Spatial gradient of bicoid is well explained by Birnbaum-Saunders distribution

bicoid is a maternally transcribed gene which plays a pivotal role during the early developmental stage of Drosophila melanogaster by acting as an essential input to the segmentation network. Therefore, fundamental insights into gene cross-regulations of segmentation network expect to be unveiled by presenting an accurate mathematical model for bicoid gene expression profile. In this paper, an extended version of Birnbaum-Saunders with four parameters is introduced and evaluated to describe the spatial gradient of this gene. Theoretical aspects of four-parameter Birnbaum-Saunders and the estimated parameters are presented and thoroughly assessed for different embryos. The reliability and validity of the results are evaluated via both simulation studies and real data sets and thereby adding more confidence and value to the findings of this research.