/// <summary> /// Computes the cumulative distribution function of the distribution. /// </summary> /// <param name="x">The location at which to compute the cumulative density.</param> /// <returns>the cumulative density at <paramref name="x"/>.</returns> public double CumulativeDistribution(double x) { int alpha = Minimum; int beta = Maximum; if (x <= alpha) { return(0.0); } if (x > beta) { return(1.0); } var sum = 0.0; var k = (int)Math.Ceiling(x - alpha) - 1; for (var i = alpha; i <= alpha + k; i++) { sum += SpecialFunctions.Binomial(_m, i) * SpecialFunctions.Binomial(_populationSize - _m, _n - i); } return(sum / SpecialFunctions.Binomial(_populationSize, _n)); }
/// <summary> /// 분포의 확률 /// </summary> /// <param name="k">시도 횟수</param> /// <returns></returns> public double Probability(int k) { if (k < 0) { return(0.0); } if (k > _n) { return(0.0); } if (_p.ApproximateEqual(0.0) && k == 0) { return(1.0); } if (_p.ApproximateEqual(0.0)) { return(0.0); } if (_p.ApproximateEqual(1.0) && k == _n) { return(1.0); } if (_p.ApproximateEqual(1.0)) { return(0.0); } return(SpecialFunctions.Binomial(_n, k) * Math.Pow(_p, k) * Math.Pow(1.0 - _p, _n - k)); }
/// <summary> /// Computes the probability mass (PMF) at k, i.e. P(X = k). /// </summary> /// <param name="k">The location in the domain where we want to evaluate the probability mass function.</param> /// <returns>the probability mass at location <paramref name="k"/>.</returns> public double Probability(int k) { if (k < 0) { return(0.0); } if (k > _trials) { return(0.0); } if (_p == 0.0 && k == 0) { return(1.0); } if (_p == 0.0) { return(0.0); } if (_p == 1.0 && k == _trials) { return(1.0); } if (_p == 1.0) { return(0.0); } return(SpecialFunctions.Binomial(_trials, k) * Math.Pow(_p, k) * Math.Pow(1.0 - _p, _trials - k)); }
static void Main(string[] args) { // 1. Calcula o coeficiente binonmial Console.WriteLine("1. Calcular o coeficiente binomial "); while (true) { Console.WriteLine("Informe um número de 1 a 100 ( 999 -> Sai )"); string input = Console.ReadLine(); int n; if (Int32.TryParse(input, out n)) { if (n == 999) { break; } Console.WriteLine(SpecialFunctions.Binomial(10, 8).ToString("N")); Console.WriteLine(); } else { Console.WriteLine("Valor inválido..."); } } Console.WriteLine("Pressione algo para encerrar..."); Console.ReadLine(); }
/// <summary> /// Run example /// </summary> /// <seealso cref="http://en.wikipedia.org/wiki/Factorial">Factorial</seealso> /// <seealso cref="http://en.wikipedia.org/wiki/Binomial_coefficient">Binomial coefficient</seealso> /// <seealso cref="http://en.wikipedia.org/wiki/Multinomial_theorem#Multinomial_coefficients">Multinomial coefficients</seealso> public void Run() { // 1. Compute the factorial of 5 Console.WriteLine(@"1. Compute the factorial of 5"); Console.WriteLine(SpecialFunctions.Factorial(5).ToString("N")); Console.WriteLine(); // 2. Compute the logarithm of the factorial of 5 Console.WriteLine(@"2. Compute the logarithm of the factorial of 5"); Console.WriteLine(SpecialFunctions.FactorialLn(5).ToString("N")); Console.WriteLine(); // 3. Compute the binomial coefficient: 10 choose 8 Console.WriteLine(@"3. Compute the binomial coefficient: 10 choose 8"); Console.WriteLine(SpecialFunctions.Binomial(10, 