mirror of
https://github.com/mihakralj/QuanTAlib.git
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364 lines
13 KiB
C#
364 lines
13 KiB
C#
using Xunit;
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using MathNet.Numerics.Distributions;
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namespace QuanTAlib.Tests;
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/// <summary>
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/// LognormdistValidationTests — validates against known mathematical properties
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/// of the Log-Normal Distribution CDF and against MathNet.Numerics LogNormal.
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/// Known-value tests call Lognormdist.StaticCdf / LogNormalCdf directly (bypassing windowing).
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/// Tolerance 1e-6 for the 5-term A&S 7.1.26 approximation (max error ~1.5e-7;
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/// using 1e-6 to give headroom). MathNet cross-validation uses 1e-6.
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/// </summary>
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public class LognormdistValidationTests
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{
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private const double ApproxTolerance = 1e-6; // A&S 7.1.26 five-term max error ~1.5e-7
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private const double LooseTolerance = 1e-4;
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// ─── Boundary: x <= 0 → CDF = 0 ──────────────────────────────────────────
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[Theory]
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[InlineData(0.0, 0.0, 1.0)]
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[InlineData(-1.0, 0.0, 1.0)]
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[InlineData(-5.0, 0.0, 1.0)]
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[InlineData(0.0, -1.0, 0.5)]
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public void StaticCdf_NonPositiveX_IsZero(double x, double mu, double sigma)
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{
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double cdf = Lognormdist.StaticCdf(x, mu, sigma);
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Assert.Equal(0.0, cdf, 1e-10);
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}
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// ─── CDF always in [0, 1] ─────────────────────────────────────────────────
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[Theory]
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[InlineData(0.001, 0.0, 1.0)]
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[InlineData(0.5, 0.0, 1.0)]
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[InlineData(1.0, 0.0, 1.0)]
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[InlineData(10.0, 0.0, 1.0)]
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[InlineData(1000.0, 0.0, 1.0)]
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[InlineData(0.1, -1.0, 0.5)]
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[InlineData(2.0, 1.0, 2.0)]
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public void StaticCdf_OutputBounded_ZeroToOne(double x, double mu, double sigma)
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{
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double cdf = Lognormdist.StaticCdf(x, mu, sigma);
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Assert.True(cdf >= 0.0 && cdf <= 1.0,
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$"CDF({x},{mu},{sigma})={cdf} out of [0,1]");
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}
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// ─── Median: F(exp(μ)) = 0.5 ─────────────────────────────────────────────
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[Theory]
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[InlineData(0.0, 1.0)]
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[InlineData(1.0, 1.0)]
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[InlineData(-2.0, 0.5)]
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[InlineData(0.0, 2.0)]
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[InlineData(3.0, 0.25)]
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public void StaticCdf_AtMedian_IsHalf(double mu, double sigma)
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{
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// Median of LogNormal(μ, σ²) = exp(μ)
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double median = Math.Exp(mu);
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double cdf = Lognormdist.StaticCdf(median, mu, sigma);
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Assert.Equal(0.5, cdf, ApproxTolerance);
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}
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// ─── Standard LogNormal(0,1) known percentiles ────────────────────────────
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[Fact]
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public void StaticCdf_LogNormal01_At1_IsHalf()
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{
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// ln(1)=0=μ, so z=0 → Φ(0)=0.5
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double cdf = Lognormdist.StaticCdf(1.0, 0.0, 1.0);
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Assert.Equal(0.5, cdf, ApproxTolerance);
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}
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[Fact]
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public void StaticCdf_LogNormal01_AtExpPlusSigma_Is0841()
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{
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// F(exp(μ+σ)) = F(exp(1)) = Φ(1) ≈ 0.8413
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double x = Math.Exp(1.0); // exp(μ+σ) with μ=0, σ=1
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double cdf = Lognormdist.StaticCdf(x, 0.0, 1.0);
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Assert.Equal(0.8413, cdf, 3);
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}
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[Fact]
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public void StaticCdf_LogNormal01_AtExpMinusSigma_Is0159()
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{
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// F(exp(μ-σ)) = F(exp(-1)) = Φ(-1) ≈ 0.1587
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double x = Math.Exp(-1.0); // exp(μ-σ) with μ=0, σ=1
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double cdf = Lognormdist.StaticCdf(x, 0.0, 1.0);
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Assert.Equal(0.1587, cdf, 3);
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}
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[Fact]
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public void StaticCdf_LogNormal01_AtExpPlus2Sigma_Is0977()
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{
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// F(exp(μ+2σ)) = Φ(2) ≈ 0.9772
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double x = Math.Exp(2.0);
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double cdf = Lognormdist.StaticCdf(x, 0.0, 1.0);
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Assert.Equal(0.9772, cdf, 3);
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}
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[Fact]
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public void StaticCdf_LogNormal01_AtExpMinus2Sigma_Is0023()
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{
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// F(exp(-2)) = Φ(-2) ≈ 0.0228
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double x = Math.Exp(-2.0);
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double cdf = Lognormdist.StaticCdf(x, 0.0, 1.0);
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Assert.Equal(0.0228, cdf, 3);
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}
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// ─── Monotonicity for x > 0 ───────────────────────────────────────────────
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[Theory]
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[InlineData(0.0, 1.0)]
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[InlineData(1.0, 0.5)]
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[InlineData(-1.0, 2.0)]
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public void StaticCdf_MonotonicIncreasing_ForPositiveX(double mu, double sigma)
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{
