Generalized order statistics: An exponential family in model parameters

Stefan Bedbur*, Eric Beutner, Udo Kamps

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review


Generalized order statistics, and thus sequential order statistics with conditional proportional hazard rates, are shown to form a regular exponential family in the model parameters. This structure is utilized to derive maximum likelihood estimators for these parameters or functions of them along with several properties of the estimators. The Fisher information matrix is stated, and asymptotic efficiency is shown.

Original languageEnglish
Pages (from-to)159-166
Number of pages8
Issue number2
Publication statusPublished - 1 Apr 2012
Externally publishedYes


  • asymptotic efficiency
  • conditional proportional hazard rates
  • Fisher information matrix
  • maximum likelihood estimation
  • regular exponential family
  • sequential k-out-of-n system
  • sequential order statistics
  • uniformly minimum variance unbiased estimation


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