8).ToString("N")); Console.WriteLine(); // 4. Compute the logarithm of the binomial coefficient: 10 choose 8 Console.WriteLine(@"4. Compute the logarithm of the binomial coefficient: 10 choose 8"); Console.WriteLine(SpecialFunctions.BinomialLn(10, 8).ToString("N")); Console.WriteLine(); // 5. Compute the multinomial coefficient: 10 choose 2, 3, 5 Console.WriteLine(@"5. Compute the multinomial coefficient: 10 choose 2, 3, 5"); Console.WriteLine(SpecialFunctions.Multinomial(10, new[] { 2, 3, 5 }).ToString("N")); Console.WriteLine(); }
/// <summary> /// Computes the probability mass (PMF) at k, i.e. P(X = k). /// </summary> /// <param name="k">The location in the domain where we want to evaluate the probability mass function.</param> /// <param name="population">The size of the population (N).</param> /// <param name="success">The number successes within the population (K, M).</param> /// <param name="draws">The number of draws without replacement (n).</param> /// <returns>the probability mass at location <paramref name="k"/>.</returns> public static double PMF(int population, int success, int draws, int k) { //if (!(population >= 0 && success >= 0 && draws >= 0 && success <= population && draws <= population)) { // throw new ArgumentException("InvalidDistributionParameters"); //} return(SpecialFunctions.Binomial(success, k) * SpecialFunctions.Binomial(population - success, draws - k) / SpecialFunctions.Binomial(population, draws)); }
public void ValidateProbability( [Values(0, 1, 2, 2, 2, 10, 10, 10, 10)] int size, [Values(0, 1, 1, 1, 2, 1, 1, 5, 5)] int m, [Values(0, 1, 1, 1, 2, 1, 1, 3, 3)] int n, [Values(0, 1, 0, 1, 2, 0, 1, 1, 3)] int x) { var d = new Hypergeometric(size, m, n); Assert.AreEqual(SpecialFunctions.Binomial(m, x) * SpecialFunctions.Binomial(size - m, n - x) / SpecialFunctions.Binomial(size, n), d.Probability(x)); }
public void CanComputeBinomial() { AssertHelpers.AlmostEqualRelative(1, SpecialFunctions.Binomial(1, 1), 14); AssertHelpers.AlmostEqualRelative(10, SpecialFunctions.Binomial(5, 2), 14); AssertHelpers.AlmostEqualRelative(35, SpecialFunctions.Binomial(7, 3), 14); AssertHelpers.AlmostEqualRelative(1, SpecialFunctions.Binomial(1, 0), 14); AssertHelpers.AlmostEqualRelative(0, SpecialFunctions.Binomial(0, 1), 14); AssertHelpers.AlmostEqualRelative(0, SpecialFunctions.Binomial(5, 7), 14); AssertHelpers.AlmostEqualRelative(0, SpecialFunctions.Binomial(5, -7), 14); }
public static Prediction GetSymmetricPrediction(double spotPrice, double volatility, double interestRate, double daysInFuture, int?numberOfPointsArg = null) { int numberOfPoints = numberOfPointsArg ?? DefaultNumberOfPredictionResults; volatility = 0.2; double t = daysInFuture / (365 * numberOfPoints); double tmp = interestRate / 100 - volatility * volatility / 2; double x = Math.Sqrt(tmp * tmp * t * t + volatility * volatility * t); double probabilityUp = x.AlmostEqual(0) ? 0.5 + tmp / 2 : 0.5 + (tmp * t) / (2 * x); double probabilityDown = 1 - probabilityUp; double[] stockPrice = new double[numberOfPoints]; double[] cumulativeProb = new double[numberOfPoints]; double prevStockPrice = stockPrice[0] = Math.Log(spotPrice) - (numberOfPoints) * x; for (int i = 0; i < numberOfPoints; i++) { prevStockPrice = prevStockPrice + 2 * x; stockPrice[i] = Math.Exp(prevStockPrice); } stockPrice[0] = Math.Exp(stockPrice[0]); double prevCumulativeProb = 0.0; for (int i = 0; i < numberOfPoints; i++) { double probability = SpecialFunctions.Binomial(numberOfPoints, i) * Math.Pow(probabilityDown, numberOfPoints - i) * Math.Pow(probabilityUp, i); probability += prevCumulativeProb; cumulativeProb[i] = probability.CoerceZero(SignificantDoubleValue); prevCumulativeProb = probability; } for (int i = numberOfPoints / 2; i < numberOfPoints; i++) { cumulativeProb[i] = 1.0 - cumulativeProb[i]; if (cumulativeProb[i] < 0) { cumulativeProb[i] = 0; } } Prediction prediction = new Prediction(cumulativeProb, stockPrice, daysInFuture); return(prediction); }
/// <summary> Gets possible lots. </summary> /// <remarks> superreeen, 09.11.2013. </remarks> /// <returns> The possible lots. </returns> //private static List<PossibleLot> GetPossibleLots() //{ // List<PossibleLot> findings = new List<PossibleLot>(); // decimal gain = 1; // decimal raiser = 1; // decimal totalGain = 0; // decimal gainStepAllocate = 0; // decimal gainAllocate = 0; // for (int n = 5; n >= 0; n--) // { // gainAllocate = (gain * (n)) / (n + raiser); // gain -= gainAllocate; // for (int s = 2; s >= 0; s--) // { // gainStepAllocate = (gainAllocate * (s + 2)) / (s + raiser + 2); // gainAllocate -= gainStepAllocate; // totalGain += gainStepAllocate; // raiser += 2; // findings.Add(new PossibleLot() // { // Numbers = n, // Stars = s, // Probability = (decimal)(SpecialFunctions.Binomial(Numbers, n) // * SpecialFunctions.Binomial(MaxNumbers - Numbers, Numbers - n) // / SpecialFunctions.Binomial(MaxNumbers, Numbers) // * SpecialFunctions.Binomial(Stars, s) // * SpecialFunctions.Binomial(MaxStars - Stars, Stars - s) // / SpecialFunctions.Binomial(MaxStars, Stars)), // Gain = gainStepAllocate // }); // } // } // return findings; //} private static List <PossibleLot> GetPossibleLots() { // key numbers & stars Dictionary <int, decimal> distribution = new Dictionary <int, decimal>(); distribution[52] = 0.300m; distribution[51] = 0.080m; distribution[50] = 0.020m; distribution[42] = 0.020m; distribution[41] = 0.010m; distribution[40] = 0.006m; distribution[32] = 0.006m; distribution[31] = 0.004m; distribution[30] = 0.002m; distribution[22] = 0.002m; distribution[21] = 0.040m; distribution[20] = 0.070m; distribution[12] = 0.090m; distribution[11] = 0.090m; distribution[10] = 0.110m; distribution[02] = 0.000m; distribution[01] = 0.000m; distribution[00] = 0.000m; List <PossibleLot> findings = new List <PossibleLot>(); for (int n = 5; n >= 0; n--) { for (int s = 2; s >= 0; s--) { findings.Add(new PossibleLot() { Numbers = n, Stars = s, Probability = (decimal)(SpecialFunctions.Binomial(Numbers, n) * SpecialFunctions.Binomial(MaxNumbers - Numbers, Numbers - n) / SpecialFunctions.Binomial(MaxNumbers, Numbers) * SpecialFunctions.Binomial(Stars, s) * SpecialFunctions.Binomial(MaxStars - Stars, Stars - s) / SpecialFunctions.Binomial(MaxStars, Stars)), Gain = distribution[(n * 10) + s] }); } } return(findings); }
