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Odd Exponentiated Half-Logistic Exponentiated Exponential Distribution: Properties, Estimation and Simulation Study
Subject area: Science,Engineering and Technology · Area of research: Mathematical Statistics
Abstract
This paper introduces a new four-parameter lifetime distribution referred to as the Odd Exponentiated Half-Logistic Exponentiated Exponential (OEHL-EE) distribution. The proposed model is obtained by incorporating the Exponentiated Exponential distribution into the Odd Exponentiated Half-Logistic-G generator framework. The additional shape parameters provide increased flexibility for modelling lifetime and reliability data exhibiting skewness, varying kurtosis and different hazard-rate behaviours. Several mathematical and statistical properties of the proposed distribution are derived, including the probability density function, cumulative distribution function, survival function, hazard function, reversed hazard function, cumulative hazard function, quantile function, moments, moment generating function, coefficient of variation, skewness, kurtosis, Rényi entropy and order statistics. Maximum likelihood estimation is employed for estimating the unknown parameters, while asymptotic confidence intervals are obtained from the observed information matrix. A Monte Carlo simulation study is conducted to investigate the performance of the maximum likelihood estimators at different sample sizes. The simulation results indicate that the estimation procedure provides useful parameter estimates and that the magnitude of estimation error generally decreases as the sample size increases. The proposed OEHL-EE distribution therefore provides a flexible alternative for lifetime and reliability modelling.
Keywords
Exponentiated Exponential distribution; Half-Logistic distribution; Odd Exponentiated Half-Logistic-G; lifetime distribution; maximum likelihood estimation; Monte Carlo simulation; reliability analysis.
References
[1] Afify, A. Z., Lee, C., & Alzaatreh, A. (2017). Odd Exponentiated Half Logistic Distribution: Properties and Applications. Journal of Statistical Theory and Practice, 11(3), 417-432.
[2] Alzaatreh, A, Lee, C, and Famoye, F. (2013). A new method for generating families of continuous distributions. Metron, 71 (1), 63–79. Springer
[3] Cordeiro, G. M., & de Castro, M. (2011). A new family of generalized distributions. Journal of Statistical Computation and Simulation, 81(7), 883–898. Taylor & Francis
[4] Gupta, R. D., and Kundu, D. (2001). Exponentiated Exponential Family: An Alternative to Gamma and Weibull Distributions. Biometrical Journal, 43(1): 117-130. Wiley
[5] Oluyede, B., Moakofi, T., & Lekono, G. (2025). The new Marshall–Olkin–type II exponentiated half-logistic–odd Burr X-G family of distributions with properties and applications. Stats, 8(2), 26. MDPI
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How to cite this paper
@article{1723509,
author = {Adewoye, Kunle Bayo, Azeez, Olasunkanmi, Isiaka, Azeez, Olabisi Omodasola},
title = {Odd Exponentiated Half-Logistic Exponentiated Exponential Distribution: Properties, Estimation and Simulation Study},
journal = {Iconic Research And Engineering Journals},
year = {2026},
volume = {10},
number = {3},
pages = {3832-3844},
issn = {2456-8880},
url = {https://www.irejournals.com/formatedpaper/1723509.pdf},
abstract = {This paper introduces a new four-parameter lifetime distribution referred to as the Odd Exponentiated Half-Logistic Exponentiated Exponential (OEHL-EE) distribution. The proposed model is obtained by incorporating the Exponentiated Exponential distribution into the Odd Exponentiated Half-Logistic-G generator framework. The additional shape parameters provide increased flexibility for modelling lifetime and reliability data exhibiting skewness, varying kurtosis and different hazard-rate behaviours. Several mathematical and statistical properties of the proposed distribution are derived, including the probability density function, cumulative distribution function, survival function, hazard function, reversed hazard function, cumulative hazard function, quantile function, moments, moment generating function, coefficient of variation, skewness, kurtosis, Rényi entropy and order statistics. Maximum likelihood estimation is employed for estimating the unknown parameters, while asymptotic confidence intervals are obtained from the observed information matrix. A Monte Carlo simulation study is conducted to investigate the performance of the maximum likelihood estimators at different sample sizes. The simulation results indicate that the estimation procedure provides useful parameter estimates and that the magnitude of estimation error generally decreases as the sample size increases. The proposed OEHL-EE distribution therefore provides a flexible alternative for lifetime and reliability modelling.},
keywords = {Exponentiated Exponential distribution; Half-Logistic distribution; Odd Exponentiated Half-Logistic-G; lifetime distribution; maximum likelihood estimation; Monte Carlo simulation; reliability analysis.},
month = {September},
}