Multivariate Normal Variance Mixtures in R: The R Package nvmix

Abstract

We present the features and implementation of the R package nvmix for the class of normal variance mixtures including Student t and normal distributions. The package provides functionalities for such distributions, notably the evaluation of the distribution and density function as well as likelihood-based parameter estimation. The distributional family is specified through the quantile function of the underlying mixing random variable. The R package nvmix thus allows one to model multivariate distributions well beyond the classical multivariate normal and t case. Additional functionalities include graphical goodness-of-fit assessment, the estimation of the risk measures value-at-risk and expected shortfall for univariate normal variance mixture distributions and functions to work with normal variance mixture copulas, such as sampling and the evaluation of normal variance mixture copulas and their densities. Furthermore, the package nvmix also provides func-tionalities for the evaluation of the distribution and density function as well as random variate generation for the more general class of grouped normal variance mixtures.