// These are the two-sided coefficients, so not much use. private DenseVector TwoSidedCoefficients(int N) { if (N % 2 == 0) { throw new Exception("Error, FilterLength must be odd!"); } int m = (int)(0.5 * (N - 3)); int M = (int)(0.5 * (N - 1)); double denominator = 1 / (Math.Pow(2, 2 * m + 1)); double[] coeff = new double[M]; for (int k = 0; k < M; ++k) { coeff[k] = (SpecialFunctions.Binomial(2 * m, m - k + 1) - SpecialFunctions.Binomial(2 * m, m - k - 1)) * denominator; } return(new DenseVector(coeff)); }
/// <summary> /// /// </summary> public List <Finding> getFindings() { List <Finding> findings = new List <Finding>(); double gain = 1; double raiser = 1; double totalGain = 0; double gainStepAllocate = 0; double gainAllocate = 0; for (int n = 5; n >= 0; n--) { gainAllocate = (gain * (n)) / (n + raiser); gain -= gainAllocate; for (int s = 2; s >= 0; s--) { gainStepAllocate = (gainAllocate * (s + 2)) / (s + raiser + 2); gainAllocate -= gainStepAllocate; totalGain += gainStepAllocate; raiser += 2; findings.Add(new Finding() { Numbers = n, Stars = s, Probability = SpecialFunctions.Binomial(NUMBERS, n) * SpecialFunctions.Binomial(MAXNUMBERS - NUMBERS, NUMBERS - n) / SpecialFunctions.Binomial(MAXNUMBERS, NUMBERS) * SpecialFunctions.Binomial(STARS, s) * SpecialFunctions.Binomial(MAXSTARS - STARS, STARS - s) / SpecialFunctions.Binomial(MAXSTARS, STARS), Gain = gainStepAllocate }); } } return(findings); }
private static void CalcularCoeficienteBinomial() { Console.WriteLine("1. Calcular o Coeficiente Binomial entre os números n e p"); while (true) { Console.WriteLine("Informe o número n entre 1 a 200 ( 999 -> Sai )"); string numero1 = Console.ReadLine(); Console.WriteLine("Informe o número p entre 1 a 200 ( 999 -> Sai )"); string numero2 = Console.ReadLine(); int n; int p; if (Int32.TryParse(numero1, out n)) { if (n == 999) { break; } if (Int32.TryParse(numero2, out p)) { if (p == 999) { break; } Console.WriteLine($" C({n},{p}) = {SpecialFunctions.Binomial(n, p).ToString("N")}"); Console.WriteLine(); } else { Console.WriteLine("Valor de p inválido..."); } } else { Console.WriteLine("Valor de n inválido..."); } } }
/// <summary> /// Returns the Matrix representing the Casteljau Algorithm for solving Bernstein functions /// </summary> /// <param name="numPoints">Number of points in this bezier curve</param> /// <returns>Returns a sparse matrix of the order numPoints X numPoints</returns> private Matrix <double> GetCasteljauMatrix(int numPoints) { if (_matrixCache.ContainsKey(numPoints)) { return(_matrixCache[numPoints]); } Matrix <double> m = new MathNet.Numerics.LinearAlgebra.Double.SparseMatrix(numPoints, numPoints); int n = numPoints - 1; for (int i = 0; i <= n; i++) { for (int k = 0; k <= n - i; k++) { // m_ij = -1^(i+k+n)*(n-1 choose k)*(n choose i) m[i, k] = Math.Pow(-1, i + k + n) * SpecialFunctions.Binomial(n - i, k) * SpecialFunctions.Binomial(n, i); } } _matrixCache[numPoints] = m; return(m); }
/// <summary> /// Computes the probability mass (PMF) at k, i.e. P(X = k). /// </summary> /// <param name="k">The location in the domain where we want to evaluate the probability mass function.</param> /// <returns>the probability mass at location <paramref name="k"/>.</returns> public double Probability(int k) { return(SpecialFunctions.Binomial(_success, k) * SpecialFunctions.Binomial(_population - _success, _draws - k) / SpecialFunctions.Binomial(_population, _draws)); }
