ml_robuststats

A small robust-statistics toolkit for building stable, outlier-resistant indicators.

Provides MAD-based robust z-scores (median/MAD, breakdown point 0.5), robust variance,
winsorization, percentile rank, multi-window boolean consensus, and inverse-variance
"precision" weighting (ridge-regularized, capped, normalized) for combining several
factors into one composite so quiet/reliable inputs get more weight and noisy ones fade.

Intended as a shared building block imported by other scripts, not as a standalone chart
indicator. MPL-2.0.

Library "ml_robuststats"

robMedian(src, len)
Parameters:
src (float)
len (simple int)

robMAD(src, len)
Parameters:
src (float)
len (simple int)

robZ(src, len)
Parameters:
src (float)
len (simple int)

robVar(src, len)
Parameters:
src (float)
len (simple int)

winsor(x, cap)
Parameters:
x (float)
cap (simple float)

pctRank(src, len)
Parameters:
src (float)
len (simple int)

consensus(sShort, sMid, sLong, mode)
Parameters:
sShort (bool)
sMid (bool)
sLong (bool)
mode (simple string)

precisionWeights(variances, wCap, ridgeFrac)
Parameters:
variances (array<float>)
wCap (simple float)
ridgeFrac (simple float)

dot(values, weights)
Parameters:
values (array<float>)
weights (array<float>)

Release Notes

ml_robuststats is a dependency-free library of robust-statistics primitives for Pine v6. It exists to fix a common weakness in indicator maths: the ordinary mean/standard-deviation z-score is dominated by a single fat-tailed bar — one gap, news spike, or expiry print stretches the σ scale and distorts every band and threshold built on it. The estimators here use the median and the median-absolute-deviation instead, which tolerate up to half the sample being outliers before they break down, so bands and scores keep a consistent meaning across regimes.

Everything is exported for reuse via import. Each function takes a series float source (and a simple int window where relevant), so they slot in wherever you currently compute a z-score, a percentile, or a weighted composite.

What's inside
robMedian(src, len) — rolling median. The robust centre of a window.
robMAD(src, len) — rolling median absolute deviation. The robust spread of a window.
robZ(src, len) — robust z-score: (x − median) / (1.4826 × MAD). The 1.4826 factor makes MAD ≈ σ under Gaussian data, so a robust z reads on the same scale as a classic z but shrugs off outliers. Returns 0 when the window has essentially no spread. This is the drop-in replacement for a mean/stdev z-score.
robVar(src, len) — robust variance, (1.4826 × MAD)². Useful as the per-factor variance input to precision weighting.
winsor(x, cap) — clamp a value to ±cap. A second layer of outlier control to apply before compositing several factors.
pctRank(src, len) — percentile rank 0–100. Self-calibrating strength that needs no fixed threshold; naturally bounded and outlier-tolerant.
consensus(sShort, sMid, sLong, mode) — multi-window boolean agreement across a short/medium/long signal, with mode "Any" | "Majority" | "All". Turns three single-window reads into one agreement gate.
precisionWeights(variances, wCap, ridgeFrac) — inverse-variance (precision) weights from an array of per-factor variances, ridge-regularized, capped per factor, and normalized to sum to 1. Quiet, reliable factors earn more weight; noisy ones fade — a principled replacement for hand-set weights. wCap prevents any single factor from dominating; ridgeFrac stabilizes the weights when a variance is near zero.
dot(values, weights) — safe dot product of a values array with a weights array (handles size mismatch and na), for turning factors + precision weights into one composite score.
How to use

Import the library, then call what you need. A robust z on any series:

//version=6
indicator("Example — robust z", overlay = false)
import Market_Logic_India/ml_robuststats/1 as rs

len = input.int(100, "Window")
z = rs.robZ(close - ta.vwap(hlc3), len) // robust vs (x - mean)/stdev
plot(z, "robZ", color = color.new(#5b9cf6, 0))
hline(0)

A precision-weighted composite of several factors:

import Market_Logic_India/ml_robuststats/1 as rs

f1 = rs.robZ(factorA, 100)
f2 = rs.robZ(factorB, 100)
f3 = rs.robZ(factorC, 100)

var array<float> vals = array.new<float>(3)
array.set(vals, 0, f1), array.set(vals, 1, f2), array.set(vals, 2, f3)

var array<float> vars = array.new<float>(3)
array.set(vars, 0, rs.robVar(factorA, 100))
array.set(vars, 1, rs.robVar(factorB, 100))
array.set(vars, 2, rs.robVar(factorC, 100))

w = rs.precisionWeights(vars, 0.6, 0.10) // cap 0.6, ridge 10%
composite = rs.dot(vals, w)
plot(composite, "composite")
Notes
Non-repainting: all estimators use only closed historical bars — no request.*, no future references. The last bar updates intrabar and settles on close.
Warm-up: the rolling estimators need len bars of history before they are meaningful; treat the start of history as warm-up.
Types: pass simple int windows and simple float caps (plain inputs or constants), not series values. consensus takes a simple string mode.
precisionWeights and dot operate on array<float> — build the arrays each bar (or as var arrays you overwrite).
Concept credits

The median / MAD robust z-score (with the 1.4826 consistency constant), winsorization, inverse-variance precision weighting, and percentile-rank strength are standard robust-statistics and meta-analysis techniques. This library is an original Pine v6 packaging of those public methods for reuse; it is not affiliated with, nor endorsed by, any originator.

License

Mozilla Public License 2.0 — as required for TradingView libraries (open source). Free to import and build on.

Release Notes

v3

Added:
pctCap(src, pct, len)
Parameters:
src (float)
pct (simple float)
len (simple int)

Pine library

In true TradingView spirit, the author has published this Pine code as an open-source library so that other Pine programmers from our community can reuse it. Cheers to the author! You may use this library privately or in other open-source publications, but reuse of this code in publications is governed by House Rules.

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Disclaimer

The information and publications are not meant to be, and do not constitute, financial, investment, trading, or other types of advice or recommendations supplied or endorsed by TradingView. Read more in the Terms of Use.

Pine library

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