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Bayesian and non-bayesian approaches for estimating the Epanechnikov-Weibull distribution with applications in
T S Taher1, H M Barakat2, H N Alqifari3
1Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, 44519, Egypt. tahersobh46@gmail.com.
Scientific Reports
|June 8, 2026
Summary
This study introduces the Epanechnikov-Weibull distribution for generalized order statistics, offering improved statistical modeling. Researchers derived key statistical features and estimation methods, demonstrating practical applications in electronics and engineering.
Area of Science:
- Statistics
- Probability Theory
- Mathematical Modeling
Background:
- Statistical models are crucial for practical scenarios but may not always provide optimal fitting.
- There is an ongoing need for more efficient and improved probability distributions in statistical analysis.
- Generalized order statistics (GOSs) offer a flexible framework for analyzing data.
Purpose of the Study:
- To examine the statistical properties of the Epanechnikov-Weibull distribution (EpWD) within the framework of generalized order statistics (GOSs).
- To derive key statistical characteristics, including the moment-generating function, rth L-moment, and trimmed L-moments for the EpWD model.
- To develop and evaluate parameter estimation techniques and information-theoretic measures for the EpWD.
Main Methods:
- Derivation of statistical features like moment-generating functions and L-moments for the EpWD GOSs.
- Application of maximum likelihood estimation (MLE) and Bayesian approaches for parameter estimation.
- Formulation of asymptotic confidence intervals (CIs) using the Fisher information matrix (FIM).
- Conducting Monte Carlo simulations with progressively type-II censored samples to assess estimator efficacy.
- Analysis of extropy and weighted extropy as information-theoretic measures.
Main Results:
- The study successfully derived various statistical properties of the Epanechnikov-Weibull distribution for generalized order statistics.
- Effective parameter estimation techniques (MLE and Bayesian) were developed and validated through simulations.
- Asymptotic confidence intervals were formulated, providing a measure of estimation precision.
- The distribution demonstrated utility through information-theoretic measures (extropy, weighted extropy).
- The practical applicability was confirmed using real-world electronic and engineering datasets.
Conclusions:
- The Epanechnikov-Weibull distribution, when analyzed using generalized order statistics, offers a valuable and flexible statistical model.
- The derived estimation methods and derived statistical features provide a robust framework for data analysis.
- The demonstrated applications highlight the distribution's potential in various scientific and engineering fields.
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