The Exponentiated Generalized Reduced Kies Distribution with Properties and Applications on Burr Measurement Datasets
DOI:
https://doi.org/10.56532/mjsat.v5i4.542Keywords:
Reduced Kies Distribution, Exponentiated Generalized , Unit-Bounded Distributions, Family of Distributions, Burr Measurement DataAbstract
This study introduces and examines a new three-parameter generalized extension of the Reduced Kies distribution, termed the Exponentiated Generalized Reduced Kies Distribution (EGRKiD). Various statistical and mathematical properties of the proposed model are derived, including its quantile function, median, order statistics, skewness, and kurtosis. In addition, key reliability characteristics such as the survival and hazard rate functions are explored. Parameter estimation is performed using maximum likelihood estimation (MLE) and maximum product spacing (MPS), with simulations showing that MLE consistently outperforms MPS, exhibiting up to 40% lower bias and 35% lower mean squared error particularly for samples less than 100. Lastly, the applicability and flexibility of the new distribution are demonstrated through its application to two real burr measurement datasets, where it outperforms eight established unit-bounded distributions. The results show that the EGRKiD provides a superior fit, reducing the AIC by 12-18% and the BIC by 10-15% compared to the next best model. Several goodness-of-fit tests further confirm its advantage, with the EGRKiD yielding KS statistics 50-60% smaller and p-values 3-5 times higher than competing models. These findings highlight the EGRKiD’s flexibility and robustness, making it a valuable tool for applications in engineering and other related fields.
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