TY - JOUR
T1 - Comparison of several Birnbaum–Saunders distributions
AU - Niu, Cuizhen
AU - Guo, Xu
AU - Xu, Wangli
AU - Zhu, Lixing
N1 - Funding Information:
The research was supported by the Fundamental Research Funds for the Central Universities and the Research Funds of Renmin University of China (No. 12XNI004). The authors thank a referee for the constructive comments and suggestions.
Publisher Copyright:
© 2014 Taylor & Francis.
PY - 2014
Y1 - 2014
N2 - 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.
AB - 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.
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U2 - 10.1080/00949655.2014.881814
DO - 10.1080/00949655.2014.881814
M3 - Article
AN - SCOPUS:84893191005
SN - 0094-9655
VL - 84
SP - 2721
EP - 2733
JO - Journal of Statistical Computation and Simulation
JF - Journal of Statistical Computation and Simulation
IS - 12
ER -