Gene promoters have variable repartition of AGCT nucleotides according to some probabilistic behaviours essentially depending on their position in a string. The paper aims to provide a model for this configuration. With this model we derive non-uniform confidence bounds for those probability distributions in the strings. A uniform bound deriving from previous works in Wu and Zhao [Inference of trends in time series. J R Stat Soc B. 2007; 69: 391-410] is more demanding for the model. A data-based study allows to clarify our suggestions and open the way for applications in molecular biology.