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lib/statistics/geomean/Geomean.md
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# GEOMEAN: Geometric Mean
| Property | Value |
| ---------------- | -------------------------------- |
| **Category** | Statistic |
| **Inputs** | Source (close) |
| **Parameters** | `period` |
| **Outputs** | Single series (Geomean) |
| **Output range** | Varies (see docs) |
| **Warmup** | `period` bars |
### TL;DR
- The Geometric Mean computes the nth root of the product of n positive values over a sliding window.
- Parameterized by `period`.
- Output range: Varies (see docs).
- Requires `period` bars of warmup before first valid output (IsHot = true).
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
> "The geometric mean is never greater than the arithmetic mean." - Mathematical inequality since antiquity
The Geometric Mean computes the nth root of the product of n positive values over a sliding window. Unlike the arithmetic mean, it captures multiplicative relationships and is the correct average for growth rates, ratios, and log-normally distributed data. For financial time series, this means it properly accounts for compounding.