We give a complete description of the rate of strong consistency of the scaled and unscaled total time on test curves, which are fundamental notions in the statistical theory of reliability and life testing. The proof is crucially based on the general Vervaat process.

For at least a century academics and governmental researchers have been developing measures that would aid them in understanding income distributions, their differences with respect to geographic regions, and changes over time periods. It is a challenging area due to a number of reasons, one of...

It is well known that, asymptotically, the appropriately normalized Vervaat process behaves like one half times the squared empirical process. Considering these two processes as elements of the Lp-space, 1[less-than-or-equals, slant]p[infinity], we give a complete description of the strong and...