Petrisor AI (2000), Empirical Spatial Distributions, Master thesis, Department of Epidemiology and Biostatistics, School of Public Health, University of South Carolina, Columbia, SC, USA, April 2000, 52 pp.

Master Thesis

BS, University of Bucharest, Romania

Empirical distributions are not strangers to the biostatistician, but binary spatial distributions constructed from random locations indexed by longitude and latitude might be. This study uses the longitude and latitude as the (X1, X2) coordinates of the homes of mothers in Spartanburg, SC who gave birth to their babies in either 1989 or 1990. Mathematically, the above coordinates have an arbitrary origin as well as arbitrary orientations of their axes. What difference does it make to change either the location of the origin or the orientation of axes? This question is herein addressed. Since empirical and theoretical cumulative distributions are unaffected in shape by translations, this study addresses the effects of those distributions by reorienting the axes.

The DAC statistic is the difference between the distribution of cases and that of population at a particular point (x1, x2), and its maximum value was chosen as the measure of effect of different orientation of axes. For any size of a random sample of locations taken from those of the 6434 plus live births there is a noticeable variation of the location of MaxDAC with rotations from 30 through 360 degrees within a given sample, when transformed back to original longitude and latitude. The orientations were incremented at intervals of 30 degrees. Furthermore, a simulation exercise indicated that the location of the Max DAC statistic is not unique, moreover there is a geometrical locus of it, and this varies as the orientation of the axes changes. Therefore, MaxDAC might not be the measure of choice when using empirical spatial distributions. Obviously, more and deeper investigations are the order of the day.