Interquartile Range (IQR)

// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("Interquartile Range (IQR)", "IQR", overlay=false, precision=4)

//@function Function to calculate percentile using linear interpolation
//@param src Source series for calculation
//@param len Lookback period for data collection
//@param p Percentile value (0-100)
//@returns Calculated percentile value
// Adapted from percentile.pine
iqr(series float src, simple int len, simple float p) =>
    if len <= 0 // Should not happen due to input minval=2
        runtime.error("Lookback Period must be greater than 0.")
        float(na)
    if p < 0 or p > 100
        runtime.error("Percentile 'p' must be between 0 and 100.")
        float(na)
    data_points = array.new_float()
    for i = 0 to len - 1
        val = src[i]
        if not na(val)
            array.push(data_points, val)
    n_valid = array.size(data_points)
    float result = na
    if n_valid == 0
        result := na
    else if n_valid == 1
        result := array.get(data_points, 0)
    else
        array.sort(data_points)
        rank = (p / 100.0) * (n_valid - 1) 
        if p == 0.0
            result := array.get(data_points, 0)
        else if p == 100.0
            result := array.get(data_points, n_valid - 1) 
        else
            k_floor_idx = math.floor(rank)
            k_ceil_idx = math.ceil(rank)
            int_k_floor = math.max(0, math.min(n_valid - 1, int(k_floor_idx)))
            int_k_ceil = math.max(0, math.min(n_valid - 1, int(k_ceil_idx)))
            if int_k_floor == int_k_ceil 
                result := array.get(data_points, int_k_floor)
            else 
                val_floor = array.get(data_points, int_k_floor)
                val_ceil = array.get(data_points, int_k_ceil)
                if val_floor == val_ceil
                    result := val_floor
                else
                    result := val_floor + (rank - k_floor_idx) * (val_ceil - val_floor)
    result

// Inputs
i_source = input.source(close, title="Source")
i_length = input.int(20, title="Lookback Period", minval=2)

// Calculate Q1 (25th percentile) and Q3 (75th percentile)
q1 = iqr(i_source, i_length, 25.0)
q3 = iqr(i_source, i_length, 75.0)

// Calculate IQR
iqr_value = q3 - q1

// Plot IQR
plot(iqr_value, title="IQR", color=color.yellow, linewidth=2)