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This paper provides three different estimators for Pr(X < Y) when X and Y have a bivariate exponential distribution. The asymptotic variances of the three estimators are also derived. A test for the equality of the means of X and Y and confidence limits for the difference of the two means are presented. Our results are directly applicable in a reliability context with underlying bivariate exponential distribution.

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In this paper the problem of interest is the bioequivalence metrics and their role in assessing the rate and extent of absorption ratios of two drug formulations. Several bioequivalence metrics were proposed by several authors in the literature to estimate the similarity or dissimilarity of two drug formulations. The existing bioequivalence metrics are reviewed. A new bioequivalence metric is proposed and motivated. The performance, in terms of the statistical power, of the previously proposed and the new bioequivalence metrics is also evaluated by simulating cross-over bioequivalence trials.

This article generalizes a characterization based on a truncated mean to include higher truncated moments, and introduces a new normality goodness-of-fit test based on the truncated mean. The test is a weighted integral of the squared distance between the empirical truncated mean and its expectation. A closed form for the test statistic is derived. Assuming known parameters, the mean and the variance of the test are derived under the normality assumption. Moreover, a limiting distributionfor the proposed test as well as an approximation are obtained. Also, based on Monte Carlo simulations, the power of the test is evaluated against stable, symmetric, and skewed classes of distributions. The test proves compatibility with prominent tests and shows higher power for a wide range of alternatives.