Confidence intervals for the mode of a lognormal distribution

Lognormally distributed data has recently appeared in a large amount of literature on confidence interval construction because they are generally regarded as more informative than significance tests for the reason that they provide a range of parameter values that reflect the degree of uncertainty in the estimation procedure. Nowadays, the amount of work involving inference on the mode is relatively limited. In this thesis, we proposed a new aspect of confidence interval construction for the lognormal mode. We compare all the proposed approaches which are based on the maximum likelihood (MAX) approach, the asymptotic normal approximation based on the delta method (NAD), the Method of Variance Estimates Recovery (MOVER), and the generalized confidence interval (GCI) approach in terms of average coverage probability (CP) and average length (AL). The simulation results showed that the GCI-M approach is appropriated for sample sizes ranging from small to large. Meanwhile, MOV-M approach is appropriated for sample sizes ranging from moderate to large. When sample sizes are large, the coverage probabilities of MAX-M and NAD-M approaches are close to the nominal confidence level of 0.95. This corresponds to the central limit theorem. Although the GCI-M approach provided the coverage probabilities close to the nominal confidence level of 0.95 by comparing to other methods. However, the average length of the GCI-M perform well only in the case of large variance with the reason that gives the shortest average length. When variance are small, NAD-M is recommended for the reason that the average length is short. The results also show that the average length of all methods decrease if the sample sizes are increased.Real-life medical and environmental data were used to confirm the effectiveness of the proposed methods. The result was found to be extremely consistent with the real data.