**Distance decay function**

It expresses changes (decrease or decay) in interactions between a centre based on the distance from this centre. These interactions can have various character, most common being transport, migration or travel-to-work flows. Taylor (1971) detailed and distinguished basic types of distance decay functions: normal, exponential, square-root exponential, lognormal and Pareto functions. During time more complex functions with more (2 – 4) parameters have been used in spatial interaction modelling, e.g. power-exponential, Tanner´s, March´s, Weibull´s squared Cauchy, Box-Cox or Richards´ functions. For modelling of nodal (core-oriented) flows of population bell-shaped functions with an inflection point changing its curve from concave to convex (see Halás et al. 2014 for more details and fig. 1 below).

**Radius of influence**

expresses statistically for distance decay function a theoretical distance of 100% influence of a regional centre. Resulting value determines radius of influence and extent of influence of a centre, but the population size of an area cannot be derived from it. In case the value of maximal interaction intensity is equal to 1 (for a distance from a centre d = 0), it is possible to express the value for radius of influence graphically (fig. 2). The radius of influence was introduced by Halás et al. (2014).

**Source**

Halás, M., Klapka, P., Kladivo P. (2014): Distance-decay functions for daily travel-to-work flows. Journal of Transport Geography 35, 107–119.

**Further reading**

Taylor, P. J. (1971).:Distance transformation and distance decay function. Geographical Analysis 3 (3), 221–238.