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.
This commit is contained in:
kingchenc
2026-05-22 19:52:04 +02:00
parent 21bbd521b3
commit 2d0ee926c5
19 changed files with 2254 additions and 12 deletions
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@@ -140,6 +140,14 @@ Rust / Python / Node examples. They are grouped by family, mirroring the
- [Indicator-ForceIndex.md](indicators/volume/Indicator-ForceIndex.md)
- [Indicator-EaseOfMovement.md](indicators/volume/Indicator-EaseOfMovement.md)
**Statistics** — price transforms and rolling regressions.
- [Indicator-TypicalPrice.md](indicators/statistics/Indicator-TypicalPrice.md)
- [Indicator-MedianPrice.md](indicators/statistics/Indicator-MedianPrice.md)
- [Indicator-WeightedClose.md](indicators/statistics/Indicator-WeightedClose.md)
- [Indicator-LinearRegression.md](indicators/statistics/Indicator-LinearRegression.md)
- [Indicator-LinRegSlope.md](indicators/statistics/Indicator-LinRegSlope.md)
## See also
- Source code: <https://github.com/kingchenc/wickra>
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@@ -1,11 +1,11 @@
# Indicators Overview
Wickra ships 58 indicators, organised in source under the four classical
families — trend, momentum, volatility, volume — that map directly to the
directory structure of `crates/wickra-core/src/indicators/`. The same family
labels are used here, plus a second-level grouping that reflects how the
indicators actually behave (which output range they live in, what data they
need, what question they answer).
Wickra ships 63 indicators, organised under the four classical families —
trend, momentum, volatility, volume — plus a fifth **statistics** group for
price transforms and rolling regressions. The same family labels are used
here, with a second-level grouping that reflects how the indicators actually
behave (which output range they live in, what data they need, what question
they answer).
Every indicator is an O(1) state machine that consumes one input at a time
and produces either `Option<f64>` (Rust), `float | None` (Python), or
@@ -185,6 +185,32 @@ price closes within each bar and how much volume backed the move.
| `ForceIndex` | `EMA((close prev_close) · volume, period)`; the conviction behind a move. | `Candle` | `f64` | unbounded around zero | `period = 13` (Python) | `period + 1` | [Indicator-ForceIndex.md](indicators/volume/Indicator-ForceIndex.md) |
| `EaseOfMovement` | `SMA` of distance travelled per unit of volume. | `Candle` | `f64` | unbounded around zero | `(period=14, divisor=1e8)` (Python) | `period + 1` | [Indicator-EaseOfMovement.md](indicators/volume/Indicator-EaseOfMovement.md) |
## Statistics
Price transforms and rolling regressions. The transforms collapse a full
OHLC bar to a single representative price; the regressions fit a
least-squares line to a sliding window of prices.
### Price transforms
Stateless per-bar reductions of an OHLC candle to one price. Each emits from
the very first candle (`warmup = 1`).
| Indicator | One-liner | Input | Output | Range | Defaults | Warmup | Deep dive |
|-----------|-----------|-------|--------|-------|----------|--------|-----------|
| `TypicalPrice` | `(high + low + close) / 3`. | `Candle` | `f64` | unbounded (price scale) | (no parameters) | `1` | [Indicator-TypicalPrice.md](indicators/statistics/Indicator-TypicalPrice.md) |
| `MedianPrice` | `(high + low) / 2`. | `Candle` | `f64` | unbounded (price scale) | (no parameters) | `1` | [Indicator-MedianPrice.md](indicators/statistics/Indicator-MedianPrice.md) |
| `WeightedClose` | `(high + low + 2·close) / 4`. | `Candle` | `f64` | unbounded (price scale) | (no parameters) | `1` | [Indicator-WeightedClose.md](indicators/statistics/Indicator-WeightedClose.md) |
### Regression
Rolling ordinary-least-squares fits over the last `period` prices.
