sketch_mann_kendall.nx

sketch_mann_kendall.nx -- streaming Mann-Kendall trend test. Non-parametric trend detection over the last W samples. No distribution assumption -- works on any ordinal data including heavy-tailed, skewed, or with outliers (vs Pearson correlation which assumes linearity + normality). MANN-KENDALL STATISTIC: For each pair (i, j) with i < j in the window: S += sign(x_j - x_i) where sign in {-1, 0, +1} S > 0 = upward trend S < 0 = downward trend |S| > threshold = significant THEORETICAL VARIANCE (no ties): Var(S) = n(n-1)(2n+5)/18 Z = S / sqrt(Var(S)) — standardized, approximately N(0,1) for large n. FOR THE STREAMING VARIANT: maintain a sliding window of W samples. On each new sample: compare against all W-1 previous samples in O(W). Total state: O(W). S incrementally updated. USE CASES: - hydrology: long-term streamflow trends - climatology: warming trend detection - SRE: monotonic latency trend - finance: directional momentum (vs mean-reverting) Production tier; exact integer arithmetic over the window.