Tweedie Distributions for Biological Sequences Alignments

An important technique in the study of the similarity between biological sequences is the analysis of their alignments score distribution. The estimation of such distribution plays a central role in the evaluation of the statistical significance of these alignments. In the amino acid sequences alignment, the scores of the ungapped aligned segments are proven to be asymptotically distributed according to the extreme value law. Their gapped alignments scores are generally fitted with poisson or Gumbel distributions. In order to widen the scope of the candidate distributions, other classes of statistical models can be used. In this paper, we proposed to use the class of exponential dispersion models which includes several common laws such as Gaussian, Poisson and Gamma distributions on top of many others. In this context, a new algorithm for this model parameters estimation was introduced. This proposed approach is based on the selection of the appropriate distribution and maximum likelihood estimation. An asymptotic confidence interval was provided to estimate the dispersion parameter. Ultimately, the suggested algorithm performance was evaluated through different numerical experiments based on random sequences using different generation techniques.