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https://github.com/mihakralj/QuanTAlib.git
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Miha Kralj
81 lines
3.1 KiB
Plaintext
81 lines
3.1 KiB
Plaintext
// Licensed under the Apache License, Version 2.0
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// © mihakralj
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//@version=6
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indicator("Normal Distribution CDF (NORMDIST)", "NORMDIST", overlay=false, precision=6)
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//@function Computes Normal Distribution CDF for a normalized price series
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//@param source Series to transform
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//@param period Lookback period for z-score normalization
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//@param mu Mean parameter (0.0 for standard normal after z-score)
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//@param sigma Standard deviation parameter (1.0 for standard normal after z-score)
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//@returns CDF value in [0,1]: Φ(z) = 0.5 × (1 + erf(z / √2))
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//@optimized O(period) per bar for mean/variance scan; CDF itself is O(1)
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normdist(series float source, simple int period, simple float mu, simple float sigma) =>
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if period <= 0
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runtime.error("Period must be greater than 0")
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if sigma <= 0.0
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runtime.error("Sigma must be greater than 0")
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// Compute rolling mean and standard deviation over lookback
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float sum = 0.0
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float sumSq = 0.0
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int count = 0
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for i = 0 to period - 1
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float v = source[i]
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if not na(v)
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sum += v
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sumSq += v * v
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count += 1
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float result = 0.5
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if count >= 2
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float mean = sum / count
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float variance = (sumSq / count) - (mean * mean)
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float stddev = variance > 0.0 ? math.sqrt(variance) : 0.0
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// Z-score: normalize source relative to its own rolling distribution
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float z = stddev > 0.0 ? (source - mean) / stddev : 0.0
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// Apply user-specified mu/sigma shift: z_final = (z - mu) / sigma
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float z_final = (z - mu) / sigma
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// Approximate erf via Abramowitz & Stegun (max error < 1.5e-7)
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// erf(x) = 1 - (a1*t + a2*t^2 + a3*t^3) * exp(-x^2)
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// where t = 1 / (1 + 0.47047 * |x|)
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float x = z_final / math.sqrt(2.0)
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float ax = math.abs(x)
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float t = 1.0 / (1.0 + 0.47047 * ax)
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float t2 = t * t
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float t3 = t2 * t
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float a1 = 0.3480242
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float a2 = -0.0958798
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float a3 = 0.7478556
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float erfApprox = 1.0 - (a1 * t + a2 * t2 + a3 * t3) * math.exp(-(ax * ax))
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float erf = x >= 0.0 ? erfApprox : -erfApprox
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// CDF: Φ(z) = 0.5 * (1 + erf(z / sqrt(2)))
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result := 0.5 * (1.0 + erf)
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result
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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, "Lookback Period", minval=2, maxval=5000, tooltip="Rolling window for z-score normalization")
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i_mu = input.float(0.0, "Mu (μ)", step=0.1, tooltip="Mean shift parameter (0 = standard normal)")
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i_sigma = input.float(1.0, "Sigma (σ)", minval=0.01, step=0.1, tooltip="Scale parameter (1 = standard normal)")
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// Calculation
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float result = normdist(i_source, i_period, i_mu, i_sigma)
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// Plot
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plot(result, "NORMDIST", 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(0.975, "Upper 2σ", color=color.red, linestyle=hline.style_dashed)
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hline(0.025, "Lower 2σ", color=color.green, linestyle=hline.style_dashed)
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hline(0.841, "Upper 1σ", color=color.orange, linestyle=hline.style_dashed)
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hline(0.159, "Lower 1σ", color=color.teal, linestyle=hline.style_dashed)
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