α-stable laws for noncoding regions in DNA sequences

In this work, we analyze the <italic>long-range dependence</italic> parameter for a nucleotide sequence in several different transformations. The long-range dependence parameter is estimated by the approximated maximum likelihood method, by a novel estimator based on the spectral envelope theory, by a regression method based on the periodogram function, and also by the <italic>detrended fluctuation analysis</italic> method. We study the length distribution of coding and noncoding regions for all <italic>Homo sapiens</italic> chromosomes available from the European Bioinformatics Institute. The parameter of the tail rate decay is estimated by the Hill estimator ˆα. We show that the tail rate decay is greater than 2 for coding regions, while for almost all noncoding regions it is less than 2.