Multivariate testing and model-checking for generalized order statistics with applications

Stefan Bedbur*, Eric Beutner, Udo Kamps

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

The exponential family structure of the joint distribution of generalized order statistics is utilized to establish multivariate tests on the model parameters. For simple and composite null hypotheses, the likelihood ratio test (LR test), Wald's test, and Rao's score test are derived and turn out to have simple representations. The asymptotic distribution of the corresponding test statistics under the null hypothesis is stated, and, in case of a simple null hypothesis, asymptotic optimality of the LR test is addressed. Applications of the tests are presented; in particular, we discuss their use in reliability, and to decide whether a Poisson process is homogeneous. Finally, a power study is performed to measure and compare the quality of the tests for both, simple and composite null hypotheses.

Original languageEnglish
Pages (from-to)1297-1310
Number of pages14
JournalStatistics
Volume48
Issue number6
DOIs
Publication statusPublished - 25 Nov 2014
Externally publishedYes

Keywords

  • conditional proportional hazard rate
  • k-out-of-n system
  • order statistic
  • Pfeifer record value
  • record value
  • sequential order statistic

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