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Miha Kralj
2026-03-13 13:47:10 -07:00
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lib/statistics/zscore/Zscore.md
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| **PineScript** | [zscore.pine](zscore.pine) |
- The Z-Score measures how many population standard deviations a value lies from the rolling mean over a lookback window.
- Parameterized by `period` (default 14).
- Output range: Unbounded.
- Requires `period` bars of warmup before first valid output (IsHot = true).
- **Similar:** [Normalize](../../numerics/normalize/Normalize.md), [StdDev](../stddev/StdDev.md) | **Trading note:** Z-score; number of standard deviations from mean. ±2σ indicates unusual move. Mean-reversion signal.
- Validated against manual computation, PineScript parity, and statistical invariants.
## Introduction
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- Pearson, K. (1894). "Contributions to the Mathematical Theory of Evolution." *Philosophical Transactions of the Royal Society.*
- TradingView PineScript Reference: [ta.zscore](https://www.tradingview.com/pine-script-reference/v6/)
- Bollinger, J. (2001). *Bollinger on Bollinger Bands.* McGraw-Hill. (Z-score normalization of Bollinger %B)
- Bollinger, J. (2001). *Bollinger on Bollinger Bands.* McGraw-Hill. (Z-score normalization of Bollinger %B)