Weibull Distribution CDF

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

//@function Calculates the Weibull Distribution CDF
//@param source Series to evaluate (typically close)
//@param period Lookback period for min-max normalization
//@param shape Shape parameter k (> 0) — controls distribution form
//@param scale Scale parameter λ (> 0) — scales the normalized price
//@returns CDF value F(x) in [0, 1]
//@description The Weibull distribution CDF has a simple closed form:
//    F(x; k, λ) = 1 − exp(−(x/λ)^k)   for x ≥ 0
//    F(x) = 0                            for x < 0
//  The source is min-max normalized over the lookback period to [0, 1],
//  then treated as the input x to the CDF (no additional scaling needed
//  since λ handles the effective range).
//  Shape k controls the distribution form:
//    k < 1: decreasing failure rate (early failures) — concave CDF
//    k = 1: constant failure rate (exponential distribution) — same as EXPDIST
//    k = 2: Rayleigh distribution — linear failure rate
//    k > 3: approaches normal-like shape — S-curve CDF
//  Scale λ controls how quickly CDF rises:
//    larger λ → slower rise (more spread), smaller λ → faster saturation
//  No special functions needed — only exp and pow. O(period) for min-max scan,
//  CDF itself is O(1). Stateless pure function — no var state.
//  Trading interpretation: CDF near 1.0 = price at top of recent range,
//  near 0.0 = price at bottom. Shape k tunes sensitivity to extremes.
weibulldist(series float source, simple int period, simple float shape, simple float scale) =>
    if period <= 0
        runtime.error("Period must be greater than 0")
    if shape <= 0.0
        runtime.error("Shape parameter must be greater than 0")
    if scale <= 0.0
        runtime.error("Scale parameter must be greater than 0")

    float src = nz(source)
    float hi = src
    float lo = src
    for i = 1 to period - 1
        float v = nz(source[i])
        hi := math.max(hi, v)
        lo := math.min(lo, v)

    float range = hi - lo
    float x = range == 0.0 ? 0.5 : (src - lo) / range

    float safeX = math.max(0.0, x)
    float ratio = safeX / scale
    float raised = math.pow(ratio, shape)
    1.0 - math.exp(-raised)

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

// Inputs
i_source = input.source(close, "Source")
i_period = input.int(50, "Period", minval=1)
i_shape  = input.float(2.0, "Shape (k)", minval=0.01, step=0.1)
i_scale  = input.float(0.5, "Scale (λ)", minval=0.01, step=0.1)

// Calculation
weibull_value = weibulldist(i_source, i_period, i_shape, i_scale)

// Plot
plot(weibull_value, "WEIBULLDIST", 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)