On logistic-normal distribution

Abstract

Existing distributions do not always provide an adequate fit to the complex real world data. Hence, the interest in developing more flexible statistical distributions remains strong in statistics profession. In this project, we present a family of generalized normal distributions, the T-normal family. We study in some details a member of the proposed family namely, the logistic-normal (LN) distribution. Some properties of the LN distribution including moments, tail behavior, and modes are examined. The distribution is symmetric and can be unimodal or bimodal. The tail of the LN distribution can be heavier or lighter than the tail of the normal distribution. The performance of the maximum likelihood estimators is evaluated through small simulation study. Two bimodal data sets are used to show the applicability of the LN distribution