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

//@function Applies the logistic (sigmoid) function to a source series.
// Formula: S(x) = 1 / (1 + exp(-k * (x - x0)))
// Maps any real-valued input to the range (0, 1).
//@param src The source series.
//@param k The steepness factor of the sigmoid curve. Higher k means a steeper curve.
//@param x0 The x-value of the sigmoid's midpoint (where the output is 0.5).
//@returns The sigmoid transformed series, values between 0 and 1.
sigmoid(series float src, simple float k, float x0) =>
    1 / (1 + math.exp(-k * (src - x0)))

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

// Inputs
i_source = input.source(close, "Source")
i_steepness_k = input.float(0.5, "Steepness (k)", minval = 0.000001, step = 0.1)

// Calculation
sigmoidValue = sigmoid(i_source, i_steepness_k, ta.sma(i_source,200))

// Plot
plot(sigmoidValue, "Sigmoid", color=color.yellow, linewidth=2)