Spatial autocorrelation and unorthodox random variables: the uniform distribution

Abstract

By definition, original Besag-conceived spatial auto-random variables incorporate an autoregressive spatial lag term (i.e., the sum/average of nearby attribute values) to characterize geospatial data. Very common variates include the auto-normal, auto-logistic, and auto-binomial; less common ones include the auto-beta and auto-multinomial. Some of these specifications can capture the full range of spatial autocorrelation, and others cannot. These latter variates are unorthodox in their nonconformist restrictions to either only positive or only negative spatial autocorrelation domains. The literature already offers successful modifications of the auto-Poisson and auto-negative binomial, two popular random variables for describing counts, but neither of which can encapsulate positive spatial autocorrelation. The literature dismissively mentions the auto-exponential variate, which cannot accommodate negative spatial autocorrelation situations. Meanwhile, the literature lacks any discussion about auto-uniform random variables, with implications especially from point pattern analysis publications that they solely refer to complete spatial randomness. The purpose of this paper is to postulate a productive and viable spatialized continuous uniform distribution specification that easily extends to its corresponding discrete version. A standard benchmark location-allocation simulation experiment for a simple p = 1 median problem, a spatial optimization circumstance that illuminates bivariate spatial median properties, illustrates its practical applicability.