Right spread order of the second-order statistic from heterogeneous exponential random variables

Peng Zhao, Xiaohu Li, Gaofeng Da

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

Let X1,..., Xn be independent exponential random variables with respective hazard rates λ1,..., λn, and Y1,..., Yn be i.i.d. exponential random variables with common hazard rate λ. It is proved that X 2:n, the second order statistic from X1,..., X n, is larger than Y2:n, the second order statistic from Y1,...,Yn, with respect to the right spread order if and only if λ≥2n-1/n(n-1)(Σi=1n1/∧-n-1/ ∧(1)) with ∧(1) and Σi=1nλ i and ∧i = ∧(1) - λi, and X 2:n is smaller than Y2:n with respect to the right spread order if and only if λ ≤ Σi=1n - max 1≤i≤nλi/n-1 Further, the case with proportional decreasing hazard rate is also studied, and the results obtained here form nice extensions to some corresponding ones known in the literature.

Original languageEnglish
Pages (from-to)3070-3081
Number of pages12
JournalCommunications in Statistics - Theory and Methods
Volume40
Issue number17
DOIs
StatePublished - Jan 2011

Keywords

  • Hazard rate order
  • Likelihood ratio order
  • MRL order
  • Majorization order
  • Order statistics
  • p-Larger order

Fingerprint

Dive into the research topics of 'Right spread order of the second-order statistic from heterogeneous exponential random variables'. Together they form a unique fingerprint.

Cite this