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Theoretical Analysis of the New Extended Exponential- Linear Distribution with Numerical Application |
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PP: 731-746 |
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doi:10.18576/jsap/140505
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Author(s) |
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Christian A. Hesse,
Evans Tee,
Dominic B. Boyetey,
Emmanuel D. Kpeglo,
Albert A. Ashiagbor,
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Abstract |
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| Traditional extensions of the exponential distribution, while aiming to capture more complex hazard rate behaviors and improve data fit, often introduce additional parameters that complicate crucial statistical processes such as estimation, inference, and model selection. This complexity is particularly evident with small or restricted datasets, where overparameterization can lead to identifiability issues and increased computational challenges. Addressing this critical need for parsimonious yet flexible models, this study proposes and explores the novel one-parameter ”Extended Exponential-Linear” (EE-L) distribution. Unlike classical extensions, the EE-L enhances modeling flexibility for data exhibiting heavier tails or increasing hazard rates by multiplicatively modifying the exponential kernel with a linear function of the variable, thus preserving a single-parameter structure for easier estimation and interpretation. Statistical properties of the EE-L distribution, including its moments, hazard rate function, and quantile function, are derived. Simulation results demonstrate that parameter estimates for the EE-L distribution remained within 10 percent of actual values across various sample sizes (1000, 500, 200, 100, 50), with the exception of very small samples (20). Furthermore, its application to life testing data revealed that the maximum likelihood parameter estimate was not significantly different from the true parameter value. Finally, a comparative analysis of a waiting time dataset demonstrated the EE-L distribution’s superior fitting performance compared to the exponential, inverse exponential, modified exponential, and Lomax distributions. |
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