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This paper considers the inference on the common mean and medians of a bivariate lognormal distribution. We propose point and interval estimators of the common mean in closed form. We derive confidence intervals of the common mean using the maximum likelihood method, generalized variable approach, method of variance estimate recovery and highest posterior density. The generalized confidence interval of the common mean under missing observations is also obtained. We obtain confidence limits for the difference of medians using first three techniques of interval estimation of the common mean and two bootstrap approaches. The coverage probability and expected length are used to assess the performance of the intervals. The proposed methodologies are exemplified through real-life data sets related to immunology, road accidents and vaccination programmes.

Interval estimation of the common mean and difference of medians for a bivariate lognormal distribution