// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("Skewness (SKEW)", "SKEW", overlay=false, precision=6)

//@function Calculates the skewness of a source series over a specified period.
// Skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean.
// This implementation calculates the population skewness (Fisher-Pearson coefficient g1).
//@param src The source series.
//@param len The lookback period. Must be > 2.
//@returns The skewness value.
//@optimized Uses efficient rolling calculations for mean, variance, and the third central moment.
skew(series float src, simple int len) =>
    if len <= 2
        runtime.error("Length must be greater than 2 for Skewness calculation.")
    var float sum_m = 0.0
    var array<float> buffer_m = array.new_float(len)
    var int head_m = 0
    if bar_index >= len 
        sum_m -= array.get(buffer_m, head_m)
    float current_src_nz = nz(src) 
    sum_m += current_src_nz
    array.set(buffer_m, head_m, current_src_nz) 
    head_m := (head_m + 1) % len
    
    float mean_val = na
    if bar_index >= len - 1
        mean_val := sum_m / len
    else 
        mean_val := sum_m / (bar_index + 1)
    float dev = src - mean_val
    var float sum_v = 0.0
    var array<float> buffer_v = array.new_float(len)
    var int head_v = 0
    float dev_sq_nz = nz(math.pow(dev, 2))
    if bar_index >= len
        sum_v -= array.get(buffer_v, head_v)
    sum_v += dev_sq_nz
    array.set(buffer_v, head_v, dev_sq_nz)
    head_v := (head_v + 1) % len
    float variance_val = na
    if bar_index >= len - 1
        variance_val := sum_v / len
    else
        variance_val := sum_v / (bar_index + 1)
    float stddev_val = variance_val > 1e-9 ? math.sqrt(variance_val) : 0.0 
    var float sum_s3 = 0.0
    var array<float> buffer_s3 = array.new_float(len)
    var int head_s3 = 0
    float dev_cubed_nz = nz(math.pow(dev, 3)) 
    if bar_index >= len
        sum_s3 -= array.get(buffer_s3, head_s3)
    sum_s3 += dev_cubed_nz
    array.set(buffer_s3, head_s3, dev_cubed_nz)
    head_s3 := (head_s3 + 1) % len
    float m3 = na 
    if bar_index >= len - 1
        m3 := sum_s3 / len
    else
        m3 := sum_s3 / (bar_index + 1)
    float skew_val = na
    if not na(m3) and not na(stddev_val)
        if stddev_val > 1e-9 
            float stddev_cubed = math.pow(stddev_val, 3)
            if stddev_cubed != 0
                skew_val := m3 / stddev_cubed
            else 
                skew_val := 0.0 
        else 
            skew_val := 0.0 
    skew_val

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

// Inputs
i_source = input.source(close, "Source")
i_length = input.int(20, "Length", minval=3) // Minval 3 for skewness

// Calculation
skewValue = skew(i_source, i_length)

// Plot
plot(skewValue, "Skewness", color=color.yellow, linewidth=2)