// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("Log-Normal Distribution CDF (LOGNORMDIST)", "LOGNORMDIST", overlay=false, precision=6)

//@function Standard normal CDF Φ(z) via Abramowitz & Stegun rational approximation (7.1.26)
//@param z Input value
//@returns Φ(z) = P(Z <= z) for Z ~ N(0,1), accurate to ~1.5e-7
normalCdf(series float z) =>
    float P = 0.2316419
    float B1 = 0.319381530
    float B2 = -0.356563782
    float B3 = 1.781477937
    float B4 = -1.821255978
    float B5 = 1.330274429
    float az = math.abs(z)
    float t = 1.0 / (1.0 + P * az)
    float phi = math.exp(-0.5 * az * az) / math.sqrt(2.0 * math.pi)
    float poly = ((((B5 * t + B4) * t + B3) * t + B2) * t + B1) * t
    float cdf = 1.0 - phi * poly
    z >= 0.0 ? cdf : 1.0 - cdf

//@function Log-Normal Distribution CDF for a normalized price series
//@param source Series to transform
//@param period Lookback period for min-max normalization
//@param mu Location parameter (mean of ln(X))
//@param sigma Scale parameter (std dev of ln(X)), sigma > 0
//@returns Log-normal CDF value in [0,1]
lognormdist(series float source, simple int period, simple float mu, simple float sigma) =>
    if period <= 0
        runtime.error("Period must be greater than 0")
    if sigma <= 0.0
        runtime.error("Sigma must be greater than 0")

    float minVal = source
    float maxVal = source
    for i = 1 to period - 1
        float v = source[i]
        if not na(v)
            if v < minVal
                minVal := v
            if v > maxVal
                maxVal := v

    float range = maxVal - minVal
    float x = range > 0.0 ? (source - minVal) / range : 0.5
    float safeX = math.max(1e-10, x)

    float z = (math.log(safeX) - mu) / sigma
    normalCdf(z)

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

// Inputs
i_source = input.source(close, "Source")
i_period = input.int(50, "Lookback Period", minval=2, maxval=5000, tooltip="Min-max normalization window")
i_mu     = input.float(0.0, "Mu (μ)", step=0.1, tooltip="Location parameter; mean of ln(X). 0 = centered on geometric mean of [0,1]")
i_sigma  = input.float(1.0, "Sigma (σ)", minval=0.01, step=0.1, tooltip="Scale parameter; std dev of ln(X). Lower = steeper S-curve")

// Calculation
float result = lognormdist(i_source, i_period, i_mu, i_sigma)

// Plot
plot(result, "LOGNORMDIST", color=color.yellow, linewidth=2)
hline(0.5, "Midline", color=color.gray, linestyle=hline.style_dotted)
hline(0.95, "Upper", color=color.red, linestyle=hline.style_dashed)
hline(0.05, "Lower", color=color.green, linestyle=hline.style_dashed)