A Generator of Bivariate Distributions: Properties, Estimation, and Applications

Manuel Franco, Juana-Maria Vivo and Debasis Kundu
Additional contact information
Manuel Franco: Department of Statistics and Operations Research, University of Murcia, CEIR Campus Mare Nostrum, IMIB-Arrixaca, 30100 Murcia, Spain
Debasis Kundu: Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur 208016, India

Mathematics, 2020, vol. 8, issue 10, 1-30

Abstract: In 2020, El-Morshedy et al. introduced a bivariate extension of the Burr type X generator (BBX-G) of distributions, and Muhammed presented a bivariate generalized inverted Kumaraswamy (BGIK) distribution. In this paper, we propose a more flexible generator of bivariate distributions based on the maximization process from an arbitrary three-dimensional baseline distribution vector, which is of interest for maintenance and stress models, and expands the BBX-G and BGIK distributions, among others. This proposed generator allows one to generate new bivariate distributions by combining non-identically distributed baseline components. The bivariate distributions belonging to the proposed family have a singular part due to the latent component which makes them suitable for modeling two-dimensional data sets with ties. Several distributional and stochastic properties are studied for such bivariate models, as well as for its marginals, conditional distributions, and order statistics. Furthermore, we analyze its copula representation and some related association measures. The EM algorithm is proposed to compute the maximum likelihood estimations of the unknown parameters, which is illustrated by using two particular distributions of this bivariate family for modeling two real data sets.

Keywords: bivariate distribution generator; copula; reversed hazard gradient; maximum likelihood estimation; EM algorithm; multivariate distribution generator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/10/1776/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/10/1776/ (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:8:y:2020:i:10:p:1776-:d:427811

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 ().