Nonhomogeneous Poisson processes and logconcavity

In this article, we identify conditions under which the epoch times and the inter-epoch intervals of a nonhomogeneous Poisson process have logconcave densities. The results are extended to relevation counting processes, We al so study discrete-time counting processes and find conditions under which t he epoch times and the inter-epoch intervals of these discrete-time process es have logconcave discrete probability densities. The results are interpre ted in terms of minimal repair and record values. Several examples illustra te the theory.