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Regionalized Variables

Geographically distributed phenomena over a one-, twoor three-dimensional metric space can be concentrated in some subset of discrete points, be collected into mutually exclusive and collectively exhaustive areal unit aggregates, or be continuous. A surface formed by one of these phenomena, such as a population density map, usually is too irregular to be described analytically by simple, smooth mathematical functions. Rather, a single variable function, called a regionalized variable, can be specified in terms of an underlying geographic coordinate system in order to describe the phenomenon in a mixed deterministic and stochastic way, by including (a) a structural component that captures geographic trends (e.g., population density declining with increasing distance from a city center), (b) a structured random component that captures spatial autocorrelation effects (e.g., ...

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