Nonparametric tolerance intervals controlling percentages in both tails and simultaneous testing of quantiles

Gboyega Adepoju and K. Krishnamoorthy

Journal of Applied Statistics, 2026, vol. 53, issue 3, 510-519

Abstract: The problem of constructing nonparametric equal-tailed tolerance intervals is considered. A method for finding minimum sample size required so that the rth order statistic and the largest rth order statistic form a p content– $ (1-\alpha ) $ (1−α) coverage equal-tailed tolerance interval is proposed. A simultaneous test for quantiles is also provided. Minimum sample sizes that are required to construct equal-tailed TIs and those to carry out hypothesis tests at a given nominal level are presented. The methods are illustrated using data collected from a new secure messaging system.

Date: 2026
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DOI: 10.1080/02664763.2025.2520339

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