public void ValidateSkewness(double lambda) { var d = new Poisson(lambda); Assert.AreEqual(1.0 / Math.Sqrt(lambda), d.Skewness); }
/// <summary> /// Run example /// </summary> /// <a href="http://en.wikipedia.org/wiki/Poisson_distribution">Poisson distribution</a> public void Run() { // 1. Initialize the new instance of the Poisson distribution class with parameter Lambda = 1 var poisson = new Poisson(1); Console.WriteLine(@"1. Initialize the new instance of the Poisson distribution class with parameter Lambda = {0}", poisson.Lambda); Console.WriteLine(); // 2. Distributuion properties: Console.WriteLine(@"2. {0} distributuion properties:", poisson); // Cumulative distribution function Console.WriteLine(@"{0} - Сumulative distribution at location '3'", poisson.CumulativeDistribution(3).ToString(" #0.00000;-#0.00000")); // Probability density Console.WriteLine(@"{0} - Probability mass at location '3'", poisson.Probability(3).ToString(" #0.00000;-#0.00000")); // Log probability density Console.WriteLine(@"{0} - Log probability mass at location '3'", poisson.ProbabilityLn(3).ToString(" #0.00000;-#0.00000")); // Entropy Console.WriteLine(@"{0} - Entropy", poisson.Entropy.ToString(" #0.00000;-#0.00000")); // Largest element in the domain Console.WriteLine(@"{0} - Largest element in the domain", poisson.Maximum.ToString(" #0.00000;-#0.00000")); // Smallest element in the domain Console.WriteLine(@"{0} - Smallest element in the domain", poisson.Minimum.ToString(" #0.00000;-#0.00000")); // Mean Console.WriteLine(@"{0} - Mean", poisson.Mean.ToString(" #0.00000;-#0.00000")); // Median Console.WriteLine(@"{0} - Median", poisson.Median.ToString(" #0.00000;-#0.00000")); // Mode Console.WriteLine(@"{0} - Mode", poisson.Mode.ToString(" #0.00000;-#0.00000")); // Variance Console.WriteLine(@"{0} - Variance", poisson.Variance.ToString(" #0.00000;-#0.00000")); // Standard deviation Console.WriteLine(@"{0} - Standard deviation", poisson.StdDev.ToString(" #0.00000;-#0.00000")); // Skewness Console.WriteLine(@"{0} - Skewness", poisson.Skewness.ToString(" #0.00000;-#0.00000")); Console.WriteLine(); // 3. Generate 10 samples of the Poisson distribution Console.WriteLine(@"3. Generate 10 samples of the Poisson distribution"); for (var i = 0; i < 10; i++) { Console.Write(poisson.Sample().ToString("N05") + @" "); } Console.WriteLine(); Console.WriteLine(); // 4. Generate 100000 samples of the Poisson(1) distribution and display histogram Console.WriteLine(@"4. Generate 100000 samples of the Poisson(1) distribution and display histogram"); var data = new double[100000]; for (var i = 0; i < data.Length; i++) { data[i] = poisson.Sample(); } ConsoleHelper.DisplayHistogram(data); Console.WriteLine(); // 5. Generate 100000 samples of the Poisson(4) distribution and display histogram Console.WriteLine(@"5. Generate 100000 samples of the Poisson(4) distribution and display histogram"); poisson.Lambda = 4; for (var i = 0; i < data.Length; i++) { data[i] = poisson.Sample(); } ConsoleHelper.DisplayHistogram(data); Console.WriteLine(); // 6. Generate 100000 samples of the Poisson(10) distribution and display histogram Console.WriteLine(@"6. Generate 100000 samples of the Poisson(10) distribution and display histogram"); poisson.Lambda = 10; for (var i = 0; i < data.Length; i++) { data[i] = poisson.Sample(); } ConsoleHelper.DisplayHistogram(data); }
public void ValidateToString() { var d = new Poisson(0.3); Assert.AreEqual(String.Format("Poisson(λ = {0})", 0.3), d.ToString()); }
public void ValidateEntropy(double lambda) { var d = new Poisson(lambda); Assert.AreEqual((0.5 * Math.Log(2 * Math.PI * Math.E * lambda)) - (1.0 / (12.0 * lambda)) - (1.0 / (24.0 * lambda * lambda)) - (19.0 / (360.0 * lambda * lambda * lambda)), d.Entropy); }
public void ValidateCumulativeDistribution(double lambda, int x, double result) { var d = new Poisson(lambda); Assert.AreEqual(d.CumulativeDistribution(x), result, 1e-12); }
public void CanCreatePoisson(double lambda) { var d = new Poisson(lambda); Assert.AreEqual(lambda, d.Lambda); }
public void CanSample() { var d = new Poisson(0.3); d.Sample(); }
public void CanSampleSequence() { var d = new Poisson(0.3); var ied = d.Samples(); GC.KeepAlive(ied.Take(5).ToArray()); }
