Ordering properties of the TTT-plot of lifetimes with Schur joint densities
type: Item
instance of: scholarly article
title: Ordering properties of the TTT-plot of lifetimes with Schur joint densities
zbMATH Open document ID: 0915.62083
DOI: 10.1016/S0167-7152(98)00021-2
published in: Statistics \& Probability Letters
publication date: 1999-03-02T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 62N05
Mathematics Subject Classification ID: 62G30
zbMATH DE Number: 1228702
zbMATH Keywords: TTT-plot
zbMATH Keywords: Schur densities
zbMATH Keywords: normalized spacings between order statistics
zbMATH Keywords: multivariate stochastic orderings
zbMATH Keywords: empirical total time on test process
author: Giovanna Nappo
author: F. Spizzichino
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1228702