IBioStat edition:2015 location:Hasselt (Belgium) date:30 January 2015
We study the estimation and use of multivariate mixtures of Erlang distributions (MME) to model dependent multivariate censored and truncated data. MME form a highly flexible class of distributions as they are dense in the space of positive continuous multivariate distributions. Moreover, the class is analytically tractable. Many quantities of interest such as the joint density and distribution function, the Laplace transform, moments, Kendall’s tau and Spearman’s rho have a closed form. The class also enjoys appealing closure properties such as the facts that any uni- or multivariate marginal or conditional distribution is a unior multivariate Erlang mixture, the distribution of the sum of the component random variables is a univariate Erlang mixture and the distribution of the residual lifetimes is a again a multivariate mixtures of Erlangs. The use of MME should be regarded as semiparametric density estimation technique to model the dependence directly and hence forms a suitable alternative to the use of copulas. We present an estimation technique for fitting MME using the EM algorithm to data that can be censored and/or truncated, which is often the case in applications such as clinical experiments (survival / failure time analysis), mastitis studies (veterinary studies), loss modeling (finance and actuarial science) and duration data (econometric studies). We demonstrate the effectiveness of the proposed algorithm and the practical use of MME on simulated data as well as on real-life data from a mastitis study.