<p>Hybrid Moment (MH); compositional data; structural change; age structure; concentration; evenness</p><p>This article considers the use of the Hybrid Moment (MH) as a simple measure for monitoring changes in the urban age structure. MH combines a normalized complement-of-dominance component derived from the Herfindahl–Hirschman index and an evenness component measured by Pielou’s J index, while the weight parameter is treated as an interpretative choice made by the user. The index is therefore understood as a practical and easy-to-communicate scalar summary for routine monitoring, rather than as a substitute for profile-based approaches. The empirical part uses annual population data for Elbląg in Poland from 2010 to 2023. The analysis tracks the behavior of MH under a fixed age-group partition, includes an illustrative check of an alternative partition for the year 2023, considers simple smoothing variants, and compares the results with including simple measures based on the 0–6 and 65 + groups. The results indicate that MH may be considered as a supporting tool for monitoring and reporting. At the same time, its values depend on the adopted age-group partition; therefore, they should be interpreted only within a given classification scheme. For the same reason, the proposed reference threshold is purely illustrative and should not be treated as universal.</p>

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A hybrid concentration-evenness indicator for structural change in compositional data

  • Joanna Julia Sitz

摘要

Hybrid Moment (MH); compositional data; structural change; age structure; concentration; evenness

This article considers the use of the Hybrid Moment (MH) as a simple measure for monitoring changes in the urban age structure. MH combines a normalized complement-of-dominance component derived from the Herfindahl–Hirschman index and an evenness component measured by Pielou’s J index, while the weight parameter is treated as an interpretative choice made by the user. The index is therefore understood as a practical and easy-to-communicate scalar summary for routine monitoring, rather than as a substitute for profile-based approaches. The empirical part uses annual population data for Elbląg in Poland from 2010 to 2023. The analysis tracks the behavior of MH under a fixed age-group partition, includes an illustrative check of an alternative partition for the year 2023, considers simple smoothing variants, and compares the results with including simple measures based on the 0–6 and 65 + groups. The results indicate that MH may be considered as a supporting tool for monitoring and reporting. At the same time, its values depend on the adopted age-group partition; therefore, they should be interpreted only within a given classification scheme. For the same reason, the proposed reference threshold is purely illustrative and should not be treated as universal.