Kurtosis, tailedness (KURTOSIS)

// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("Kurtosis, tailedness (KURTOSIS)", "KURTOSIS", overlay=false, precision=8)

//@function Calculates the excess kurtosis of a series over a lookback period.
//@param src Source series.
//@param len Lookback period. Must be greater than 1.
//@returns The excess kurtosis value.
kurtosis(series float src, simple int len) =>
    if len <= 1
        runtime.error("Length must be greater than 1")
    var float sumY = 0.0, var float sumY2 = 0.0, var float sumY3 = 0.0, var float sumY4 = 0.0
    var int validCount = 0, var array<float> y_values = array.new_float(len), var int head = 0, var bool filled = false
    float oldY = filled ? array.get(y_values, head) : na
    if not na(oldY)
        sumY -= oldY, sumY2 -= oldY * oldY, sumY3 -= oldY * oldY * oldY, sumY4 -= oldY * oldY * oldY * oldY, validCount -= 1
    float currentY = src
    array.set(y_values, head, currentY)
    if not na(currentY)
        sumY += currentY, sumY2 += currentY * currentY, sumY3 += currentY * currentY * currentY, sumY4 += currentY * currentY * currentY * currentY, validCount += 1
    head := (head + 1) % len
    if not filled and head == 0
        filled := true
    float excessKurtosis = na
    if validCount >= 4
        float n = float(validCount), mean = sumY / n, m2 = sumY2 / n, m3 = sumY3 / n, m4 = sumY4 / n
        float variance = math.max(m2 - mean * mean, 0.0)
        if variance > 1e-10
            float moment4 = m4 - 4 * mean * m3 + 6 * mean * mean * m2 - 3 * mean * mean * mean * mean
            excessKurtosis := moment4 / (variance * variance) - 3.0
        else
            excessKurtosis := 0.0
    excessKurtosis

// ---------- Main loop ----------

// Inputs
i_period = input.int(14, "Period", minval=4) // Minval 4 for kurtosis
i_source = input.source(close, "Source")

// Calculation
k = kurtosis(i_source, i_period)

// Plot
plot(k, "Kurtosis", color=color.yellow, linewidth=2)