public void ValidateMaximum() { var d = new Poisson(0.3); Assert.AreEqual(int.MaxValue, d.Maximum); }
public void ValidateProbabilityLn(double lambda, int x, double result) { var d = new Poisson(lambda); Assert.AreEqual(d.ProbabilityLn(x), Math.Log(result), 1e-12); }
public void ValidateMinimum() { var d = new Poisson(0.3); Assert.AreEqual(0, d.Minimum); }
public void ValidateMedian(double lambda) { var d = new Poisson(lambda); Assert.AreEqual((int)Math.Floor(lambda + (1.0 / 3.0) - (0.02 / lambda)), d.Median); }
public void ValidateMode(double lambda) { var d = new Poisson(lambda); Assert.AreEqual((int)Math.Floor(lambda), d.Mode); }
public static void GenerateShortReadsFromDonorGenome(string donorGenomeFile, string readsFile, int readLength, double coverage, long limit) { Poisson poisson = new Poisson(coverage / readLength) { RandomSource = new MersenneTwister() }; using (var donorFile = File.OpenRead(donorGenomeFile)) using (var file = File.Open(readsFile, FileMode.Create)) { var writer = new BinaryWriter(file); var reader = new BinaryReader(donorFile); writer.Write(readLength); for (long donorIndex = 0, numReads = 0; donorIndex <= donorFile.Length - readLength && numReads < limit; donorIndex++) { var numReadsAtPos = poisson.Sample(); numReads += numReadsAtPos; if (numReadsAtPos > 0) { donorFile.Seek(donorIndex, SeekOrigin.Begin); var chars = reader.ReadChars(readLength); string read = new string(chars); DnaSequence dna = DnaSequence.CreateGenomeFromString(read); for (int i = 0; i < numReadsAtPos; i++) writer.Write(dna.Bytes); } } } }
public JsonResult SpotPriceSimulation( int[] timeStepsInLevels, double[] priceLevels, double timeStep, double reversionRate, double volatility, int numberOfSimulations) { if (timeStepsInLevels.Length != priceLevels.Length) throw new Exception("Lengths not consistent"); //hourly simulation var horizon = timeStepsInLevels.Sum()*24; // //TODO: add daily/hourly resolution... if it makes sense... but not really. //estimate an hourly ARMA... var d = AppData.GetHistoricalSeries(PricesController._timeSeries); var data = d .Select(x => x.Value != null ? (double)x.Value : 0) //0 for now, when interpolation is done... etc.. .ToArray(); //just take last 3 years... mhm... var threeYears = 24 * 7 * 4 * 12 * 3; if (data.Length > threeYears) { data = data.Skip(data.Length - threeYears).Take(threeYears).ToArray(); } //detrend to make stationary data = TimeSeries.toStationary(data); //hourly //var seasons = new int[] { 24, 24 * 7, 24 * 7 * 4, 24 * 7 * 4 * 6, 24 * 7 * 4 * 12}; //var arSes = new int[] { 1, 2, 24, 25 }; //daily //var seasons = new int[] { 7, 7*4, 7*4*12 }; //var arSes = new int[] { 1, 7, 7*4 }; //var arma = TimeSeries.ARMASimple2(data, arSes, seasons); //fitted model from matlab var arlags = new int[] { 1, 2, 24, 25 }; //var ar = new TimeSeries.LagOp(new double[] { 1.04216, -0.125323, 0.777886, -0.699448 }, arlags); var malags = new int[] { 24, 168 }; //var ma = new TimeSeries.LagOp(new double[] { -0.44595, 0.175135 }, malags); //var xarma = TimeSeries.ARMASimple3(ar, ma, 0.166685, 2.80023); //our fitting procedure.. difference...? not much... var arma = TimeSeries.ARMASimple2(data, arlags, malags); arma = TimeSeries.ARMASimple3(arma.AR, arma.MA, arma.Const, volatility); var inSampleRes = TimeSeries.Infer(arma, data); var sims = arma.Simulate(numberOfSimulations, horizon, data, inSampleRes); var hoursSteps = timeStepsInLevels.Select(x => x * 24).ToArray(); var desezonalizedData = Desezonalize(data, 168); //add the spikes //Then perform the spike estimation var spikesThreshold = 1.7; var spikeIndices = EstimateSpikesOnMovSDs(desezonalizedData, 24, 2, spikesThreshold); //select hour var peakHour = 16; var peakhourData = TakeShortPeriods(data, 1, peakHour, 24); var peakSpikeIndices = EstimateSpikesOnMovSDs(peakhourData, 7, 2, spikesThreshold); var distrib = EstimateSpikesDistribution(peakhourData, peakSpikeIndices, Forecast.SpikePreprocess.SimilarDay, spikesThreshold); //for testing.. var n = new Normal(distrib.Item1.Mean, distrib.Item1.Variance); var p = new Poisson(distrib.Item2.Lambda * 24); //replace spikes now... //TODO: replace at the right hour... yes... sims = Simulations.spikeSimulationsReplace(sims, p, n); //fit the forward curve sims = Simulations.liftSeriesToPriceCurve(sims, hoursSteps, priceLevels); return Json(sims); }