mirror of
https://github.com/mihakralj/QuanTAlib.git
synced 2026-07-27 17:27:43 +00:00
Miha Kralj
69 lines
2.9 KiB
Plaintext
69 lines
2.9 KiB
Plaintext
// 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)
|