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

Hugo Salinas, Hassan Bakouch, Najla Qarmalah () and Guillermo Martínez-Flórez
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Hugo Salinas: Departamento de Matemática, Facultad de Ingeniería, Universidad de Atacama, Copiapó 7500015, Chile
Hassan Bakouch: Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
Najla Qarmalah: Department of Mathematical Sciences, Princess Nourah Bint Abdulrahman University, Riyadh 11671, Saudi Arabia
Guillermo Martínez-Flórez: Departamento de Matemáticas y Estadística, Facultad de Ciencias Básicas, Universidad de Córdoba, Montería 230002, Colombia

Mathematics, 2023, vol. 11, issue 5, 1-14

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.

Keywords: biaxial fatigue data; folded normal distribution; statistical model; simulation; kurtosis; ultrasound weight data; uni/bimodal distribution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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