New Regression Models Based on the Unit-Sinh-Normal Distribution: Properties, Inference, and Applications

In this paper, two new distributions were introduced to model unimodal and/or bimodal data. The first distribution, which was obtained by applying a simple transformation to a unit-Birnbaum-Saunders random variable, is useful for modeling data with positive support, while the second is appropriate for fitting data on the (0,1) interval. Extensions to regression models were also studied in this work, and statistical inference was performed from a classical perspective by using the maximum likelihood method. A small simulation study is presented to evaluate the benefits of the maximum likelihood estimates of the parameters. Finally, two applications to real data sets are reported to illustrate the developed methodology.

Automated summary

This paper introduces two new distributions for modeling data, suitable for data with positive support and data on the (0,1) interval. The extensions to regression models were studied, and statistical inference was conducted using the maximum likelihood method. A small simulation study and applications to real data sets were used to evaluate the effectiveness of the methodology.