The Bivariate Unit-Sinh-Normal Distribution and Its Related Regression Model

Guillermo Martínez-Flórez (), Artur J. Lemonte (), Germán Moreno-Arenas and Roger Tovar-Falón ()
Additional contact information
Guillermo Martínez-Flórez: Departamento de Matemáticas y Estadística, Facultad de Ciencias Básicas, Universidad de Córdoba, Monteria 230002, Colombia
Artur J. Lemonte: Departamento de Estatística, Universidade Federal do Rio Grande do Norte, Natal 59078970, RN, Brazil
Germán Moreno-Arenas: Escuela de Matemáticas, Universidad Industrial de Santander, Bucaramanga 680006, Colombia
Roger Tovar-Falón: Departamento de Matemáticas y Estadística, Facultad de Ciencias Básicas, Universidad de Córdoba, Monteria 230002, Colombia

Mathematics, 2022, vol. 10, issue 17, 1-26

Abstract: In this paper, a new bivariate absolutely continuous probability distribution is introduced. The new distribution, which is called the bivariate unit-sinh-normal (BVUSHN) distribution, arises by applying a transformation to the bivariate Birnbaum–Saunders distribution (BVBS). The main properties of the new proposal are studied in detail. In addition, from the new distribution, the BVUSHN regression model is also introduced. For both the bivariate probability distribution and the respective associated regression model, parameter estimation is conducted from a classical approach by using the maximum likelihood method together with the two-step estimation method. A small Monte Carlo simulation study is carried out to evaluate the behavior of the used estimation method and the properties of the estimators. Finally, for illustrative purposes, two applications with real data are presented in which the usefulness of the proposals is evidenced.

Keywords: multivariate probability distribution; regression model for bounded data; proportion data; two-step estimation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/17/3125/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/17/3125/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:17:p:3125-:d:902925

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().