median_absolute_deviation()

double MayaFlux::Kinesis::Stochastic::Estimate::median_absolute_deviation ( std::span< const double >  samples )

staticnoexcept

Median absolute deviation of a span.

Parameters

samples

Values to analyze

Returns

Median of |x_i - median(samples)|, scaled by 1.4826 to be a consistent estimator of standard deviation under a normal distribution assumption. Robust to single-sample spikes in a way variance is not, since one wild outlier can dominate a variance estimate but only shifts a median by at most one rank.

Definition at line 229 of file Estimate.cpp.

{
    if (samples.empty())
        return 0.0;
 
    std::vector<double> sorted(samples.begin(), samples.end());
    std::ranges::sort(sorted);
    const double median = sorted[sorted.size() / 2];
 
    std::vector<double> deviations;
    deviations.reserve(sorted.size());
    for (double v : sorted)
        deviations.push_back(std::abs(v - median));
    std::ranges::sort(deviations);
 
    return deviations[deviations.size() / 2] * 1.4826;
}

Referenced by update_mad().

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