feat: add new indicators (Decay, Edecay, MinusDi, MinusDm, PlusDi, PlusDm, Maxindex, Minindex, Sarext) and update pine scripts, core libs, validation tests, and python bindings
2026-03-09 13:45:46 -07:00
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// Licensed under the Apache License, Version 2.0
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2026-02-20 18:44:56 -08:00
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// © mihakralj
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//@version=6
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indicator("Weibull Distribution CDF (WEIBULLDIST)", "WEIBULLDIST", overlay=false, precision=6)
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//@function Calculates the Weibull Distribution CDF
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//@param source Series to evaluate (typically close)
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//@param period Lookback period for min-max normalization
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//@param shape Shape parameter k (> 0) — controls distribution form
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//@param scale Scale parameter λ (> 0) — scales the normalized price
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//@returns CDF value F(x) in [0, 1]
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//@description The Weibull distribution CDF has a simple closed form:
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// F(x; k, λ) = 1 − exp(−(x/λ)^k) for x ≥ 0
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// F(x) = 0 for x < 0
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// The source is min-max normalized over the lookback period to [0, 1],
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// then treated as the input x to the CDF (no additional scaling needed
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// since λ handles the effective range).
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// Shape k controls the distribution form:
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// k < 1: decreasing failure rate (early failures) — concave CDF
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// k = 1: constant failure rate (exponential distribution) — same as EXPDIST
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// k = 2: Rayleigh distribution — linear failure rate
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// k > 3: approaches normal-like shape — S-curve CDF
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// Scale λ controls how quickly CDF rises:
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// larger λ → slower rise (more spread), smaller λ → faster saturation
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// No special functions needed — only exp and pow. O(period) for min-max scan,
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// CDF itself is O(1). Stateless pure function — no var state.
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// Trading interpretation: CDF near 1.0 = price at top of recent range,
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// near 0.0 = price at bottom. Shape k tunes sensitivity to extremes.
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weibulldist(series float source, simple int period, simple float shape, simple float scale) =>
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if period <= 0
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runtime.error("Period must be greater than 0")
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if shape <= 0.0
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runtime.error("Shape parameter must be greater than 0")
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if scale <= 0.0
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runtime.error("Scale parameter must be greater than 0")
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float src = nz(source)
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float hi = src
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float lo = src
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for i = 1 to period - 1
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float v = nz(source[i])
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hi := math.max(hi, v)
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lo := math.min(lo, v)
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float range = hi - lo
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float x = range == 0.0 ? 0.5 : (src - lo) / range
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float safeX = math.max(0.0, x)
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float ratio = safeX / scale
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float raised = math.pow(ratio, shape)
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1.0 - math.exp(-raised)
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// ---------- Main loop ----------
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// Inputs
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i_source = input.source(close, "Source")
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i_period = input.int(50, "Period", minval=1)
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i_shape = input.float(2.0, "Shape (k)", minval=0.01, step=0.1)
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i_scale = input.float(0.5, "Scale (λ)", minval=0.01, step=0.1)
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// Calculation
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weibull_value = weibulldist(i_source, i_period, i_shape, i_scale)
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// Plot
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plot(weibull_value, "WEIBULLDIST", color=color.yellow, linewidth=2)
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hline(0.5, "Midline", color=color.gray, linestyle=hline.style_dotted)
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hline(0.95, "Upper", color=color.red, linestyle=hline.style_dashed)
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hline(0.05, "Lower", color=color.green, linestyle=hline.style_dashed)
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