mirror of
https://github.com/mihakralj/QuanTAlib.git
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Miha Kralj
68 lines
2.6 KiB
Plaintext
68 lines
2.6 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("Log-Normal Distribution CDF (LOGNORMDIST)", "LOGNORMDIST", overlay=false, precision=6)
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//@function Standard normal CDF Φ(z) via Abramowitz & Stegun rational approximation (7.1.26)
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//@param z Input value
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//@returns Φ(z) = P(Z <= z) for Z ~ N(0,1), accurate to ~1.5e-7
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normalCdf(series float z) =>
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float P = 0.2316419
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float B1 = 0.319381530
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float B2 = -0.356563782
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float B3 = 1.781477937
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float B4 = -1.821255978
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float B5 = 1.330274429
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float az = math.abs(z)
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float t = 1.0 / (1.0 + P * az)
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float phi = math.exp(-0.5 * az * az) / math.sqrt(2.0 * math.pi)
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float poly = ((((B5 * t + B4) * t + B3) * t + B2) * t + B1) * t
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float cdf = 1.0 - phi * poly
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z >= 0.0 ? cdf : 1.0 - cdf
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//@function Log-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 min-max normalization
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//@param mu Location parameter (mean of ln(X))
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//@param sigma Scale parameter (std dev of ln(X)), sigma > 0
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//@returns Log-normal CDF value in [0,1]
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lognormdist(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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float minVal = source
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float maxVal = source
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for i = 1 to period - 1
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float v = source[i]
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if not na(v)
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if v < minVal
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minVal := v
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if v > maxVal
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maxVal := v
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float range = maxVal - minVal
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float x = range > 0.0 ? (source - minVal) / range : 0.5
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float safeX = math.max(1e-10, x)
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float z = (math.log(safeX) - mu) / sigma
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normalCdf(z)
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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="Min-max normalization window")
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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]")
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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")
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// Calculation
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float result = lognormdist(i_source, i_period, i_mu, i_sigma)
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// Plot
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plot(result, "LOGNORMDIST", 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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