A general SLLN for the one-dimensional class cover problem

Abstract

The class cover catch digraph (CCCD) is motivated by applications in statistical pattern classification. For the special case of uniformly distributed data in one dimension, Priebe et al. [Priebe, C.E., DeVinney, J.G., Marchette, D.J., 2001. On the distribution of the domination number for random class cover catch digraphs. Statist. Probab. Lett. 55, 239–246] found the exact distribution of the domination number of the random data-induced CCCD, and DeVinney and Wierman [DeVinney, J.G., Wierman, J.C., 2002. A SLLN for a one-dimensional class cover problem. Statist. Probab. Lett. 59, 425–435] proved the Strong Law of Large Numbers (SLLN). This paper proves the generalized SLLN for the domination number of CCCDs for non-uniform data in one dimension.