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Statistical Inference for the Induced Moment Exponential Distribution: Bayesian and Non-Bayesian Approaches with Applications to Physics and Reliability Data |
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PP: 1107-1126 |
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doi:10.18576/jsap/150410
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Author(s) |
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Mohammed Elgarhy,
Doaa Basalamah,
Ahmed Mohamed El Gazar,
Dina A. Ramadan,
Ghareeb A. Marei,
Said G. Nassr,
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Abstract |
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| The induced moment exponential distribution is introduced with a flexible probability density function that can decrease, while its hazard rate exhibits increasing patterns. These properties make it suitable for survival analysis, reliability, and uncertainty modeling. Several distributional characteristics are derived, including moments, moment generating function, probability-weighted moments, and measures of skewness and kurtosis. Parameter estimation is addressed using maximum likelihood, maximum product of spacings, and Bayesian methods. To evaluate the efficacy of these estimating approaches across varying sample sizes, Monte Carlo simulations are performed. The efficacy of each estimator is evaluated through comparisons of average relative bias and mean squared error, highlighting their suitability for the samples used. Three applications utilizing real-world datasets related to physics and reliability data demonstrate the significance of the new model in relation to several established competitive models. This empirical investigation further supports the utility and adaptability of the induced moment exponential model in capturing the intricacies of distinct datasets, hence delivering significant insights for practitioners in numerous domains. |
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