public void ValidateProbability(int N, int m, int n, int x) { var d = new Hypergeometric(N, m, n); Assert.AreEqual <double>(SpecialFunctions.Binomial(m, x) * SpecialFunctions.Binomial(N - m, n - x) / SpecialFunctions.Binomial(N, n), d.Probability(x)); }
/// <summary> /// Executes the example. /// </summary> public override void ExecuteExample() { // <seealso cref="http://en.wikipedia.org/wiki/Beta_function">Beta function</seealso> MathDisplay.WriteLine("<b>Beta fuction</b>"); // 1. Compute the Beta function at z = 1.0, w = 3.0 MathDisplay.WriteLine(@"1. Compute the Beta function at z = 1.0, w = 3.0"); MathDisplay.WriteLine(SpecialFunctions.Beta(1.0, 3.0).ToString()); MathDisplay.WriteLine(); // 2. Compute the logarithm of the Beta function at z = 1.0, w = 3.0 MathDisplay.WriteLine(@"2. Compute the logarithm of the Beta function at z = 1.0, w = 3.0"); MathDisplay.WriteLine(SpecialFunctions.BetaLn(1.0, 3.0).ToString()); MathDisplay.WriteLine(); // 3. Compute the Beta incomplete function at z = 1.0, w = 3.0, x = 0.7 MathDisplay.WriteLine(@"3. Compute the Beta incomplete function at z = 1.0, w = 3.0, x = 0.7"); MathDisplay.WriteLine(SpecialFunctions.BetaIncomplete(1.0, 3.0, 0.7).ToString()); MathDisplay.WriteLine(); // 4. Compute the Beta incomplete function at z = 1.0, w = 3.0, x = 1.0 MathDisplay.WriteLine(@"4. Compute the Beta incomplete function at z = 1.0, w = 3.0, x = 1.0"); MathDisplay.WriteLine(SpecialFunctions.BetaIncomplete(1.0, 3.0, 1.0).ToString()); MathDisplay.WriteLine(); // 5. Compute the Beta regularized function at z = 1.0, w = 3.0, x = 0.7 MathDisplay.WriteLine(@"5. Compute the Beta regularized function at z = 1.0, w = 3.0, x = 0.7"); MathDisplay.WriteLine(SpecialFunctions.BetaRegularized(1.0, 3.0, 0.7).ToString()); MathDisplay.WriteLine(); // 6. Compute the Beta regularized function at z = 1.0, w = 3.0, x = 1.0 MathDisplay.WriteLine(@"6. Compute the Beta regularized function at z = 1.0, w = 3.0, x = 1.0"); MathDisplay.WriteLine(SpecialFunctions.BetaRegularized(1.0, 3.0, 1.0).ToString()); MathDisplay.WriteLine(); MathDisplay.WriteLine("<b>Common functions</b>"); // 1. Calculate the Digamma function at point 5.0 // <seealso cref="http://en.wikipedia.org/wiki/Digamma_function">Digamma function</seealso> MathDisplay.WriteLine(@"1. Calculate the Digamma function at point 5.0"); MathDisplay.WriteLine(SpecialFunctions.DiGamma(5.0).ToString()); MathDisplay.WriteLine(); // 2. Calculate the inverse Digamma function at point 1.5 MathDisplay.WriteLine(@"2. Calculate the inverse Digamma function at point 1.5"); MathDisplay.WriteLine(SpecialFunctions.DiGammaInv(1.5).ToString()); MathDisplay.WriteLine(); // 3. Calculate the 10'th Harmonic number // <seealso cref="http://en.wikipedia.org/wiki/Harmonic_number">Harmonic number</seealso> MathDisplay.WriteLine(@"3. Calculate the 10'th Harmonic number"); MathDisplay.WriteLine(SpecialFunctions.Harmonic(10).ToString()); MathDisplay.WriteLine(); // 4. Calculate the generalized harmonic number of order 10 of 3.0. // <seealso cref="http://en.wikipedia.org/wiki/Harmonic_number#Generalized_harmonic_numbers">Generalized harmonic