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AIMS Mathematics

2022, Volume 7, Issue 8: 15584-15611. doi: 10.3934/math.2022854
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Research article

Some bivariate and multivariate families of distributions: Theory, inference and application

  • 1.
    Department of Statistics, College of Science, University of Jeddah, Jeddah, Saudi Arabia
  • 2.
    Department of Statistics, College of Science, King Abdulaziz University, Jeddah, Saudi Arabia
  • Received: 11 April 2022 Revised: 09 June 2022 Accepted: 16 June 2022 Published: 23 June 2022

  • MSC : 62D05, 62G30, 62P99

  • The bivariate and multivariate probability distributions are useful in joint modeling of several random variables. The development of bivariate and multivariate distributions is relatively tedious as compared with the development of univariate distributions. In this paper we have proposed a new method of developing bivariate and multivariate families of distributions from the univariate marginals. The properties of the proposed families of distributions have been studies. These properties include marginal and conditional distributions; product, ratio and conditional moments; joint reliability function and dependence measures. Statistical inference about the proposed families of distributions has also been done. The proposed bivariate family of distributions has been studied for Weibull baseline distribution giving rise to a new bivariate Weibull distribution. The properties of the proposed bivariate Weibull distribution have been studied alongside maximum likelihood estimation of the unknown parameters. The proposed bivariate Weibull distribution has been used for modeling of real bivariate data sets and we have found that the proposed bivariate Weibull distribution has been a suitable choice for the modeling of data used.

    Citation: Jumanah Ahmed Darwish, Saman Hanif Shahbaz, Lutfiah Ismail Al-Turk, Muhammad Qaiser Shahbaz. Some bivariate and multivariate families of distributions: Theory, inference and application[J]. AIMS Mathematics, 2022, 7(8): 15584-15611. doi: 10.3934/math.2022854

    Related Papers:

  • The bivariate and multivariate probability distributions are useful in joint modeling of several random variables. The development of bivariate and multivariate distributions is relatively tedious as compared with the development of univariate distributions. In this paper we have proposed a new method of developing bivariate and multivariate families of distributions from the univariate marginals. The properties of the proposed families of distributions have been studies. These properties include marginal and conditional distributions; product, ratio and conditional moments; joint reliability function and dependence measures. Statistical inference about the proposed families of distributions has also been done. The proposed bivariate family of distributions has been studied for Weibull baseline distribution giving rise to a new bivariate Weibull distribution. The properties of the proposed bivariate Weibull distribution have been studied alongside maximum likelihood estimation of the unknown parameters. The proposed bivariate Weibull distribution has been used for modeling of real bivariate data sets and we have found that the proposed bivariate Weibull distribution has been a suitable choice for the modeling of data used.


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