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The Exponentiated Discrete Linear Exponential Distribution: Theory, Risk Profiles, and Applications to Biological and Engineering Data |
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PP: 599-621 |
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doi:10.18576/jsap/150316
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Author(s) |
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Hend S. Shahen,
Mohamed S. Eliwa,
Mahmoud El-Morshedy,
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Abstract |
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| This paper presents a novel two-parameter exponentiated discrete linear exponential (EDLE) distribution designed to effectively model discrete data exhibiting diverse risk behaviors and dispersion patterns. The primary statistical features of the EDLE distribution, including the probability mass function, hazard rate function, moments, skewness, kurtosis, index of dispersion, entropies, and L-moments of order statistics, are calculated and analyzed. Due to its adaptability, the EDLE distribution may accommodate danger rates that increase, decrease, or exhibit a bathtub configuration. This renders it highly beneficial for reliability and survival analysis in discrete settings. The distribution provides a robust framework for modeling complex discrete events, accurately representing positively skewed data with varying kurtosis, overdispersion, and heavy-tailed characteristics. The maximum likelihood method is used to estimate parameters, ensuring the reliability of the inference. A Monte Carlo simulation analysis was performed in R to assess the efficacy of the estimators. We examine various sample sizes and coverage probability predicated on 95% confidence intervals. The practical usefulness of the EDLE distribution is demonstrated using three empirical datasets: (i) epidemiological data, (ii) biological-entomological data from agricultural research, and (iii) turbocharger failure data from reliability tests. The EDLE distribution consistently demonstrates superior fitting across all scenarios and is more adept at managing complex discrete data structures compared to numerous alternative discrete models. The results indicate that the model is adaptable, robust, and applicable in various disciplines. |
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