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Likelihood‐based confidence intervals for a log‐normal mean
Author(s) -
Wu Jianrong,
Wong A. C. M.,
Jiang Guoyong
Publication year - 2003
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.1381
Subject(s) - statistics , confidence interval , mathematics , likelihood ratio test , likelihood principle , coverage probability , maximum likelihood , interval (graph theory) , likelihood function , combinatorics , quasi maximum likelihood
To construct a confidence interval for the mean of a log‐normal distribution in small samples, we propose likelihood‐based approaches – the signed log‐likelihood ratio and modified signed log‐likelihood ratio methods. Extensive Monte Carlo simulation results show the advantages of the modified signed log‐likelihood ratio method over the signed log‐likelihood ratio method and other methods. In particular, the modified signed log‐likelihood ratio method produces a confidence interval with a nearly exact coverage probability and highly accurate and symmetric error probabilities even for extremely small sample sizes. We then apply the methods to two sets of real‐life data. Copyright © 2003 John Wiley & Sons, Ltd.