Confidence interval estimation for negative binomial group distribution

Wei Yu, Wangli Xu*, Lixing ZHU

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

Abstract

Negative binomial group distribution was proposed in the literature which was motivated by inverse sampling when considering group inspection: products are inspected group by group, and the number of non-conforming items of a group is recorded only until the inspection of the whole group is finished. The non-conforming probability p of the population is thus the parameter of interest. In this paper, the confidence interval construction for this parameter is investigated. The common normal approximation and exact method are applied. To overcome the drawbacks of these commonly used methods, a composite method that is based on the confidence intervals of the negative binomial distribution is proposed, which benefits from the relationship between negative binomial distribution and negative binomial group distribution. Simulation studies are carried out to examine the performances of our methods. A real data example is also presented to illustrate the application of our method.

Original languageEnglish
Pages (from-to)524-534
Number of pages11
JournalJournal of Statistical Computation and Simulation
Volume86
Issue number3
DOIs
Publication statusPublished - 11 Feb 2016

Scopus Subject Areas

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

User-Defined Keywords

  • confidence interval
  • negative binomial distribution
  • negative binomial group distribution
  • weighted method

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