A new skew-bimodal distribution with applications

ABSTRACT

The modeling and analysis of experiments is an important aspect of statistical work in a wide variety of scientific and technological fields. We introduce and study the odd log-logistic skew-normal model, which can be interpreted as a generalization of the skew-normal distribution. The new distribution can be used effectively in the analysis of experiments data since it accommodates unimodal, bimodal, symmetric, bimodal and right-skewed, and bimodal and left-skewed density function depending on the parameter values. We illustrate the importance of the new model by means of three real data sets in analysis of experiments.

KEYWORDS:

• Log-logistic distribution
• maximum-likelihood estimation
• mean deviation
• skew bimodality
• skew distribution.

Acknowledgments

We are very grateful to a referee and an associate editor for helpful comments that considerably improved the paper. We gratefully acknowledge financial support from CAPES and CNPq.