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It is generally accepted that the perception of homeowners towards certain potential risks or amenities fades as distance from the risk or amenity increases. This study aims to illustrate the distance–decay pattern with an appropriate mathematical function. Distance–decay functions and parameters that yield the minimum residual sum of squares (RSS) for a given regression model are considered to be the optimal approximation for the pattern of decay. The effect of flood risk and mass rapid transit (MRT) accessibility on residential housing prices in Taipei, Taiwan, are used as examples to test the optimization process. The results indicate that the type of distance function affects both the significance and the magnitude of the regression coefficients. In the case of Taipei, concave functions provide better fits for both the flood risk and MRT accessibility. RSS reduction is up to 10% compared to the blank. Surprisingly, the impact range for the flood risk is found to be larger than that for MRT accessibility, which suggested that the impact range of perception for uncertain risks is larger than expected.