| Indicator | One-liner | Input | Output | Range | Defaults | Warmup | Deep dive |
|-----------|-----------|-------|--------|-------|----------|--------|-----------|
| `LinearRegression` | Endpoint of the rolling least-squares line — a low-lag smoothed price. | `f64` | `f64` | unbounded (price scale) | `period = 14` (Python) | `period` | [Indicator-LinearRegression.md](indicators/statistics/Indicator-LinearRegression.md) |
| `LinRegSlope` | Slope of the rolling least-squares line — trend steepness per bar. | `f64` | `f64` | unbounded around zero | `period = 14` (Python) | `period` | [Indicator-LinRegSlope.md](indicators/statistics/Indicator-LinRegSlope.md) |
## Pick the right indicator for…
A short cheat-sheet of "I want X, which indicator?" answers, grounded in
@@ -0,0 +1,150 @@
# LinRegSlope
> Linear Regression Slope — the slope of a rolling ordinary-least-squares
> fit over the last `period` prices.
## Quick reference
| Field | Value |
|-------|-------|
| Family | Statistics |
| Sub-category | Regression |
| Input type | `f64` (price) |
| Output type | `f64` |
| Output range | unbounded around zero (price units per bar) |
| Default parameters | `period = 14` (Python) |
| Warmup period | `period` |
| Interpretation | How steeply price trends; positive up, negative down, zero flat. |
## Formula
Over the last `period` inputs, indexed `x = 0, 1, …, period 1`:
```
b = (n·Σxy Σx·Σy) / (n·Σxx (Σx)²)
```
`LinRegSlope` fits a straight line to the window by ordinary least squares —
the same fit as [`LinearRegression`](Indicator-LinearRegression.md) — but
reports the *slope* `b` instead of the endpoint. The slope is in price units
per bar: positive while price trends up, negative while it trends down, near
zero when it is ranging. This is TA-Lib's `LINEARREG_SLOPE`.
## Parameters
`period` — the regression window. Must be at least `2` (a line needs two
points). The Python binding defaults it to `14`; the Rust and Node
constructors require it explicitly.
## Inputs / Outputs
From `crates/wickra-core/src/indicators/linreg_slope.rs`:
```rust
impl Indicator for LinRegSlope {
type Input = f64;
type Output = f64;
// update(&mut self, input: f64) -> Option<f64>
}
```
`LinRegSlope` is a **scalar** indicator: it consumes one `f64` price per step.
Because `Input = f64` it can sit inside a [`Chain`](../../Indicator-Chaining.md).
## Warmup
`LinRegSlope::new(14).warmup_period() == 14`. The first value lands once the
window holds a full `period` prices — on input index `period 1`.
## Edge cases
- **`period < 2`.** Rejected at construction — a regression line is undefined
for fewer than two points.
- **Perfect line.** Fed a series rising by a fixed step, the slope is exactly
that step (`perfect_line_returns_its_step` pins this).
- **Constant series.** A flat input returns a slope of `0`.
- **Falling series.** A descending input returns a negative slope.
- **Reset.** `ls.reset()` clears the rolling window.
## Examples
### Rust
```rust
use wickra::{BatchExt, Indicator, LinRegSlope};
fn main() -> Result<(), Box<dyn std::error::Error>> {
let mut ls = LinRegSlope::new(3)?;
// Fit over [1, 2, 9]: the least-squares line is y = 4x, slope 4.
let out = ls.batch(&[1.0, 2.0, 9.0]);
println!("{:?}", out);
Ok(())
}
```
Output:
```
[None, None, Some(4.0)]
```
This matches the `reference_values` test in
`crates/wickra-core/src/indicators/linreg_slope.rs`.
### Python
```python
import numpy as np
import wickra as ta
ls = ta.LinRegSlope(3)
print(ls.batch(np.array([1.0, 2.0, 9.0])))
```
Output:
```
[nan nan 4.]
```
### Node
```javascript
const ta = require('wickra');
const ls = new ta.LinRegSlope(3);
console.log(ls.batch([1, 2, 9]));
```
Output:
```
[ NaN, NaN, 4 ]
```
## Interpretation
`LinRegSlope` is a momentum gauge: its sign is the trend direction and its
magnitude is the trend's steepness in price-per-bar. A slope crossing zero
marks a trend change; a slope that flattens while price still rises warns the
trend is losing pace. Unlike a difference-based oscillator it uses every bar
in the window, so it is less jumpy.
