Pivot Length Percentiles Oscillator

# Pivot Length Percentiles Oscillator: Technical Mechanics Explained

## Introduction
The Pivot Length Percentiles Oscillator is a statistical approach to identifying potential market reversals by analyzing the distribution of price movements relative to pivot points. This publication explains the technical mechanics behind the indicator.

## Core Mechanics

### 1. Pivot Point Detection
The indicator begins by identifying significant pivot highs and lows using a user-defined lookback period:
- `lft`: Number of bars to the left of potential pivot point
- `rht`: Number of bars to the right of potential pivot point

These parameters determine how "significant" a pivot needs to be to qualify for analysis.

### 2. Distance Measurement & Historical Database
For each new pivot point identified, the indicator:
- Calculates the absolute price distance from the previous pivot of the same type
- Records the number of candles between consecutive pivots
- Stores these measurements in dynamic arrays that build a historical database

### 3. Statistical Distribution Analysis
Rather than using fixed values, the oscillator analyzes the complete distribution of historical pivot distances and calculates key percentile values:
- `lw` (Low Percentile): Lower boundary for statistical significance
- `md` (Mid Percentile): Median statistical boundary
- `hi` (High Percentile): Upper boundary for statistical extremes

### 4. Oscillator Construction
Two primary oscillator lines are calculated:
- Green line (`osc1`): Measures current price's fall below recent highs with `low - ta.highest(high, lft)`
- Red line (`osc2`): Measures current price's rise above recent lows with `high - ta.lowest(low, lft)`

### 5. Threshold Generation
The percentile values from the historical distribution create dynamic threshold lines:
- For downside movements: Scaled versions of the low percentile (`lw_distance_low`) and high percentile (`hi_distance_low`)
- For upside movements: Scaled versions of the low percentile (`lw_distance_high`) and high percentile (`hi_distance_high`)

### 6. Signal Logic
Entry signals are generated when:
- **Bullish Signal**: The downside oscillator crosses below a statistical threshold while price continues showing downward momentum (close < previous close AND close < previous open)
- **Bearish Signal**: The upside oscillator crosses above a statistical threshold while price continues showing upward momentum (close > previous close AND close > previous open)

### 7. Visualization Options
Users can toggle between:
- Standard view: Shows the oscillator and threshold lines
- Percentile view: Displays the current movement's percentile rank within the historical distribution

## Implementation Notes
- The indicator scales threshold values by 0.9 to create a slight buffer that reduces false signals
- The movement's continuation is confirmed by checking both close-to-close and close-to-open relationships
- Arrays dynamically update throughout the chart's history, making the indicator increasingly accurate as more data is processed

## Mathematical Framework
The core statistical function calculates percentiles using linear interpolation between values when needed:
```
calculate_percentile(array, percentile) =
sortedValue[floor(index)] +
fraction * (sortedValue[ceil(index)] - sortedValue[floor(index)])
```
where `index = (array.size - 1) * percentile / 100`

This mathematical approach ensures the thresholds adapt dynamically to changing market conditions rather than relying on fixed values.