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

Author

Listed:
  • 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
    Department of Mathematics, Faculty of Science, Tanta University, Tanta 31111, Egypt)

  • 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)

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.

Suggested Citation

  • Hugo Salinas & Hassan Bakouch & Najla Qarmalah & Guillermo Martínez-Flórez, 2023. "A Flexible Class of Two-Piece Normal Distribution with a Regression Illustration to Biaxial Fatigue Data," Mathematics, MDPI, vol. 11(5), pages 1-14, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:5:p:1271-:d:1089054
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    References listed on IDEAS

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    1. Michelli Barros & Manuel Galea & Manuel González & Víctor Leiva, 2010. "Influence diagnostics in the tobit censored response model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(3), pages 379-397, August.
    2. Ortega, Edwin M. M. & Bolfarine, Heleno & Paula, Gilberto A., 2003. "Influence diagnostics in generalized log-gamma regression models," Computational Statistics & Data Analysis, Elsevier, vol. 42(1-2), pages 165-186, February.
    3. Shuo Wang & Wangxue Chen & Meng Chen & Yawen Zhou, 2023. "Maximum likelihood estimation of the parameters of the inverse Gaussian distribution using maximum rank set sampling with unequal samples," Mathematical Population Studies, Taylor & Francis Journals, vol. 30(1), pages 1-21, January.
    4. Guillermo Martínez-Flórez & Heleno Bolfarine & Héctor W. Gómez, 2017. "The Log-Linear Birnbaum-Saunders Power Model," Methodology and Computing in Applied Probability, Springer, vol. 19(3), pages 913-933, September.
    5. Milton A. Cortés & David Elal-Olivero & Juan F. Olivares-Pacheco, 2018. "A New Class of Distributions Generated by the Extended Bimodal-Normal Distribution," Journal of Probability and Statistics, Hindawi, vol. 2018, pages 1-10, November.
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