## Common pitfalls
- **Comparing slopes across instruments.** The slope is in the instrument's
own price units per bar — normalise (e.g. divide by price) to compare.
- **Tiny periods.** `period = 2` reduces the slope to the last simple
difference; use a meaningful window.
## References
The slope of an ordinary least-squares fit to a rolling price window; matches
TA-Lib's `LINEARREG_SLOPE`.
## See also
- [Indicator-LinearRegression.md](Indicator-LinearRegression.md) — the
endpoint of the same rolling fit.
- [Indicator-Mom.md](../momentum/Indicator-Mom.md) — raw price-difference
momentum, the unsmoothed cousin.
- [Indicators-Overview.md](../../Indicators-Overview.md) — the full taxonomy.
@@ -0,0 +1,152 @@
# LinearRegression
> Linear Regression — the endpoint of a rolling ordinary-least-squares fit
> over the last `period` prices.
## Quick reference
| Field | Value |
|-------|-------|
| Family | Statistics |
| Sub-category | Regression |
| Input type | `f64` (price) |
| Output type | `f64` |
| Output range | unbounded (price scale) |
| Default parameters | `period = 14` (Python) |
| Warmup period | `period` |
| Interpretation | A low-lag smoothed price — the trend line extrapolated to now. |
## Formula
Over the last `period` inputs, indexed `x = 0, 1, …, period 1`:
```
b (slope) = (n·Σxy Σx·Σy) / (n·Σxx (Σx)²)
a (intercept) = (Σy b·Σx) / n
LinearReg = a + b·(period 1)
```
The indicator fits a straight line to the window by ordinary least squares,
then reports that line's value at the most recent bar. Because it
extrapolates the *local trend* forward rather than averaging it away, it lags
a same-period [`Sma`](../trend/Indicator-Sma.md) noticeably less. This is
TA-Lib's `LINEARREG`.
## Parameters
`period` — the regression window. Must be at least `2` (a line needs two
points). The Python binding defaults it to `14`; the Rust and Node
constructors require it explicitly.
## Inputs / Outputs
From `crates/wickra-core/src/indicators/linreg.rs`:
```rust
impl Indicator for LinearRegression {
type Input = f64;
type Output = f64;
// update(&mut self, input: f64) -> Option<f64>
}
```
`LinearRegression` is a **scalar** indicator: it consumes one `f64` price per
step. Because `Input = f64` it can sit inside a [`Chain`](../../Indicator-Chaining.md).
## Warmup
`LinearRegression::new(14).warmup_period() == 14`. The first value lands once
the window holds a full `period` prices — on input index `period 1`.
## Edge cases
- **`period < 2`.** Rejected at construction — a regression line is undefined
for fewer than two points.
- **Perfect line.** Fed a perfectly linear series, the fit *is* that line, so
the endpoint equals the current value (`perfect_line_returns_current_value`
pins this).
- **Constant series.** A flat input returns that constant.
- **Reset.** `lr.reset()` clears the rolling window.
## Examples
### Rust
```rust
use wickra::{BatchExt, Indicator, LinearRegression};
fn main() -> Result<(), Box<dyn std::error::Error>> {
let mut lr = LinearRegression::new(3)?;
// Fit over [1, 2, 9]: the least-squares line is y = 4x, endpoint 4·2 = 8.
let out = lr.batch(&[1.0, 2.0, 9.0]);
println!("{:?}", out);
Ok(())
}
```
Output:
```
[None, None, Some(8.0)]
```
This matches the `reference_values` test in
`crates/wickra-core/src/indicators/linreg.rs`.
### Python
```python
import numpy as np
import wickra as ta
lr = ta.LinearRegression(3)
print(lr.batch(np.array([1.0, 2.0, 9.0])))
```
Output:
```
[nan nan 8.]
