About Birnbaum–Saunders Distributions Based on the Johnson System

A new five-parameter Birnbaum-Saunders distribution for modeling bicoid gene expression data

An extended version of Birnbaum-Saunders distribution with five parameters is introduced. Theoretical aspects of five-parameter Birnbaum-Saunders distribution and the maximum likelihood estimation of parameters are presented. The reliability and applicability of the proposed distribution is evaluated using both simulation and real-world data namely bicoid gene expression profile. The findings of this research confirm that the newly proposed five-parameter Birnbaum-Saunders distribution can be utilized to describe the distribution of bicoid gene expression profile.

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.