Strong and weak approximations of k-spacings processes

Summary We obtain strong approximation results for the empirical process and the quantile process based on non-overlapping k-spacings using a characterization of uniform spacings in terms of independent exponential random variables. Moreover the weak convergence of these processes in /q-metrics is discussed. Applications to spacing statistics are included.Part of this research was done while the author was a visiting scientist at the Department of Mathematics and Statistics, Carleton University, supported by Canadian NSERC operating grant of M. Csörg. This research was also supported by a research grant of the Research Center of the College of Science, King Saud University