A Flexible Class of Two-Piece Normal Distribution with a Regression Illustration to Biaxial Fatigue Data

Abstract

Using a two-piece normal distribution for modeling univariate data that exhibits symmetry, and uni/bimodality is notably effective. In this respect, the shape parameter value determines whether unimodality or bimodality is present. This paper proposes a flexible uni/bimodal distribution with platykurtic density, which can be used to simulate a variety of data. The concept is based on the transforming of a random variable into a folded distribution. Further, the proposed class includes the normal distribution as a sub-model. In the current study, the maximum likelihood method is considered for deriving the main structural properties and for the estimation of parameters. In addition, simulation experiments are presented to evaluate the behavior of estimators. Finally, fitting and regression applications are presented to illustrate the usefulness of the proposed distribution for data modeling in different real-life scenarios.