mirror of
https://github.com/mihakralj/QuanTAlib.git
synced 2026-07-29 18:17:43 +00:00
Miha Kralj
101 lines
3.6 KiB
Plaintext
101 lines
3.6 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("Binomial Distribution CDF (BINOMDIST)", "BINOMDIST", overlay=false, precision=6)
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//@function Log-gamma via Lanczos approximation (g=7, 9 coefficients)
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//@param z Input value (z > 0)
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//@returns ln(Gamma(z))
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lnGamma(simple float z) =>
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float g = 7.0
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array<float> c = array.from(
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0.99999999999980993,
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676.5203681218851,
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-1259.1392167224028,
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771.32342877765313,
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-176.61502916214059,
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12.507343278686905,
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-0.13857109526572012,
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9.9843695780195716e-6,
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1.5056327351493116e-7)
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float zz = z - 1.0
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float x = array.get(c, 0)
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for i = 1 to 8
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x += array.get(c, i) / (zz + i)
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float t = zz + g + 0.5
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0.5 * math.log(2.0 * math.pi) + (zz + 0.5) * math.log(t) - t + math.log(x)
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//@function Log of binomial coefficient C(n, i) = ln(n!) - ln(i!) - ln((n-i)!)
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//@param n Number of trials
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//@param i Number of successes
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//@returns ln(C(n, i))
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lnBinom(simple int n, int i) =>
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lnGamma(float(n + 1)) - lnGamma(float(i + 1)) - lnGamma(float(n - i + 1))
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//@function Binomial Distribution CDF: P(X <= k) = sum_{i=0}^{k} C(n,i) * p^i * (1-p)^(n-i)
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//@param p Probability of success per trial (0 <= p <= 1)
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//@param n Number of trials
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//@param k Threshold (compute P(X <= k))
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//@returns CDF value in [0,1]
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//@optimized Log-space summation avoids factorial overflow for large n
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binomCdf(series float p, simple int n, simple int k) =>
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if p <= 0.0
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k >= 0 ? 1.0 : 0.0
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else if p >= 1.0
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k >= n ? 1.0 : 0.0
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else
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float lnP = math.log(p)
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float lnQ = math.log(1.0 - p)
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float cdf = 0.0
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int kk = math.min(k, n)
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for i = 0 to kk
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float lnTerm = lnBinom(n, i) + i * lnP + (n - i) * lnQ
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cdf += math.exp(lnTerm)
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math.min(cdf, 1.0)
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//@function Computes Binomial 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 to [0,1] as probability p
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//@param trials Number of Bernoulli trials (n)
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//@param threshold Success threshold (k) — compute P(X <= k)
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//@returns Binomial CDF value in [0,1]
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binomdist(series float source, simple int period, simple int trials, simple int threshold) =>
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if period <= 0
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runtime.error("Period must be greater than 0")
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if trials <= 0
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runtime.error("Trials must be greater than 0")
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if threshold < 0
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runtime.error("Threshold must be non-negative")
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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 p = range > 0.0 ? (source - minVal) / range : 0.5
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binomCdf(p, trials, threshold)
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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_trials = input.int(20, "Trials (n)", minval=1, maxval=1000, tooltip="Number of Bernoulli trials")
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i_threshold = input.int(10, "Threshold (k)", minval=0, maxval=1000, tooltip="Compute P(X <= k)")
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// Calculation
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result = binomdist(i_source, i_period, i_trials, i_threshold)
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// Plot
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plot(result, "BINOMDIST", 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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