The Odd Exponential–Rayleigh-Fréchet Distribution: Structural Properties, Estimation Methods, and Applications
DOI:
https://doi.org/10.62933/rqcrpb69Keywords:
Exponential–Rayleigh-Fréchet, Odd Exponential–Rayleigh-G, survival function , QLS , MLEAbstract
This research presents a novel probability model called the Odd Exponential–Rayleigh–Fréchet (OERFR) distribution, which combines the power of the Odd-Exponentiated Rayleigh probability transformation with the flexibility of the Fréchet distribution, known for its ability to represent data with heavy tails and extreme values. The new model aims to address the problems that arise when using traditional distributions in the analysis of reliability and engineering data characterized by significant skewness and nonlinearity in risk behavior. The mathematical construction of the distribution is based on combining the T-X transformation with the odd-ratio transformation, adding two additional shape parameters to the basic distribution. These parameters enhance the distribution's ability to control tail shape, density slope, and the variety of risk function shapes. The basic functions of the model were derived. The study included conducting extensive simulation experiments using eight different estimation methods and at various sample sizes to evaluate the accuracy and statistical stability of each method. The results showed that some methods, such as QLS, MP, and WLSE, were superior in reducing bias and root-squared error at small and medium sample sizes. To confirm the applicability of the distribution, the model was tested on real data representing turbocharger failure times for diesel trucks. The OERFR model demonstrated a clear advantage over several competing distributions according to AIC, BIC, KS, AD, and CV metrics. This performance indicates that the new distribution possesses high flexibility and strong ability to represent real-world data in the areas of engineering, reliability, and extreme value analysis.
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Copyright (c) 2026 Raghad W. Faris, Mundher A. khaleel (Author)
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