// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("Cumulative Moving Average", "CMA", overlay=true)

//@function Calculates Cumulative Moving Average (Running Average / Cumulative Mean)
//@param   source Series to calculate CMA from
//@returns CMA value - running mean of all historical values
cma(series float source) =>
    // Persistent state
    var float mean = 0.0
    var int count = 0

    float val = nz(source, mean)
    count += 1

    // Welford's algorithm: M_n = M_(n-1) + alpha * (x_n - M_(n-1))
    float alpha = 1.0 / count
    float delta = val - mean
    mean := mean + alpha * delta

    mean

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

// Inputs
i_source = input.source(close, "Source")

// Calculation
cma_value = cma(i_source)

// Plot
plot(cma_value, "CMA", color=color.yellow, linewidth=2)