Comparison of several Birnbaum–Saunders distributions

Cuizhen Niu, Xu Guo, Wangli Xu*, Lixing ZHU

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

12 Citations (Scopus)


Birnbaum–Saunders (BS) distribution is widely used in reliability applications to model failure times. For several samples from possible different BS distributions, to prevent wrong conclusions in any further analysis, it is of importance to accompany a formal comparison for characteristic quantities of the distributions, including mean, quantile and reliability function difference. To this end, two test statistics, which are respectively based on the exact generalized p-value approach and the Delta method, are proposed and their behaviours are investigated. Simulation studies are carried out to examine the size and power performance of the newly proposed statistics. An interesting phenomenon is that in the finite sample simulations we conduct, the Delta method-based test almost uniformly outperforms the generalized p-value-based testal though its sampling null distribution is simulated by Monte Carlo method. This might suggest that the sampling null distribution of the Delta method-based test statistic would have a fast convergence to its limit. The tests are also applied to analyse a real example on the fatigue life of 6061-T6 aluminium coupons for illustration.

Original languageEnglish
Pages (from-to)2721-2733
Number of pages13
JournalJournal of Statistical Computation and Simulation
Issue number12
Publication statusPublished - 2014

Scopus Subject Areas

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

User-Defined Keywords

  • Birnbaum–Saunders distribution
  • Delta method
  • Generalized p-value
  • Quantities comparison


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