```
### Node
```javascript
const ta = require('wickra');
const lr = new ta.LinearRegression(3);
console.log(lr.batch([1, 2, 9]));
```
Output:
```
[ NaN, NaN, 8 ]
```
## Interpretation
Read `LinearRegression` as a low-lag moving average: it tracks price more
closely than an SMA of the same period because it projects the window's trend
to the current bar instead of centring on the window. A shorter `period`
hugs price; a longer one is a smoother trend line. Pair it with
[`LinRegSlope`](Indicator-LinRegSlope.md) to read the same fit's steepness.
## Common pitfalls
- **Confusing it with an SMA.** It is a *projected* fit, not a centred
average, so it leads an SMA of the same period.
- **Tiny periods.** `period = 2` is allowed but the "fit" just passes through
the last two points; use a meaningful window.
## References
Ordinary least-squares linear regression applied to a rolling price window;
the endpoint formulation matches TA-Lib's `LINEARREG`.
## See also
- [Indicator-LinRegSlope.md](Indicator-LinRegSlope.md) — the slope of the same
rolling fit.
- [Indicator-Sma.md](../trend/Indicator-Sma.md) — the centred average it is
often compared against.
- [Indicators-Overview.md](../../Indicators-Overview.md) — the full taxonomy.
@@ -0,0 +1,136 @@
# MedianPrice
> Median Price — the bar's `(high + low) / 2`, the midpoint of its range.
## Quick reference
| Field | Value |
|-------|-------|
| Family | Statistics |
| Sub-category | Price transforms |
| Input type | `Candle` (uses `high`, `low`) |
| Output type | `f64` |
| Output range | unbounded (price scale) |
| Default parameters | none (no parameters) |
| Warmup period | `1` |
| Interpretation | The midpoint of the bar's range, ignoring open and close. |
## Formula
```
MedianPrice = (high + low) / 2
```
The median price is the centre of the bar's range — it discards where the bar
opened and closed entirely. It is the price series Bill Williams'
[`AwesomeOscillator`](../momentum/Indicator-AwesomeOscillator.md) is built on,
and a useful close substitute when the close is noisy relative to the range.
## Parameters
`MedianPrice` takes **no parameters**`MedianPrice::new()` in Rust,
`wickra.MedianPrice()` in Python, `new ta.MedianPrice()` in Node.
## Inputs / Outputs
From `crates/wickra-core/src/indicators/median_price.rs`:
```rust
impl Indicator for MedianPrice {
type Input = Candle;
type Output = f64;
// update(&mut self, input: Candle) -> Option<f64>
}
```
`MedianPrice` is a **candle-input** indicator that reads `high` and `low`. In
Python the streaming `update` accepts a 6-tuple or a dict; the batch helper
takes `high`, `low` numpy arrays. Node and WASM expose `update(high, low)` and
the matching `batch`.
## Warmup
`MedianPrice::new().warmup_period() == 1`. It is a stateless per-bar transform
— it emits a value from the very first candle.
## Edge cases
- **No warmup.** Every candle produces a value immediately.
- **Reset.** `mp.reset()` only clears the `is_ready` flag; there is no
rolling state to discard.
## Examples
### Rust
```rust
use wickra::{Candle, Indicator, MedianPrice};
fn main() -> Result<(), Box<dyn std::error::Error>> {
let mut mp = MedianPrice::new();
let v = mp.update(Candle::new(10.0, 12.0, 8.0, 11.0, 1.0, 0)?);
println!("{:?}", v);
Ok(())
}
```
Output:
```
Some(10.0)
```
`(12 + 8) / 2 = 10`. This matches the `reference_value` test in
`crates/wickra-core/src/indicators/median_price.rs`.
### Python
```python
import numpy as np
import wickra as ta
mp = ta.MedianPrice()
print(mp.batch(np.array([12.0]), np.array([8.0])))
```
Output:
```
[10.]
```
### Node
```javascript
const ta = require('wickra');
const mp = new ta.MedianPrice();
console.log(mp.batch([12], [8]));
```
Output:
```
[ 10 ]
```
## Interpretation
The median price is the most range-centric of the three transforms — it is
blind to the close. Use it when the question is "where did this bar trade?"
rather than "where did it settle?", or as the input to a Bill Williams setup.
