Statistical Estimation of Mean of Delta-Lognormal Distribution

Abstract

In this article, we propose the following approaches derive from the method of variance estimate recovery based on the variance-stabilizing transformation (MOVER-VST), Wilson score (MOVER-Wilson) and Jeffreys (MOVER-Jeffreys) compared with the generalized confidence interval (GCI) to develop the statistical estimation being confidence intervals for single and difference between two means in delta-lognormal distribution. Monte Carlo simulation is used as a technique to evaluate the performance of these confidence intervals in terms of coverage probability and average length. In simulation study, the numerical results of single mean showed that the MOVER-VST and MOVER-Wilson can be considered as the recommended CIs to estimate the delta-lognormal mean in the important cases. For the difference between two delta-lognormal means, numerical computation indicated that the MOVER-Jeffreys achieved the given target when the dispersion was not large for the large probability of additional zero. For application, we illustrate the presented confidence intervals with real world data sets in several fields: the airborne chlorine record for environmental problem, the red cod density for fishery survey and the distance traveled of mice for biology.