kurtosis()

std::vector< double > MayaFlux::Kinesis::Discrete::kurtosis	(	std::span< const double >	data,
		size_t	n_windows,
		uint32_t	hop_size,
		uint32_t	window_size
	)

Excess kurtosis (fourth central moment - 3) per window.

Normal distribution yields 0. Returns 0 when variance is below epsilon.

Definition at line 292 of file Analysis.cpp.

{
    std::vector<double> out(n_windows);
    std::vector<size_t> idx(n_windows);
    std::iota(idx.begin(), idx.end(), 0);
 
    Parallel::for_each(Parallel::par_unseq, idx.begin(), idx.end(),
        [&](size_t i) {
            const size_t start = i * hop_size;
            auto w = data.subspan(start, std::min<size_t>(window_size, data.size() - start));
            if (w.size() < 2) {
                out[i] = 0.0;
                return;
            }
            double s = 0.0;
            for (double v : w)
                s += v;
            const double m = s / static_cast<double>(w.size());
            double sq = 0.0, fo = 0.0;
            for (double v : w) {
                const double d = v - m;
                const double d2 = d * d;
                sq += d2;
                fo += d2 * d2;
            }
            const double var = sq / static_cast<double>(w.size());
            const double var2 = std::max(var * var, k_epsilon);
            out[i] = (fo / static_cast<double>(w.size())) / var2 - 3.0;
        });
 
    return out;
}

References kurtosis().

Referenced by kurtosis().

Here is the call graph for this function:

Here is the caller graph for this function: