Advanced Bimodal Skew-Symmetric Distributions: Methodology and Application to Cancer Cell Protein Data

Abstract

This paper explores bimodal skew-symmetric distributions, a versatile family of distributions characterized by parameters that control asymmetry and kurtosis. These distributions encapsulate both symmetrical and well-known asymmetrical behaviors. A simulation study evaluates the model’s estimation accuracy, detailing the score function and the robustness of the observed information matrix, which is proven to be non-singular under specific conditions. We apply the bimodal skew-normal model to protein data from cancer cells, comparing its performance against four established distributions supported on the entire real line. Results indicate superior performance by the proposed model, underscoring its potential for enhancing analytical precision in biological research.