← Mathematical handbook

Proposition 4(i): parameter ordering of the source family

theorem Papers.AnsariRockel2026XiRho.normalizedBand_parameter_order {b d : ℝ} (hb : 0 ≤ b) (hd : 0 ≤ d) (hbd : b ≤ d) (u v : ↑unitInterval) : (normalizedBand b hb).cdf ![u, v] ≤ (normalizedBand d hd).cdf ![u, v]

Every pair of nonnegative parameters is ordered pointwise, including independence.

theorem Papers.AnsariRockel2026XiRho.sourceBand_parameter_order {b d : ℝ} (hb : 0 < b) (hd : 0 < d) (hbd : b ≤ d) (u v : ↑unitInterval) : (sourceBand b hb).cdf ![u, v] ≤ (sourceBand d hd).cdf ![u, v]

Proposition 4(i) for the displayed positive source parameters.

theorem Papers.AnsariRockel2026XiRho.negativeSourceBand_parameter_order {b d : ℝ} (hb : 0 < b) (hd : 0 < d) (hbd : b ≤ d) (u v : ↑unitInterval) : (negativeSourceBand d hd).cdf ![u, v] ≤ (negativeSourceBand b hb).cdf ![u, v]

The source negative-parameter family has the reversed order in its positive magnitude.