numbers</seealso> MathDisplay.WriteLine(@"4. Calculate the generalized harmonic number of order 10 of 3.0"); MathDisplay.WriteLine(SpecialFunctions.GeneralHarmonic(10, 3.0).ToString()); MathDisplay.WriteLine(); // 5. Calculate the logistic function of 3.0 // <seealso cref="http://en.wikipedia.org/wiki/Logistic_function">Logistic function</seealso> MathDisplay.WriteLine(@"5. Calculate the logistic function of 3.0"); MathDisplay.WriteLine(SpecialFunctions.Logistic(3.0).ToString()); MathDisplay.WriteLine(); // 6. Calculate the logit function of 0.3 // <seealso cref="http://en.wikipedia.org/wiki/Logit">Logit function</seealso> MathDisplay.WriteLine(@"6. Calculate the logit function of 0.3"); MathDisplay.WriteLine(SpecialFunctions.Logit(0.3).ToString()); MathDisplay.WriteLine(); // <seealso cref="http://en.wikipedia.org/wiki/Error_function">Error function</seealso> MathDisplay.WriteLine("<b>Error function</b>"); // 1. Calculate the error function at point 2 MathDisplay.WriteLine(@"1. Calculate the error function at point 2"); MathDisplay.WriteLine(SpecialFunctions.Erf(2).ToString()); MathDisplay.WriteLine(); // 2. Sample 10 values of the error function in [-1.0; 1.0] MathDisplay.WriteLine(@"2. Sample 10 values of the error function in [-1.0; 1.0]"); var data = Generate.LinearSpacedMap <double>(10, -1.0, 1.0, SpecialFunctions.Erf); for (var i = 0; i < data.Length; i++) { MathDisplay.Write(data[i].ToString("N") + @" "); } MathDisplay.WriteLine(); MathDisplay.WriteLine(); // 3. Calculate the complementary error function at point 2 MathDisplay.WriteLine(@"3. Calculate the complementary error function at point 2"); MathDisplay.WriteLine(SpecialFunctions.Erfc(2).ToString()); MathDisplay.WriteLine(); // 4. Sample 10 values of the complementary error function in [-1.0; 1.0] MathDisplay.WriteLine(@"4. Sample 10 values of the complementary error function in [-1.0; 1.0]"); data = Generate.LinearSpacedMap <double>(10, -1.0, 1.0, SpecialFunctions.Erfc); for (var i = 0; i < data.Length; i++) { MathDisplay.Write(data[i].ToString("N") + @" "); } MathDisplay.WriteLine(); MathDisplay.WriteLine(); // 5. Calculate the inverse error function at point z=0.5 MathDisplay.WriteLine(@"5. Calculate the inverse error function at point z=0.5"); MathDisplay.WriteLine(SpecialFunctions.ErfInv(0.5).ToString()); MathDisplay.WriteLine(); // 6. Sample 10 values of the inverse error function in [-1.0; 1.0] MathDisplay.WriteLine(@"6. Sample 10 values of the inverse error function in [-1.0; 1.0]"); data = Generate.LinearSpacedMap <double>(10, -1.0, 1.0, SpecialFunctions.ErfInv); for (var i = 0; i < data.Length; i++) { MathDisplay.Write(data[i].ToString("N") + @" "); } MathDisplay.WriteLine(); MathDisplay.WriteLine(); // 7. Calculate the complementary inverse error function at point z=0.5 MathDisplay.WriteLine(@"7. Calculate the complementary inverse error function at point z=0.5"); MathDisplay.WriteLine(SpecialFunctions.ErfcInv(0.5).ToString()); MathDisplay.WriteLine(); // 8. Sample 10 values of the complementary inverse error function in [-1.0; 1.0] MathDisplay.WriteLine(@"8. Sample 10 values of the complementary inverse error function in [-1.0; 1.0]"); data = Generate.LinearSpacedMap <double>(10, -1.0, 