A Comparison of Distribution Models for Ranked Architectural Sizes at Tikal: An Empirical Assessment of an Archaeological Economic Indicator

When ranked data exhibit regime shifts, model choice becomes part of the substantive claim rather than a technical detail. Within the framework of Material Culture Macroecology (MME), a macroecological approach to material inequality, this preprint uses a single rank–value dataset (n = 501) derived from architectural group size at Tikal (Guatemala) to empirically compare three candidate distribution models: a power-law (Pareto) model, an exponential model, and a connected two-part model that combines a power-law regime with an exponential regime separated by an estimated cutoff rank. The results show that the ranking is not adequately captured by a single distribution form; instead, it exhibits a composite structure in which distributional properties change across ranking regions, consistent with an MME view that inequality can be continuous yet structurally patterned. In addition, the preprint addresses a practical issue in archaeological description: how to relate a continuous, distribution-based economic-indicator structure to categorical hierarchies used in reporting and comparison. As a worked example, it provisionally proposes a nine-level hierarchy based on structural attributes and demonstrates how continuous quantities can be translated into classificatory practice without negating distribution-analytic results. For reproducibility, the study provides detailed preprocessing and estimation procedures in Appendices A–C and makes the rank–value dataset and integrated analysis code publicly available on Zenodo (doi:10.5281/zenodo.18500507).