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Comparing the means and variances of a bivariate log‐normal distribution
Author(s) -
Bebu Ionut,
Mathew Thomas
Publication year - 2007
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.3080
Subject(s) - confidence interval , statistics , mathematics , bivariate analysis , cdf based nonparametric confidence interval , sample size determination , likelihood ratio test , equivalence (formal languages) , coverage probability , confidence distribution , binomial proportion confidence interval , multivariate normal distribution , confidence region , robust confidence intervals , monte carlo method , credible interval , tolerance interval , multivariate statistics , negative binomial distribution , discrete mathematics , poisson distribution
For a bivariate log‐normal distribution, a confidence interval is developed for the ratio of the means. The generalized confidence interval approach is used for this purpose, and the procedure is applicable regardless of the sample size. It is also noted that the same approach can be used to obtain a confidence interval for the ratio of the variances. A modified signed log‐likelihood ratio procedure is also described for computing confidence intervals. The coverage probabilities of the proposed confidence intervals are estimated by Monte Carlo, and the generalized confidence intervals are found to exhibit satisfactory performance even for small sample sizes. Numerical results also show that the corresponding test procedures provide larger power compared with the modified signed log‐likelihood ratio test. Two examples are given: one dealing with the comparison of the means and variances of health‐care costs and the other dealing with testing mean equivalence in quantitative assays. Copyright © 2007 John Wiley & Sons, Ltd.