Beta-Transformed Inverse Length-Biased Exponential Distribution: Properties and Applications

Jabir Bengalath; Mohamed Nejib Ouertani; Hanene  Hamdani; Fasna Kottakkunnan; Mohammed  Elgarhy

doi:10.47852/bonviewJCCE52027030

Authors

Jabir Bengalath Government Arts and Science College Calicut, University of Calicut, India
Mohamed Nejib Ouertani College of Business, Imam Mohammad Ibn Saud Islamic University (IMSIU), Saudi Arabia
Hanene Hamdani College of Business, Imam Mohammad Ibn Saud Islamic University (IMSIU), Saudi Arabia
Fasna Kottakkunnan Department of Statistics, Stockholm University, Sweden https://orcid.org/0000-0003-4862-8967
Mohammed Elgarhy Department of Basic Sciences, Higher Institute of Administrative Sciences, Egypt and Department of Computer Engineering, Biruni University, Türkiye https://orcid.org/0000-0002-1333-3862

DOI:

https://doi.org/10.47852/bonviewJCCE52027030

Keywords:

beta transformation, inverse length-biased exponential distribution, statistical properties, maximum likelihood estimation, simulation, applications

Abstract

In this article, we introduce a novel probability distribution, the beta-transformed inverse length-biased exponential (BTILBE) distribution, derived from the exponential distribution using the beta transformation technique. This approach is advantageous because it introduces no additional parameters beyond those of the baseline distribution. The BTILBE distribution features a highly flexible hazard function and exhibits unique statistical properties that we comprehensively analyze. We explore key statistical characteristics, including moments, inverted moments, incomplete moments, generating functions, mean residual life, and mean inactivity times. Additionally, we provide numerical illustrations of moments, skewness, kurtosis, and the coefficient of variation to offer a thorough understanding of the proposed model. We also derive expressions for entropy measures, such as Shannon entropy, Tsallis entropy, and Renyi entropy, accompanied by numerical examples. The parameters of the BTILBE distribution are estimated using maximum likelihood estimation (MLE), and a simulation study validates their accuracy. To demonstrate the model's practical applicability, we apply it to two real-world datasets, where the BTILBE distribution exhibits exceptional flexibility and outperforms several established distributions, establishing it as a robust and valuable tool for statistical modeling.

Received: 1 August 2025 | Revised: 10 November 2025 | Accepted: 21 November 2025

Conflicts of Interest

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

Data Availability Statement

The data supporting the findings of this study are openly availableat https://doi.org/10.1007/0-387-21645-6_3, reference number [45], and https://doi.org/10.1175/1520-0493(1973)101<0701:TKDMLE>2.3.CO;2, reference number [46].

Author Contribution Statement

Jabir Bengalath: Conceptualization, Methodology, Software, Formal analysis, Investigation, Writing – review & editing, Visualization, Supervision. Mohamed Nejib Ouertani: Software, Validation, Formal analysis, Data curation. Hanene Hamdani: Software, Validation, Formal analysis, Data curation. Fasna Kottakkunnan: Conceptualization, Methodology, Software, Resources. Mohammed Elgarhy: Validation, Investigation, Writing – original draft, Writing – review & editing, Project administration, Funding acquisition.