## Common pitfalls
- **Expecting the close to matter.** It does not — by definition the median
price ignores both the open and the close.
## References
The Median Price; the `(H + L) / 2` definition is standard (TA-Lib's
`MEDPRICE`).
## See also
- [Indicator-TypicalPrice.md](Indicator-TypicalPrice.md) — `(H + L + C) / 3`.
- [Indicator-WeightedClose.md](Indicator-WeightedClose.md) — `(H + L + 2C) / 4`.
- [Indicators-Overview.md](../../Indicators-Overview.md) — the full taxonomy.
@@ -0,0 +1,137 @@
# TypicalPrice
> Typical Price — the bar's `(high + low + close) / 3`, a single
> representative price per candle.
## Quick reference
| Field | Value |
|-------|-------|
| Family | Statistics |
| Sub-category | Price transforms |
| Input type | `Candle` (uses `high`, `low`, `close`) |
| Output type | `f64` |
| Output range | unbounded (price scale) |
| Default parameters | none (no parameters) |
| Warmup period | `1` |
| Interpretation | A representative per-bar price; a smoother stand-in for the close. |
## Formula
```
TypicalPrice = (high + low + close) / 3
```
The typical price collapses a full OHLC bar to one number, giving the close
no more weight than the two extremes. It is the price series that
[`Cci`](../momentum/Indicator-Cci.md) and [`Mfi`](../momentum/Indicator-Mfi.md)
are defined on, and a common input to feed any close-driven indicator when you
want the bar's range reflected in the value.
## Parameters
`TypicalPrice` takes **no parameters**`TypicalPrice::new()` in Rust,
`wickra.TypicalPrice()` in Python, `new ta.TypicalPrice()` in Node.
## Inputs / Outputs
From `crates/wickra-core/src/indicators/typical_price.rs`:
```rust
impl Indicator for TypicalPrice {
type Input = Candle;
type Output = f64;
// update(&mut self, input: Candle) -> Option<f64>
}
```
`TypicalPrice` is a **candle-input** indicator that reads `high`, `low` and
`close`. In Python the streaming `update` accepts a 6-tuple or a dict; the
batch helper takes `high`, `low`, `close` numpy arrays. Node and WASM expose
`update(high, low, close)` and the matching `batch`.
## Warmup
`TypicalPrice::new().warmup_period() == 1`. It is a stateless per-bar
transform — it emits a value from the very first candle.
## Edge cases
- **No warmup.** Every candle produces a value immediately.
- **Reset.** `tp.reset()` only clears the `is_ready` flag; there is no
rolling state to discard.
## Examples
### Rust
```rust
use wickra::{Candle, Indicator, TypicalPrice};
fn main() -> Result<(), Box<dyn std::error::Error>> {
let mut tp = TypicalPrice::new();
let v = tp.update(Candle::new(9.0, 12.0, 6.0, 9.0, 1.0, 0)?);
println!("{:?}", v);
Ok(())
}
```
Output:
```
Some(9.0)
```
`(12 + 6 + 9) / 3 = 9`. This matches the `reference_value` test in
`crates/wickra-core/src/indicators/typical_price.rs`.
### Python
```python
import numpy as np
import wickra as ta
tp = ta.TypicalPrice()
print(tp.batch(np.array([12.0]), np.array([6.0]), np.array([9.0])))
```
Output:
```
[9.]
```
### Node
```javascript
const ta = require('wickra');
const tp = new ta.TypicalPrice();
console.log(tp.batch([12], [6], [9]));
```
Output:
```
[ 9 ]
```
## Interpretation
Use it wherever you would use the close but want the bar's range to count —
feeding a moving average, an oscillator, or a band. It is marginally smoother
than the raw close because a wild close is pulled back toward the bar's mid.
## Common pitfalls
- **Feeding it scalar prices.** It needs the full `high`/`low`/`close` bar.
## References
The Typical Price (also "pivot price"); the `(H + L + C) / 3` definition is
standard (StockCharts, TA-Lib's `TYPPRICE`).
