Interval Estimation Methods for the Variance of a Lognormal Model with Zero Inflation and Their Applications

Data on natural rainfall and fish density often exhibit positively right-skewed distributions and include zero observations, thus making them fit a lognormal model with zero inflation. Estimation methods for the variance of a lognormal model with zero inflation using the modified Fletcher (MFL) interval, the generalized confidence interval, and the method of variance estimate recovery are derived herein. The coverage rates and average widths of the proposed methods were assessed via Monte Carlo simulation. Numerical results reveal that the MFL satisfied the requirements for handling large variances, even in situations where the proportion of zero data items was high. Natural rainfall and fish density and data are used to illustrate the efficacies of the proposed methods for estimating rainfall and fish dispersion, respectively.