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Ordering properties of the TTT-plot of lifetimes with Schur joint densities

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  • Nappo, G.
  • Spizzichino, F.

Abstract

In this note we study the law of scaled empirical 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.

Suggested Citation

  • Nappo, G. & Spizzichino, F., 1998. "Ordering properties of the TTT-plot of lifetimes with Schur joint densities," Statistics & Probability Letters, Elsevier, vol. 39(3), pages 195-203, August.
    • Handle: RePEc:eee:stapro:v:39:y:1998:i:3:p:195-203
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    Cited by:

    1. Chu, Yu-Ming & Xia, Wei-Feng & Zhang, Xiao-Hui, 2012. "The Schur concavity, Schur multiplicative and harmonic convexities of the second dual form of the Hamy symmetric function with applications," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 412-421.

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