Fractional poisson process: Long-range dependence in DNA sequences

Abstract

Modeling DNA sequences with stochastic models and developing statistical methods to analyze the multiple projects of DNA sequencing are challenging questions for statisticians and biologists. Some of the most manifestations are the study of long-range dependence in DNA sequences that transform the DNA sequence into a numerical time series to study the long-range dependence in a DNA sequence. It is still discussed in the works if the type of transformation can alter the conclusion of long-range dependence on the DNA sequence. Here we model the DNA sequence considering the Fractional Poisson Process, propose a method based on moments for estimating the parameters of the Fractional Poisson Process in the DNA sequence, and analyze the long-range dependence in various DNA sequences by the detrended fluctuation analysis method.