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// 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)