Class library ranlip for multivariate nonuniform random variate generation

This paper describes generation of nonuniform random variates from Lipschitz-continuous densities using acceptance/rejection, and the class library ranlip which implements this method. It is assumed that the required distribution has Lipschitz-continuous density, which is either given analytically or as a black box. The algorithm builds a piecewise constant upper approximation to the density (the hat function), using a large number of its values and subdivision of the domain into hyperrectangles. The class library ranlip provides very competitive preprocessing and generation times, and yields small rejection constant, which is a measure of efficiency of the generation step. It exhibits good performance for up to five variables, and provides the user with a black box nonuniform random variate generator for a large class of distributions, in particular, multimodal distributions. It will be valuable for researchers who frequently face the task of sampling from unusual distributions, for which specialized random variate generators are not available.<br /

Gene Copy Number Analysis for Family Data Using Semiparametric Copula Model

Gene copy number changes are common characteristics of many genetic disorders. A new technology, array comparative genomic hybridization (a-CGH), is widely used today to screen for gains and losses in cancers and other genetic diseases with high resolution at the genome level or for specific chromosomal region. Statistical methods for analyzing such a-CGH data have been developed. However, most of the existing methods are for unrelated individual data and the results from them provide explanation for horizontal variations in copy number changes. It is potentially meaningful to develop a statistical method that will allow for the analysis of family data to investigate the vertical kinship effects as well. Here we consider a semiparametric model based on clustering method in which the marginal distributions are estimated nonparametrically, and the familial dependence structure is modeled by copula. The model is illustrated and evaluated using simulated data. Our results show that the proposed method is more robust than the commonly used multivariate normal model. Finally, we demonstrated the utility of our method using a real dataset

Generating random variates from a bicompositional Dirichlet distribution

A composition is a vector of positive components summing to a constant. The sample space of a composition is the simplex and the sample space of two compositions, a bicomposition, is a Cartesian product of two simplices. We present a way of generating random variates from a bicompositional Dirichlet distribution defined on the Cartesian product of two simplices using the rejection method. We derive a general solution for finding a dominating density function and a rejection constant, and also compare this solution to using a uniform dominating density function. Finally some examples of generated bicompositional random variates, with varying number of components, are presented