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double prev = -1.0;
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for (int i = -20; i <= 20; i++)
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{
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double x = Math.Exp(i * 0.25); // x in (exp(-5), exp(5)) — always positive
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double cdf = Lognormdist.StaticCdf(x, mu, sigma);
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Assert.True(cdf >= prev - LooseTolerance,
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$"CDF not monotonic at x={x} (μ={mu}, σ={sigma}): got {cdf}, prev={prev}");
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prev = cdf;
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}
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}
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// ─── MathNet.Numerics cross-validation ────────────────────────────────────
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[Theory]
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[InlineData(1.0, 0.0, 1.0)]
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[InlineData(2.0, 0.0, 1.0)]
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[InlineData(0.5, 0.0, 1.0)]
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[InlineData(0.1, 0.0, 1.0)]
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[InlineData(10.0, 0.0, 1.0)]
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[InlineData(1.0, 1.0, 1.0)]
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[InlineData(0.5, 0.0, 2.0)]
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[InlineData(3.0, 2.0, 0.5)]
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[InlineData(0.1, -1.0, 0.5)]
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[InlineData(1.0, 0.0, 0.25)]
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public void StaticCdf_VsMathNet_KnownValues(double x, double mu, double sigma)
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{
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var dist = new LogNormal(mu, sigma);
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double expected = dist.CumulativeDistribution(x);
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double actual = Lognormdist.StaticCdf(x, mu, sigma);
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Assert.Equal(expected, actual, ApproxTolerance);
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}
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[Theory]
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[InlineData(1.0, 0.0, 1.0)]
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[InlineData(2.718, 0.0, 1.0)]
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[InlineData(0.368, 0.0, 1.0)]
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[InlineData(1.0, 1.0, 2.0)]
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[InlineData(5.0, 1.0, 0.5)]
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public void LogNormalCdf_VsMathNet_KnownValues(double x, double mu, double sigma)
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{
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var dist = new LogNormal(mu, sigma);
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double expected = dist.CumulativeDistribution(x);
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double actual = Lognormdist.LogNormalCdf(x, mu, sigma);
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Assert.Equal(expected, actual, ApproxTolerance);
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}
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// ─── Multiple points all match MathNet ───────────────────────────────────
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[Fact]
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public void StaticCdf_MultiplePoints_AllMatchMathNet()
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{
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double mu = 0.0, sigma = 1.0;
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var dist = new LogNormal(mu, sigma);
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double[] testX = { 0.01, 0.1, 0.25, 0.5, 1.0, 2.0, 5.0, 10.0, 50.0, 100.0 };
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foreach (double x in testX)
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{
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double expected = dist.CumulativeDistribution(x);
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double actual = Lognormdist.StaticCdf(x, mu, sigma);
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Assert.Equal(expected, actual, ApproxTolerance);
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}
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}
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// ─── Output bounded [0,1] with streaming indicator ───────────────────────
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[Fact]
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public void LognormdistCdf_OutputBounded_Zero_To_One()
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{
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int count = 200;
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var gbm = new GBM(startPrice: 100, mu: 0.05, sigma: 0.3, seed: 85001);
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var bars = gbm.Fetch(count, DateTime.UtcNow.Ticks, TimeSpan.FromMinutes(1));
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var indicator = new Lognormdist(mu: 0.0, sigma: 1.0, period: 20);
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for (int i = 0; i < count; i++)
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{
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indicator.Update(bars.Close[i]);
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double v = indicator.Last.Value;
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Assert.True(v >= 0.0 && v <= 1.0, $"Output {v} at bar {i} out of [0,1]");
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}
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}
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// ─── Flat range → finite output ──────────────────────────────────────────
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[Fact]
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public void LognormdistCdf_FlatRange_IsFinite()
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{
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var ind = new Lognormdist(mu: 0.0, sigma: 1.0, period: 10);
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var time = DateTime.UtcNow;
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for (int i = 0; i < 10; i++)
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{
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ind.Update(new TValue(time.AddSeconds(i), 100.0));
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}
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Assert.True(double.IsFinite(ind.Last.Value));
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Assert.True(ind.Last.Value >= 0.0 && ind.Last.Value <= 1.0);
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}
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// ─── NormalCdf internal correctness ──────────────────────────────────────
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[Fact]
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public void NormalCdf_AtZero_IsHalf()
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{
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double v = Lognormdist.NormalCdf(0.0);
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Assert.Equal(0.5, v, ApproxTolerance);
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}
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[Fact]
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public void NormalCdf_AtLargePositive_ApproachesOne()
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{
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double v = Lognormdist.NormalCdf(10.0);
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Assert.True(v > 0.9999, $"Φ(10) should approach 1, got {v}");
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}
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[Fact]
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public void NormalCdf_AtLargeNegative_ApproachesZero()
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{
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double v = Lognormdist.NormalCdf(-10.0);
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Assert.True(v < 1e-4, $"Φ(-10) should approach 0, got {v}");
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}
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[Fact]
