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Concordance ordering of normalized quadratic-band copulas

theorem Verification.quadraticBand_cdf_mono (b d : ℝ) (hb : 0 ≤ b) (hd : 0 ≤ d) (hbd : b ≤ d) (u v : ↑unitInterval) : (quadraticBand b hb).cdf ![u, v] ≤ (quadraticBand d hd).cdf ![u, v]

A larger slope moves conditional mass toward the left in every section.

theorem Verification.quadraticBand_cdf_abs_sub_le (b d : ℝ) (hb : 0 ≤ b) (hd : 0 ≤ d) (u v : ↑unitInterval) : |(quadraticBand b hb).cdf ![u, v] - (quadraticBand d hd).cdf ![u, v]| ≤ 2 * |b - d|

Uniform dependence on the nonnegative slope, including independence.