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validation and profiles

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Miha Kralj
2026-02-26 22:02:52 -08:00
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lib/statistics/quantile/Quantile.md
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@@ -63,6 +63,20 @@ Relationship to Percentile: $Q(q) = P(100q)$ where $P$ is the percentile functio
## Performance Profile
### Operation Count (Streaming Mode)
Quantile uses the same sorted-buffer approach as Percentile, with fraction [0,1] mapped to sorted indices.
| Operation | Count | Cost (cycles) | Subtotal |
| :--- | :---: | :---: | :---: |
| Ring buffer evict oldest | 1 | 3 cy | ~3 cy |
| Binary search + array shift insert | log N + N/2 | 2 cy | ~N cy |
| Rank interpolation (linear) | 1 | 3 cy | ~3 cy |
| NaN guard + state update | 1 | 2 cy | ~2 cy |
| **Total (N=20)** | **O(N)** | — | **~28 cy** |
O(N) per update. Linear interpolation between adjacent order statistics matches the standard R-7 quantile method used by NumPy and R by default.
| Operation | Cost | Notes |
|-----------|------|-------|
| BinarySearch | O(log N) | `Array.BinarySearch` for insert/remove position |