public static Resultant ( double angles ) : double | ||
angles | double | A double array containing the angles in radians. |
Результат | double |
/// <summary> /// Computes the circular kurtosis of the given circular angles. /// </summary> /// /// <param name="angles">A double array containing the angles in radians.</param> /// /// <returns>The circular kurtosis for the given <paramref name="angles"/>.</returns> /// public static double Kurtosis(double[] angles) { // Compute mean direction double R = Circular.Resultant(angles); double theta = Circular.Mean(angles); // Compute central moments double rho2 = CentralMoments(angles, 2).Magnitude; double mu2 = NoncentralMoments(angles, 2).Phase; // compute skewness double k = 0; for (int i = 0; i < angles.Length; i++) // Pewsey, Metrika, 2004 { k += Math.Cos(2 * Circular.Distance(angles[i], theta)); } k /= angles.Length; /* * double k0 = 0; * double R4 = (R * R * R * R); * double omR2 = (1 - R) * (1 - R); * for (int i = 0; i < angles.Length; i++) // Fisher, Circular Statistics, p. 34 * k0 += (rho2 * Math.Cos(Circular.Distance(mu2, 2 * theta)) - R4) / omR2; // (formula 2.30) */ return(k); }
/// <summary> /// Computes the circular skewness of the given circular angles. /// </summary> /// /// <param name="angles">A double array containing the angles in radians.</param> /// /// <returns>The circular skewness for the given <paramref name="angles"/>.</returns> /// public static double Skewness(double[] angles) { // compute necessary values double R = Circular.Resultant(angles); double theta = Circular.Mean(angles); Complex m = CentralMoments(angles, 2); double rho2 = m.Magnitude; double mu2 = m.Phase; // compute skewness double b = 0; // Pewsey, Metrika, 2004 for (int i = 0; i < angles.Length; i++) { b += Math.Sin(2 * Distance(angles[i], theta)); } b /= angles.Length; /* * // alternative skewness measure from Fisher * // Statistical Analysis of Circular Data, p. 34 * double b0 = 0; // (formula 2.29) * double omR = Math.Pow(1 - R, 3 / 2.0); * * for (int i = 0; i < angles.Length; i++) * b0 += rho2 * Math.Sin(Distance(mu2, 2 * theta)) / omR; */ return(b); }