## See also
- [Indicator-MedianPrice.md](Indicator-MedianPrice.md) — `(H + L) / 2`.
- [Indicator-WeightedClose.md](Indicator-WeightedClose.md) — `(H + L + 2C) / 4`.
- [Indicators-Overview.md](../../Indicators-Overview.md) — the full taxonomy.
@@ -0,0 +1,137 @@
# WeightedClose
> Weighted Close — the bar's `(high + low + 2·close) / 4`, a per-bar price
> that gives the close double weight.
## Quick reference
| Field | Value |
|-------|-------|
| Family | Statistics |
| Sub-category | Price transforms |
| Input type | `Candle` (uses `high`, `low`, `close`) |
| Output type | `f64` |
| Output range | unbounded (price scale) |
| Default parameters | none (no parameters) |
| Warmup period | `1` |
| Interpretation | A representative per-bar price that leans on the close. |
## Formula
```
WeightedClose = (high + low + 2·close) / 4
```
Like the [`TypicalPrice`](Indicator-TypicalPrice.md), the weighted close
collapses an OHLC bar to one number — but it counts the close twice, so the
result sits closer to where the bar settled than to its range. Reach for it
when the closing print carries more signal than the extremes.
## Parameters
`WeightedClose` takes **no parameters**`WeightedClose::new()` in Rust,
`wickra.WeightedClose()` in Python, `new ta.WeightedClose()` in Node.
## Inputs / Outputs
From `crates/wickra-core/src/indicators/weighted_close.rs`:
```rust
impl Indicator for WeightedClose {
type Input = Candle;
type Output = f64;
// update(&mut self, input: Candle) -> Option<f64>
}
```
`WeightedClose` is a **candle-input** indicator that reads `high`, `low` and
`close`. In Python the streaming `update` accepts a 6-tuple or a dict; the
batch helper takes `high`, `low`, `close` numpy arrays. Node and WASM expose
`update(high, low, close)` and the matching `batch`.
## Warmup
`WeightedClose::new().warmup_period() == 1`. It is a stateless per-bar
transform — it emits a value from the very first candle.
## Edge cases
- **No warmup.** Every candle produces a value immediately.
- **Reset.** `wc.reset()` only clears the `is_ready` flag; there is no
rolling state to discard.
## Examples
### Rust
```rust
use wickra::{Candle, Indicator, WeightedClose};
fn main() -> Result<(), Box<dyn std::error::Error>> {
let mut wc = WeightedClose::new();
let v = wc.update(Candle::new(10.0, 12.0, 8.0, 11.0, 1.0, 0)?);
println!("{:?}", v);
Ok(())
}
```
Output:
```
Some(10.5)
```
`(12 + 8 + 2·11) / 4 = 42 / 4 = 10.5`. This matches the `reference_value`
test in `crates/wickra-core/src/indicators/weighted_close.rs`.
### Python
```python
import numpy as np
import wickra as ta
wc = ta.WeightedClose()
print(wc.batch(np.array([12.0]), np.array([8.0]), np.array([11.0])))
```
Output:
```
[10.5]
```
### Node
```javascript
const ta = require('wickra');
const wc = new ta.WeightedClose();
console.log(wc.batch([12], [8], [11]));
```
Output:
```
[ 10.5 ]
```
## Interpretation
The weighted close sits on the spectrum between the raw close and the
[`TypicalPrice`](Indicator-TypicalPrice.md): closer to the close, but still
nudged by the bar's range. Use it as a drop-in close replacement when you want
the settlement to dominate without ignoring the extremes entirely.
## Common pitfalls
- **Feeding it scalar prices.** It needs the full `high`/`low`/`close` bar.
## References
The Weighted Close; the `(H + L + 2C) / 4` definition is standard (TA-Lib's
`WCLPRICE`).
## See also
- [Indicator-TypicalPrice.md](Indicator-TypicalPrice.md) — `(H + L + C) / 3`.
- [Indicator-MedianPrice.md](Indicator-MedianPrice.md) — `(H + L) / 2`.
- [Indicators-Overview.md](../../Indicators-Overview.md) — the full taxonomy.