The distribution of the domination number of class cover catch digraphs for non-uniform one-dimensional data

For two or more classes of points in RdRd with d≥1d≥1, the class cover catch digraphs (CCCDs) can be constructed using the relative positions of the points from one class with respect to the points from one or all of the other classes. The CCCDs were introduced by Priebe et al. [C.E. Priebe, J.G. DeVinney, D.J. Marchette, On the distribution of the domination number of random class catch cover digraphs. Statistics and Probability Letters 55 (2001) 239–246] who investigated the case of two classes, XX and YY. They calculated the exact (i.e., finite sample) distribution of the domination number of the CCCDs based on XX points relative to YY points both of which were uniformly distributed on a bounded interval. We investigate the distribution of the domination number of the CCCDs based on data from non-uniform XX points on an interval with end points from YY. Then we extend these calculations for multiple YY points on bounded intervals.