Next Article in Journal
Multi-Stage Change Point Detection with Copula Conditional Distribution with PCA and Functional PCA
Previous Article in Journal
Novel Parametric Solutions for the Ideal and Non-Ideal Prouhet Tarry Escott Problem
Article

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

1
Department of Statistics and Operations Research, University of Murcia, CEIR Campus Mare Nostrum, IMIB-Arrixaca, 30100 Murcia, Spain
2
Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur 208016, India
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(10), 1776; https://doi.org/10.3390/math8101776
Received: 3 September 2020 / Revised: 6 October 2020 / Accepted: 8 October 2020 / Published: 14 October 2020
(This article belongs to the Section Probability and Statistics Theory)
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. View Full-Text
Keywords: bivariate distribution generator; copula; reversed hazard gradient; maximum likelihood estimation; EM algorithm; multivariate distribution generator bivariate distribution generator; copula; reversed hazard gradient; maximum likelihood estimation; EM algorithm; multivariate distribution generator
Show Figures

Figure 1

MDPI and ACS Style

Franco, M.; Vivo, J.-M.; Kundu, D. A Generator of Bivariate Distributions: Properties, Estimation, and Applications. Mathematics 2020, 8, 1776. https://doi.org/10.3390/math8101776

AMA Style

Franco M, Vivo J-M, Kundu D. A Generator of Bivariate Distributions: Properties, Estimation, and Applications. Mathematics. 2020; 8(10):1776. https://doi.org/10.3390/math8101776

Chicago/Turabian Style

Franco, Manuel, Juana-María Vivo, and Debasis Kundu. 2020. "A Generator of Bivariate Distributions: Properties, Estimation, and Applications" Mathematics 8, no. 10: 1776. https://doi.org/10.3390/math8101776

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop