A rank is a distribution
Observation and data Amina Okafor Observation and data Amina Okafor

A rank is a distribution

Sorting point estimates creates an order even when observations cannot reliably resolve the differences. This methods note distinguishes descriptive ranks from uncertainty in rank, drawing on league-table methodology, the JCGM uncertainty framework, and NASA's GISTEMP ensemble documentation. A fictional two-estimate comparison holds marginal uncertainties fixed while changing error correlation, showing why individual uncertainty bars cannot determine support for a lead. The note then explains joint propagation through ranking, finite-ensemble limits, comparison-set definitions, and public displays that retain magnitude alongside position. It calculates no actual climate ranking and does not extend NASA's documented ensemble beyond its stated period. The principal implication is to report an estimated order separately from its model-dependent stability, especially when ordinal cutoffs carry decision consequences.

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