Lower confidence bounds for percentiles of weibull and birnbaum-saunders distributions

Approximate lower confidence bounds on percentiles of the Weibull and the Birnbaum-Saunders distributions are investigated. Asymptotic lower confidence bounds based on Bonferroni's inequality and the Fisher information are discussed, and parametric bootstrap methods to provide better bounds are considered. Since the standard percentile bootstrap method typically does not perform well for confidence bounds on quantiles, several other bootstrap procedures are studied via extensive computer simulations. Results of the simulations indicate that the bootstrap methods generally give sharper lower bounds than the Bonferroni bounds but with coverages still near the nominal confidence level. Two illustrative examples are also presented, one for tensile strength of carbon micro-composite specimens and the other for cycles-to-failure data.

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