Distance-Based Methods: Ripley's K function vs. K density function

In this paper, we propose an analytical and methodological comparison between two of the most known distance-based methods in the evaluation of the geographic concentration of economic activity. These two methods are Ripley's K function, a cumulative function popularised by Marcon and Puech (2003) that counts the average number of neighbours of each point within a circle of a given radius, and K density function, a probability density function of point-pair distances introduced by Duranton and Overman (2005), which considers the distribution of distances between pairs of points. To carry out this comparison, we first apply both methodologies to an exhaustive database containing Spanish manufacturing establishments and we evaluate the spatial location patterns obtained from both analysis. After an initial analysis, we realise that although these functions have always been treated as substitutes they should be considered as complementary, as both cumulative function and probability density function provide relevant and necessary information about the distribution of activity in space. Therefore, our next step will be to assess what are the advantages and disadvantages of each methodology from a descriptive and analytical way.