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public void NormalCdf_IsSymmetric()
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{
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// Φ(z) + Φ(-z) = 1
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double[] testZ = { 0.5, 1.0, 1.5, 2.0, 3.0 };
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foreach (double z in testZ)
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{
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double pos = Lognormdist.NormalCdf(z);
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double neg = Lognormdist.NormalCdf(-z);
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Assert.Equal(1.0, pos + neg, ApproxTolerance);
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}
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}
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// ─── Parameter combos all within [0,1] ────────────────────────────────────
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[Theory]
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[InlineData(0.0, 1.0, 5)]
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[InlineData(0.0, 1.0, 14)]
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[InlineData(-1.0, 0.5, 10)]
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[InlineData(0.0, 2.0, 20)]
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[InlineData(1.0, 1.0, 30)]
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public void LognormdistCdf_ParameterCombos_OutputBounded(double mu, double sigma, int period)
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{
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int count = period + 50;
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var gbm = new GBM(startPrice: 100, mu: 0.05, sigma: 0.2, seed: 85002 + (int)(sigma * 100));
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var bars = gbm.Fetch(count, DateTime.UtcNow.Ticks, TimeSpan.FromMinutes(1));
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var indicator = new Lognormdist(mu, sigma, period);
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for (int i = 0; i < count; i++)
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{
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indicator.Update(bars.Close[i]);
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double v = indicator.Last.Value;
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Assert.True(v >= 0.0 && v <= 1.0,
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$"Out of [0,1] at bar {i}: {v} (μ={mu}, σ={sigma}, period={period})");
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}
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}
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// ─── Large dataset stable ─────────────────────────────────────────────────
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[Fact]
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public void LognormdistCdf_LargeDataset_Stable()
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{
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int count = 2000;
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var gbm = new GBM(startPrice: 100, mu: 0.05, sigma: 0.2, seed: 85003);
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var bars = gbm.Fetch(count, DateTime.UtcNow.Ticks, TimeSpan.FromMinutes(1));
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var indicator = new Lognormdist(mu: 0.0, sigma: 1.0, period: 50);
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for (int i = 0; i < count; i++)
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{
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indicator.Update(bars.Close[i]);
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double v = indicator.Last.Value;
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Assert.True(double.IsFinite(v) && v >= 0.0 && v <= 1.0,
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$"Invalid output {v} at bar {i}");
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}
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}
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// ─── Span batch vs TSeries consistency ────────────────────────────────────
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[Fact]
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public void Batch_Span_MatchesTSeries()
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{
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int count = 150;
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var gbm = new GBM(startPrice: 100, mu: 0.05, sigma: 0.25, seed: 85004);
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var bars = gbm.Fetch(count, DateTime.UtcNow.Ticks, TimeSpan.FromMinutes(1));
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double[] rawValues = new double[count];
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for (int i = 0; i < count; i++)
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{
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rawValues[i] = bars.Close[i].Value;
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}
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var tseriesResult = Lognormdist.Batch(bars.Close, period: 30);
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double[] spanResult = new double[count];
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Lognormdist.Batch(rawValues, spanResult, period: 30);
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for (int i = 0; i < count; i++)
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{
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Assert.Equal(tseriesResult[i].Value, spanResult[i], 1e-10);
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}
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}
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// ─── High-period streaming convergence ────────────────────────────────────
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[Fact]
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public void LognormdistCdf_HighPeriod_StillConverges()
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{
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int period = 200;
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var indicator = new Lognormdist(mu: 0.0, sigma: 1.0, period: period);
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var gbm = new GBM(startPrice: 100, mu: 0.05, sigma: 0.3, seed: 85005);
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var bars = gbm.Fetch(period + 50, DateTime.UtcNow.Ticks, TimeSpan.FromMinutes(1));
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for (int i = 0; i < bars.Close.Count; i++)
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{
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indicator.Update(bars.Close[i]);
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Assert.True(double.IsFinite(indicator.Last.Value),
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$"Non-finite output at bar {i}");
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}
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}
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// ─── MathNet parameter sweep ──────────────────────────────────────────────
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[Theory]
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[InlineData(0.0, 0.5)]
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[InlineData(0.0, 1.0)]
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[InlineData(0.0, 2.0)]
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[InlineData(1.0, 1.0)]
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[InlineData(-1.0, 0.5)]
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public void StaticCdf_SweepX_VsMathNet(double mu, double sigma)
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{
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var dist = new LogNormal(mu, sigma);
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double[] xs = { 0.01, 0.05, 0.1, 0.25, 0.5, 1.0, 2.0, 5.0, 10.0, 20.0 };
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foreach (double x in xs)
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{
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double expected = dist.CumulativeDistribution(x);
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double actual = Lognormdist.StaticCdf(x, mu, sigma);
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Assert.Equal(expected, actual, ApproxTolerance);
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}
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}
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}
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