Providing a new distribution is always precious for statisticians. A new three-parameter model called the odd log-logistic normal (OLLN) distribution is defined and studied. The distribution is symmetric, platykurtic, leptokurtic, and may be unimodal or bimodal. Various structural properties are derived, including explicit expressions for the ordinary and incomplete moments, generating function, and mean deviations. We use maximum likelihood to estimate the parameters of the new model. We prove empirically that the proposed distribution is a very competitive model to other classical models by means of three real data sets with one example in analysis of experiments. We can conclude that this model can give more realistic fits than other special regression models.
Financed by the National Centre for Research and Development under grant No. SP/I/1/77065/10 by the strategic scientific research and experimental development program:
SYNAT - “Interdisciplinary System for Interactive Scientific and Scientific-Technical Information”.