1.0, SpecialFunctions.ErfcInv); for (var i = 0; i < data.Length; i++) { MathDisplay.Write(data[i].ToString("N") + @" "); } MathDisplay.WriteLine(); // <seealso cref="http://en.wikipedia.org/wiki/Factorial">Factorial</seealso> MathDisplay.WriteLine("<b>Factorial</b>"); // 1. Compute the factorial of 5 MathDisplay.WriteLine(@"1. Compute the factorial of 5"); MathDisplay.WriteLine(SpecialFunctions.Factorial(5).ToString("N")); MathDisplay.WriteLine(); // 2. Compute the logarithm of the factorial of 5 MathDisplay.WriteLine(@"2. Compute the logarithm of the factorial of 5"); MathDisplay.WriteLine(SpecialFunctions.FactorialLn(5).ToString("N")); MathDisplay.WriteLine(); // <seealso cref="http://en.wikipedia.org/wiki/Binomial_coefficient">Binomial coefficient</seealso> MathDisplay.WriteLine("<b>Binomial coefficient</b>"); // 3. Compute the binomial coefficient: 10 choose 8 MathDisplay.WriteLine(@"3. Compute the binomial coefficient: 10 choose 8"); MathDisplay.WriteLine(SpecialFunctions.Binomial(10, 8).ToString("N")); MathDisplay.WriteLine(); // 4. Compute the logarithm of the binomial coefficient: 10 choose 8 MathDisplay.WriteLine(@"4. Compute the logarithm of the binomial coefficient: 10 choose 8"); MathDisplay.WriteLine(SpecialFunctions.BinomialLn(10, 8).ToString("N")); MathDisplay.WriteLine(); // <seealso cref="http://en.wikipedia.org/wiki/Multinomial_theorem#Multinomial_coefficients">Multinomial coefficients</seealso> MathDisplay.WriteLine("<b>Multinomial coefficient</b>"); // 5. Compute the multinomial coefficient: 10 choose 2, 3, 5 MathDisplay.WriteLine(@"5. Compute the multinomial coefficient: 10 choose 2, 3, 5"); MathDisplay.WriteLine(SpecialFunctions.Multinomial(10, new[] { 2, 3, 5 }).ToString("N")); MathDisplay.WriteLine(); // <seealso cref="http://en.wikipedia.org/wiki/Gamma_function">Gamma function</seealso> MathDisplay.WriteLine("<b>Gamma function</b>"); // 1. Compute the Gamma function of 10 MathDisplay.WriteLine(@"1. Compute the Gamma function of 10"); MathDisplay.WriteLine(SpecialFunctions.Gamma(10).ToString("N")); MathDisplay.WriteLine(); // 2. Compute the logarithm of the Gamma function of 10 MathDisplay.WriteLine(@"2. Compute the logarithm of the Gamma function of 10"); MathDisplay.WriteLine(SpecialFunctions.GammaLn(10).ToString("N")); MathDisplay.WriteLine(); // 3. Compute the lower incomplete gamma(a, x) function at a = 10, x = 14 MathDisplay.WriteLine(@"3. Compute the lower incomplete gamma(a, x) function at a = 10, x = 14"); MathDisplay.WriteLine(SpecialFunctions.GammaLowerIncomplete(10, 14).ToString("N")); MathDisplay.WriteLine(); // 4. Compute the lower incomplete gamma(a, x) function at a = 10, x = 100 MathDisplay.WriteLine(@"4. Compute the lower incomplete gamma(a, x) function at a = 10, x = 100"); MathDisplay.WriteLine(SpecialFunctions.GammaLowerIncomplete(10, 100).ToString("N")); MathDisplay.WriteLine(); // 5. Compute the upper incomplete gamma(a, x) function at a = 10, x = 0 MathDisplay.WriteLine(@"5. Compute the upper incomplete gamma(a, x) function at a = 10, x = 0"); MathDisplay.WriteLine(SpecialFunctions.GammaUpperIncomplete(10, 0).ToString("N")); MathDisplay.WriteLine(); // 6. Compute the upper incomplete gamma(a, x) function at a = 10, x = 10 