Multivariate Cubic Transmuted Family of Distribution with Applications

Abstract

Multivariate distributions are useful in modeling several dependent random variables. It is difficult to develop a unique multivariate skewed distribution. There are different forms to the same distribution are available. For this reason, the research is ongoing into ways to construct multivariate families from univariate margins. In this paper, we have proposed a generalization of univariate cubic transmuted family to a multivariate family named a multivariate cubic transmuted (MCT) family. This new family applied to (p) baseline Weibull variables named multivariate cubic transmuted Weibull distribution (CTPW). Statistical properties of (CTPW) have been studied, and the parameters have been estimated by maximum likelihood (ML) method. A real data set for bone density test by photon absorption in the peripheral bones of olderly women fitted by (CTpW), trivariate transmuted Weibull (T3W) and FGMW distributions. The important theoretical conclusions are, the marginal distributions belong to multivariate cubic family with dimension less than p, joint moments of any order depend on raw moments of each baseline variable and moments of the largest order statistics of random samples of sizes two and three drawn from each baseline distribution. In real application, the (CT3W) is a better fit to bone density data.