compute_kurtosis_statistic()

std::vector< double > MayaFlux::Yantra::compute_kurtosis_statistic	(	std::span< const double >	data,
		const size_t	num_windows,
		const uint32_t	hop_size,
		const uint32_t	window_size
	)

Compute kurtosis statistic using zero-copy processing.

This function computes the kurtosis (fourth moment) for a given data span. It measures the tail heaviness of the distribution in each window.

Parameters

data	Input data span
num_windows	Number of windows to process
hop_size	Hop size for windowing
window_size	Size of each window

Returns

Vector of kurtosis values (excess kurtosis, normal = 0)

Definition at line 458 of file AnalysisHelper.cpp.

{
    std::vector<double> kurtosis_values(num_windows);
 
    std::vector<size_t> indices(num_windows);
    std::iota(indices.begin(), indices.end(), 0);
 
    std::for_each(std::execution::par_unseq, indices.begin(), indices.end(),
        [&](size_t i) {
            const size_t start_idx = i * hop_size;
            const size_t end_idx = std::min(start_idx + window_size, data.size());
            auto window = data.subspan(start_idx, end_idx - start_idx);
 
            if (window.size() < 2) {
                kurtosis_values[i] = 0.0;
                return;
            }
 
            double sum = 0.0;
            for (double sample : window) {
                sum += sample;
            }
            double mean = sum / static_cast<double>(window.size());
 
            double sum_sq_diff = 0.0;
            double sum_fourth_diff = 0.0;
            for (double sample : window) {
                double diff = sample - mean;
                double sq_diff = diff * diff;
                sum_sq_diff += sq_diff;
                sum_fourth_diff += sq_diff * sq_diff;
            }
 
            double variance = sum_sq_diff / static_cast<double>(window.size());
            if (variance <= 0.0) {
                kurtosis_values[i] = 0.0;
                return;
            }
 
            double fourth_moment = sum_fourth_diff / static_cast<double>(window.size());
 
            kurtosis_values[i] = (fourth_moment / (variance * variance)) - 3.0;
        });
 
    return kurtosis_values;
}

References compute_kurtosis_statistic(), and MayaFlux::mean().

Referenced by compute_kurtosis_statistic(), MayaFlux::Yantra::StatisticalAnalyzer< InputType, OutputType >::compute_statistical_values(), and MayaFlux::Yantra::StatisticalAnalyzer< InputType, OutputType >::create_analysis_result().

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