(U₂ ≤ q | U₁ ≤ q) - Upper tail: λ_U(q) = P(U₂ ≥ q | U₁ ≥ q) where U₁ and U₂ are the pseudo-observations. * **Parameters:** **X** *array-like of shape (n_observations, 2)* : A 2D array with exactly 2 columns representing the pseudo-observations. **quantiles** *array-like of shape (n_quantiles,)* : A 1D array of quantile levels (values between 0 and 1) at which to compute the concentration. * **Returns:** **concentration** *ndarray of shape (n_quantiles,)* : An array of empirical tail concentration values for the given quantiles. * **Raises:** ValueError : If X is not a 2D array with exactly 2 columns or if quantiles are not in [0, 1]. ### References * **[1]** “Quantitative Risk Management: Concepts, Techniques, and Tools”, McNeil, Frey, Embrechts (2005)