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# A new multivariate transmuted family of distributions: theory and application for modelling of daily world COVID-19 cases

#### JA Darwish,

##### University of Jeddah, SA
Department of Statistics, College of Science

#### LI Al-Turk,

##### King Abdulaziz University, SA
Department of Statistics, College of Science

#### MQ Shahbaz

##### King Abdulaziz University, SA
Department of Statistics, College of Science

## Abstract

Multivariate distributions are helpful in the simultaneous modeling of several dependent random variables. The development of a unique multivariate distribution has been a difficult task and different multivariate versions of the same distribution are available. The need is, therefore, to suggest a method of obtaining a multivariate distribution from the univariate marginals. In this paper, we have proposed a new method of generating the multivariate families of distributions when information on univariate marginals is available. Specifically, we have proposed a multivariate family of distributions which provides a univariate transmuted family of distributions as marginal. The proposed family is a re-parameterization of the Cambanis (1977) family. Some properties of the proposed family of distributions have been studied. These properties include marginal and joint marginal distributions, conditional distributions, and marginal and conditional moments. We have also obtained the dependence measures alongside the maximum likelihood estimation of the parameters. The proposed multivariate family of distributions is studied for the Weibull baseline distributions giving rise to the multivariate transmuted Weibull (MTW) distribution. Real data application of the proposed MTW distribution is given in the context of modeling the daily COVID-19 cases of the World. It is observed that the proposed MTW distribution is a suitable fit for the joint modeling of the COVID-19 data.

##### Keywords: Transmuted distributions,Multivariate T–X family of distributions,Dependence functions,Maximum likelihood estimation,Weibull Distribution
How to Cite: Darwish, J., Al-Turk, L. and Shahbaz, M., 2022. A new multivariate transmuted family of distributions: theory and application for modelling of daily world COVID-19 cases. Journal of the National Science Foundation of Sri Lanka, 50(4), pp.771–784. DOI: http://doi.org/10.4038/jnsfsr.v50i4.10621
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