An Innovative Exponential Distribution for Modeling Various Risk Trends: Theory, Bayesian Inference, and Applications in Partially Accelerated Life Tests with Dispersion Data

Abstract

This paper presents a new asymmetric generalization of the exponential distribution tailored for non-negative datasets that display unimodal or bimodal characteristics. A shape-controlling parameter substantially improves the model's flexibility, enabling it to accommodate a broader spectrum of distributional shapes compared to the traditional exponential distribution. The theoretical study offers a thorough derivation of essential features, encompassing the moment-generating function, raw moments, mean deviation, entropy measures, and stochastic representations. An in-depth examination of the hazard rate demonstrates its capacity to represent both increasing and bathtub-shaped functions, rendering it especially appropriate for dependability and lifespan data analysis. Additionally, multiple characterization outcomes are produced to reinforce the theoretical foundation, and a modeling framework for partially accelerated life-test conditions is created. Parameter estimation is performed utilizing both conventional and Bayesian inferential methodologies. A thorough simulation analysis assesses the efficacy of these estimators in terms of bias and mean squared error. The model’s practical applicability is illustrated through two real-world asymmetric datasets: walking dimension metrics and breast cancer survival durations. Ultimately, likelihood ratio tests are utilized to evaluate the proposed distribution against nested alternatives, consistently demonstrating its enhanced performance and effectiveness in hypothesis testing.



Received: 29 August 2025 | Revised: 16 April 2026 | Accepted: 18 May 2026



Conflicts of Interest

The authors declare that they have no conflicts of interest to this work.



Data Availability Statement

The data that support the findings of this study are openly available at https://doi.org/10.1109/TR.1986.4335370, reference number [29], and at https://doi.org/10.21608/cjmss.2022.271186, reference number [30].



Author Contribution Statement

Mohamed S. Eliwa: Methodology, Software, Formal analysis, Investigation, Data curation, Writing – original draft, Writing – review & editing, Supervision, Project administration. Mohamed F. Abouelenein: Software, Validation, Investigation, Resources, Data curation, Writing – original draft, Writing – review & editing, Visualization, Funding acquisition. Jondeep Das: Conceptualization, Methodology, Software, Validation, Resources, Data curation, Writing – original draft, Writing – review & editing, Visualization. Lakhimi Doley: Conceptualization, Methodology, Formal analysis, Investigation, Data curation, Writing – original draft, Writing – review & editing. Partha Jyoti Hazarika: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Resources, Data curation, Writing – original draft, Writing – review & editing, Visualization, Supervision, Project administration. Gholamhossein G. Hamedani: Methodology, Software, Investigation, Data curation, Writing – original draft, Writing – review & editing, Visualization. Ehab M. Almetwally: Methodology, Resources, Data curation, Software, Writing – review & editing.