MathDisplay.WriteLine(@"6. Compute the upper incomplete gamma(a, x) function at a = 10, x = 100"); MathDisplay.WriteLine(SpecialFunctions.GammaLowerIncomplete(10, 10).ToString("N")); MathDisplay.WriteLine(); // 7. Compute the lower regularized gamma(a, x) function at a = 10, x = 14 MathDisplay.WriteLine(@"7. Compute the lower regularized gamma(a, x) function at a = 10, x = 14"); MathDisplay.WriteLine(SpecialFunctions.GammaLowerRegularized(10, 14).ToString("N")); MathDisplay.WriteLine(); // 8. Compute the lower regularized gamma(a, x) function at a = 10, x = 100 MathDisplay.WriteLine(@"8. Compute the lower regularized gamma(a, x) function at a = 10, x = 100"); MathDisplay.WriteLine(SpecialFunctions.GammaLowerRegularized(10, 100).ToString("N")); MathDisplay.WriteLine(); // 9. Compute the upper regularized gamma(a, x) function at a = 10, x = 0 MathDisplay.WriteLine(@"9. Compute the upper regularized gamma(a, x) function at a = 10, x = 0"); MathDisplay.WriteLine(SpecialFunctions.GammaUpperRegularized(10, 0).ToString("N")); MathDisplay.WriteLine(); // 10. Compute the upper regularized gamma(a, x) function at a = 10, x = 10 MathDisplay.WriteLine(@"10. Compute the upper regularized gamma(a, x) function at a = 10, x = 100"); MathDisplay.WriteLine(SpecialFunctions.GammaUpperRegularized(10, 10).ToString("N")); MathDisplay.WriteLine(); MathDisplay.WriteLine("<b>Numerical stability</b>"); // 1. Compute numerically stable exponential of 10 minus one MathDisplay.WriteLine(@"1. Compute numerically stable exponential of 4.2876 minus one"); MathDisplay.WriteLine(SpecialFunctions.ExponentialMinusOne(4.2876).ToString()); MathDisplay.WriteLine(); // 2. Compute regular System.Math exponential of 15.28 minus one MathDisplay.WriteLine(@"2. Compute regular System.Math exponential of 4.2876 minus one "); MathDisplay.WriteLine((Math.Exp(4.2876) - 1).ToString()); MathDisplay.WriteLine(); // 3. Compute numerically stable hypotenuse of a right angle triangle with a = 5, b = 3 MathDisplay.WriteLine(@"3. Compute numerically stable hypotenuse of a right angle triangle with a = 5, b = 3"); MathDisplay.WriteLine(SpecialFunctions.Hypotenuse(5, 3).ToString()); MathDisplay.WriteLine(); }
public void ValidateProbability(int size, int m, int n, int x) { var d = new Hypergeometric(size, m, n); Assert.AreEqual(SpecialFunctions.Binomial(m, x) * SpecialFunctions.Binomial(size - m, n - x) / SpecialFunctions.Binomial(size, n), d.Probability(x)); }
/// <summary> /// Computes values of the probability mass function. /// </summary> /// <param name="k">The location in the domain where we want to evaluate the probability mass function.</param> /// <returns> /// the probability mass at location <paramref name="k"/>. /// </returns> public double Probability(int k) { return(SpecialFunctions.Binomial(_m, k) * SpecialFunctions.Binomial(_populationSize - _m, _n - k) / SpecialFunctions.Binomial(_populationSize, _n)); }
public void ValidateProbability(int population, int success, int draws, int x) { var d = new Hypergeometric(population, success, draws); Assert.AreEqual(SpecialFunctions.Binomial(success, x) * SpecialFunctions.Binomial(population - success, draws - x) / SpecialFunctions.Binomial(population, draws), d.Probability(x)); }