/// <summary>Gets the absolute n-th central moment, i.e. E[|X- E[X]|^n], where E is the expectation operator. /// </summary> /// <param name="order">The order of the central moment.</param> /// <returns>The value of the absolute n-th central moment, i.e. E[|X- E[X]|^n], where E is the expectation operator.</returns> /// <remarks>The implementation is based on a numerical integral approach (Gauss-Laguerre).</remarks> public override double GetAbsCentralValue(int order) { var algorithm = Integrator.Create(); algorithm.FunctionToIntegrate = (xk, k) => DoMath.Pow(Math.Abs(xk - 1.0), order); // |\beta * x - \beta|^n = \beta^n * |x-1.0|^n return(algorithm.GetValue() * DoMath.Pow(Distribution.Beta, order)); }