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Statistical Inference under Censored Data for the New Exponential-X Fréchet Distribution: Simulation and Application
Omar Alzeley1, Ehab M Almetwally2, Ahmed M Gemeay3
1Department of Mathematics, Umm Al-Qura University, Al-Qunfudah University College, Mecca, Saudi Arabia.
Computational Intelligence and Neuroscience
|September 9, 2021
Summary
A new Exponential-X Fréchet (NEXF) distribution offers superior reliability by accurately modeling nonmonotone hazard functions. This novel model outperforms existing distributions in lifetime predictions and survival analysis.
Area of Science:
- Statistics
- Reliability Engineering
- Survival Analysis
Background:
- Accurate lifetime models are crucial for reliable predictions, especially with nonmonotone hazard functions.
- Existing models like exponential and Fréchet distributions may not adequately capture complex reliability data.
- The development of novel statistical distributions is essential for advancing reliability studies.
Purpose of the Study:
- To introduce and analyze the statistical properties of the new Exponential-X Fréchet (NEXF) distribution.
- To evaluate the performance of the NEXF distribution in modeling reliability data with nonmonotone hazard functions.
- To compare the NEXF distribution against established models like the exponential and Fréchet distributions.
Main Methods:
- The study introduces the novel Exponential-X Fréchet (NEXF) distribution.
- Statistical properties of the NEXF distribution were investigated.
- Parameter estimation techniques were developed for complete and Type-I censored data.
- Numerical simulations were conducted to assess estimation methods.
- A modified Kolmogorov-Smirnov (KS) algorithm was used for fitting Type-I censored data.
Main Results:
- The NEXF distribution demonstrates superior fitting capabilities for reliability models with nonmonotone hazard functions.
- The proposed parameter estimation methods were validated through numerical simulations.
- The NEXF distribution provided a better fit compared to competitive models in a real-life application.
- The modified KS algorithm effectively assessed the fit of Type-I censored data.
Conclusions:
- The novel Exponential-X Fréchet (NEXF) distribution is a promising and effective model for reliability studies, particularly for data exhibiting nonmonotone hazard functions.
- The NEXF distribution offers improved accuracy in parameter estimation and prediction compared to traditional models.
- The proposed estimation and fitting techniques are robust and applicable to real-world survival data analysis.
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