F12: add price transforms and rolling linear regression
- Rust core: typical_price.rs ((H+L+C)/3), median_price.rs ((H+L)/2), weighted_close.rs ((H+L+2C)/4) — stateless per-bar OHLC transforms — and linreg.rs (LinearRegression — endpoint of a rolling ordinary-least-squares fit) and linreg_slope.rs (LinRegSlope — slope of that fit). Each with a full Indicator impl, runnable doctest and reference / property / warmup / reset / batch==streaming tests. - Python: PyTypicalPrice / PyMedianPrice / PyWeightedClose / PyLinearRegression / PyLinRegSlope PyO3 classes + module registration + .pyi stubs. - Node: explicit TypicalPriceNode / MedianPriceNode / WeightedCloseNode / LinearRegressionNode / LinRegSlopeNode; index.d.ts and index.js updated. - WASM: explicit WasmTypicalPrice / WasmMedianPrice / WasmWeightedClose; WasmLinearRegression / WasmLinRegSlope via the scalar macro. - Wiki: a new indicators/statistics/ folder with five Indicator-*.md pages, a new "Statistics" family in Indicators-Overview.md and Home.md. cargo fmt + clippy (core/wickra/data/wasm/node) clean; 454 core tests, 25 data tests and 66 doctests green.
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# TypicalPrice
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> Typical Price — the bar's `(high + low + close) / 3`, a single
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> representative price per candle.
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## Quick reference
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| Field | Value |
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|-------|-------|
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| Family | Statistics |
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| Sub-category | Price transforms |
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| Input type | `Candle` (uses `high`, `low`, `close`) |
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| Output type | `f64` |
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| Output range | unbounded (price scale) |
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| Default parameters | none (no parameters) |
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| Warmup period | `1` |
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| Interpretation | A representative per-bar price; a smoother stand-in for the close. |
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## Formula
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```
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TypicalPrice = (high + low + close) / 3
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```
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The typical price collapses a full OHLC bar to one number, giving the close
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no more weight than the two extremes. It is the price series that
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[`Cci`](../momentum/Indicator-Cci.md) and [`Mfi`](../momentum/Indicator-Mfi.md)
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are defined on, and a common input to feed any close-driven indicator when you
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want the bar's range reflected in the value.
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## Parameters
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`TypicalPrice` takes **no parameters** — `TypicalPrice::new()` in Rust,
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`wickra.TypicalPrice()` in Python, `new ta.TypicalPrice()` in Node.
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## Inputs / Outputs
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From `crates/wickra-core/src/indicators/typical_price.rs`:
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```rust
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impl Indicator for TypicalPrice {
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type Input = Candle;
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type Output = f64;
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// update(&mut self, input: Candle) -> Option<f64>
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}
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```
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`TypicalPrice` is a **candle-input** indicator that reads `high`, `low` and
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`close`. In Python the streaming `update` accepts a 6-tuple or a dict; the
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batch helper takes `high`, `low`, `close` numpy arrays. Node and WASM expose
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`update(high, low, close)` and the matching `batch`.
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## Warmup
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`TypicalPrice::new().warmup_period() == 1`. It is a stateless per-bar
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transform — it emits a value from the very first candle.
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## Edge cases
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- **No warmup.** Every candle produces a value immediately.
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- **Reset.** `tp.reset()` only clears the `is_ready` flag; there is no
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rolling state to discard.
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## Examples
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### Rust
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```rust
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use wickra::{Candle, Indicator, TypicalPrice};
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fn main() -> Result<(), Box<dyn std::error::Error>> {
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let mut tp = TypicalPrice::new();
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let v = tp.update(Candle::new(9.0, 12.0, 6.0, 9.0, 1.0, 0)?);
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println!("{:?}", v);
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Ok(())
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}
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```
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Output:
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```
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Some(9.0)
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```
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`(12 + 6 + 9) / 3 = 9`. This matches the `reference_value` test in
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`crates/wickra-core/src/indicators/typical_price.rs`.
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### Python
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```python
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import numpy as np
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import wickra as ta
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tp = ta.TypicalPrice()
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print(tp.batch(np.array([12.0]), np.array([6.0]), np.array([9.0])))
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```
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Output:
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```
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[9.]
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```
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### Node
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```javascript
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const ta = require('wickra');
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const tp = new ta.TypicalPrice();
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console.log(tp.batch([12], [6], [9]));
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```
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Output:
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```
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[ 9 ]
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```
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## Interpretation
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Use it wherever you would use the close but want the bar's range to count —
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feeding a moving average, an oscillator, or a band. It is marginally smoother
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than the raw close because a wild close is pulled back toward the bar's mid.
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## Common pitfalls
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- **Feeding it scalar prices.** It needs the full `high`/`low`/`close` bar.
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## References
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The Typical Price (also "pivot price"); the `(H + L + C) / 3` definition is
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standard (StockCharts, TA-Lib's `TYPPRICE`).
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## See also
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- [Indicator-MedianPrice.md](Indicator-MedianPrice.md) — `(H + L) / 2`.
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- [Indicator-WeightedClose.md](Indicator-WeightedClose.md) — `(H + L + 2C) / 4`.
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- [Indicators-Overview.md](../../Indicators-Overview.md) — the full taxonomy.
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