Spatial Choice Processes and the Gamma Distribution

Abstract

From commuting literature we know that the distribution of dis-tance to spatial choices often is unimodally distributed with skew to the right; often the distribution is close to a Gamma distribution. The pattern appears robust. This paper constructs a mathematical statis-tical choice model to account for this fact. The key idea is that there is a tension between costs increasing with distance parallel with the number of offers per radial segment increasing with distance. The first effect induces short-distance choices whereas the second gives incen-tives to choose options located far away. We show by simulation that these two effects are likely to give rise to Gamma distributed choice patterns under a wide array of distributional assumptions. After this, a more general theory for stochastic optimization in space is outlined where offers of random value are distributed randomly in space. Ap-proximations are made using extreme value theory, and under these

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