Exact nonparametric confidence, prediction and tolerance intervals based on multi-sample Type-II right censored data

William Volterman, N. Balakrishnan

Research output: Contribution to journalArticle

12 Scopus citations

Abstract

Exact nonparametric inference based on ordinary Type-II right censored samples has been extended here to the situation when there are multiple samples with Type-II censoring from a common continuous distribution. It is shown that marginally, the order statistics from the pooled sample are mixtures of the usual order statistics with multivariate hypergeometric weights. Relevant formulas are then derived for the construction of nonparametric confidence intervals for population quantiles, prediction intervals, and tolerance intervals in terms of these pooled order statistics. It is also shown that this pooled-sample approach assists in achieving higher confidence levels when estimating large quantiles as compared to a single Type-II censored sample with same number of observations from a sample of comparable size. We also present some examples to illustrate all the methods of inference developed here.

Original languageEnglish (US)
Pages (from-to)3306-3316
Number of pages11
JournalJournal of Statistical Planning and Inference
Volume140
Issue number11
DOIs
StatePublished - Nov 1 2010

Keywords

  • Maximum coverage probability
  • Minimum-width confidence interval
  • Mixtures
  • Multivariate hypergeometric distribution
  • Nonparametric confidence intervals
  • Nonparametric prediction intervals
  • Nonparametric tolerance intervals
  • Pooled sample
  • Type-II right censoring

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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