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. © 2022, National Science Foundation. All rights reserved.
ABSTRACT
Statistical methodologies have broader applications in almost every sector of life including education, hydrology, reliability, management, and healthcare sciences. Among these sectors, statistical modeling and predicting data in the healthcare sector is very crucial. In this paper, we introduce a new method, namely, a new extended exponential family to update the distributional flexibility of the existing models. Based on this approach, a new version of the Weibull model, namely, a new extended exponential Weibull model is introduced. The applicability of the new extended exponential Weibull model is shown by considering two data sets taken from the health sciences. The first data set represents the mortality rate of the patients infected by the coronavirus disease 2019 (COVID-19) in Mexico. Whereas, the second set represents the mortality rate of COVID-19 patients in Holland. Utilizing the same data sets, we carry out forecasting using three machine learning (ML) methods including support vector regression (SVR), random forest (RF), and neural network autoregression (NNAR). To assess their forecasting performances, two statistical accuracy measures, namely, root mean square error (RMSE) and mean absolute error (MAE) are considered. Based on our findings, it is observed that the RF algorithm is very effective in predicting the death rate of the COVID-19 data in Mexico. Whereas, for the second data, the SVR performs better as compared to the other methods.