Modelling microarray gene expression using alpha-stable distributions

After normalization, the distribution of gene expressions for very different organisms have a similar shape, they usually exhibit heavier tails than a Gaussian distribution and a certain degree of asymmetry. Therefore, this distribution has been modelled in the literature using different parametric families of distributions, such the Asymmetric Laplace or the Cauchy distribution. Moreover, it is known that the tails of spot intensity distributions are described by a power law and the variance of a given array increases as the number of gene considered increases. These features of the distribution of gene expression strongly suggest that the alpha-stable distribution is suitable to model it. In this work, we model the error distribution for gene expression data using the alpha-stable distribution. This distribution is tested successfully for four different datasets. The Kullback-Leibler, ?2 and Hellinger tests are performed to compare how alpha-stable, Asymmetric Laplace and Gaussian fit the spot intensity distribution. The alpha-stable is proved to perform much better for every array in every dataset considered.