Ordering properties of the TTT-plot of lifetimes with Schur joint densities
We study the law of scaled empirical total time on test (TTT)-plots of exchangeable lifetimes. By means of very simple arguments, we prove a monotonicity property in the case of absolutely continuous distributions with Schur-concave (or Schur-convex) densities. A stochastic comparison between the laws of TTT-plots for i.i.d. exponential variables and for Schur-concave (or Schur-convex) densities follows as a direct consequence. This can be seen as a natural analogue of a well-known fact valid for the case of i.i.d. lifetimes with monotone failure rates. It is remarkable that a stochastic comparison is even obtained in the likelihood ratio ordering sense. Note added in proof: When writing this paper we were not aware of the article of \textit{S. C. Kochar} and \textit{S. N. U. A. Kirmani} [J. Stat. Plann. Inference 46, No. 1, 47-57 (1995; Zbl 0822.62081)]. In this paper they prove a result linked to ours.
normalized spacings between order statistics
scientific article; zbMATH DE number 1228702