This chapter studies the joint distribution of equivalised household income (eHI) in a country over a sequence of years. The relevant data is from the longitudinal part of the European Union Statistics on Income and Living Conditions (EU-SILC). The study complements Chapter 4, where we studied the univariate distributions of eHI for the separate years, and Chapter 6, where we studied transitions between poverty states in consecutive years. Among classes of multivariate distributions, the normal has no competitor with its tractability, completeness of covariance structures and our understanding of its properties. We consider the multivariate normal distributions as the basis of mixtures for describing the joint distribution of log-eHI over the four years of a panel. We describe the EM algorithm for fitting mixtures, devise methods for summarising the fit and compare the results for the countries in EU-SILC.

The multivariate normal distribution is defined by the density