Inference for multivariate bounded data with mass at zero

Multivariate bounded data with clumping at one or both end points of the domain are present in many fields of science such as in microbiome data and in economics where data maybe presented in the form of proportions. In general, any compositional data will fall under the jurisdiction of multivariate bounded data. In this study, we propose the use of copula with marginals that follow the so called Kumaraswamy distribution to model data that are bounded between zero and one and have clumping at zero (a mass at zero). We use Gaussian and FRank copulae to illustrate the method and we employ maximum likelihood estimators to estimate the parameters of the model. We perform Monte Carlo simulations to assess the performance of the proposed methods and illustrate the use of these methods on real data.