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A new class of Lindley distribution: System reliability, simulation and applications
Danish Qayoom1, Aafaq A Rather1, Najwan Alsadat2
1Symbiosis Statistical Institute, Symbiosis International (Deemed University), Pune, 411004, India.
Heliyon
|October 15, 2024
Summary
Researchers introduced the DUS Lindley distribution, a novel probability model derived from the Lindley distribution. This new distribution demonstrates superior performance in real-world data fitting compared to existing models.
Area of Science:
- Statistics
- Probability Theory
- Mathematical Modeling
Background:
- The Lindley distribution is a widely used probability distribution in various fields.
- There is a continuous need for new probability distributions with improved flexibility and applicability.
- Transformations of existing distributions are a common method for developing novel statistical models.
Purpose of the Study:
- To introduce and analyze the statistical properties of the novel DUS Lindley distribution.
- To investigate parameter estimation methods for the DUS Lindley distribution.
- To assess the performance and applicability of the DUS Lindley distribution using real-world data.
Main Methods:
- The DUS transformation was applied to the Lindley distribution to derive the new DUS Lindley distribution.
- Comprehensive analysis of statistical properties including PDF, CDF, failure rate, moments, and entropy measures.
- Parameter estimation using methods such as Maximum Likelihood Estimation (MLE), Weighted Least Squares (WLS), and Anderson-Darling (AD).
- System reliability estimation and performance evaluation of MLE through simulation studies.
- Application and comparison with existing distributions on two real-world datasets.
Main Results:
- The DUS Lindley distribution was successfully derived and its key statistical properties were detailed.
- Various estimation techniques were applied, with MLE performance evaluated via simulations.
- The DUS Lindley distribution exhibited a better fit to the analyzed real-world datasets compared to other established distributions.
- The likelihood ratio test was employed for model comparison.
Conclusions:
- The DUS Lindley distribution is a promising new probability model with desirable statistical properties.
- The proposed estimation methods are effective for the DUS Lindley distribution.
- The DUS Lindley distribution offers a valuable alternative for modeling real-world phenomena, outperforming existing distributions in specific applications.
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