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 Volume 10, Issue 6 (June 2023), Pages: 71-79


 Original Research Paper

The exponentiated new exponential-gamma distribution: Properties and applications


 Lulah Alnaji 1, *, Amani S. Alghamdi 2


 1Department of Mathematics, University of Hafr Al Batin, Hafar Al-Batin, Saudi Arabia
 2Department of Statistics, King Abdulaziz University, Jeddah, Saudi Arabia

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 * Corresponding Author. 

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We propose a novel lifetime model by extending the new exponential-gamma distribution to the exponentiated new exponential-gamma distribution. This extension allows for the derivation of a more flexible density function that combines the characteristics of the exponential and gamma distributions. We present various statistical properties of the newly proposed method, including the cumulative function, probability density function, moment-generating function, and moments. Additionally, we discuss the estimation of parameters using maximum likelihood. To compare the performance of our newly developed model with existing probability distributions (gamma, exponential, Lindley, generalized gamma, generalization of the generalized gamma, and new exponential-gamma distribution), we employ model selection criteria such as the Akaike Information Criterion (AIC), the corrected Akaike Information Criterion (AICC), and the Bayesian Information Criterion (BIC). The application of these criteria to different models demonstrates that our proposed model outperforms the other six models across various datasets. For instance, in the first dataset, the AIC, AICC, and BIC values for our model are 366.975, 373.805, and 373.805, respectively, whereas the values for the other six models (exponential, Lindley, generalized gamma, generalization of the generalized gamma) range from 503.012 to 834.327. We conduct simulation studies to assess the efficiency of our proposed model. Furthermore, we apply the proposed method to three real data applications to further examine its effectiveness. It is important to note that the quantile function of the proposed model does not have a closed-form solution, requiring the computation of the quantile function through the Newton-Raphson iterative approach.

 © 2023 The Authors. Published by IASE.

 This is an open access article under the CC BY-NC-ND license (

 Keywords: Exponentiated, Exponential, Gamma, Moment-generating function, ๐‘Ÿ๐‘กโ„Ž moment

 Article History: Received 9 December 2022, Received in revised form 6 April 2023, Accepted 8 April 2023


No Acknowledgment.

 Compliance with ethical standards

 Conflict of interest: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.


 Alnaji L and Alghamdi AS (2023). The exponentiated new exponential-gamma distribution: Properties and applications. International Journal of Advanced and Applied Sciences, 10(6): 71-79

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 Fig. 1 Fig. 2


 Table 1 Table 2 Table 3 Table 4 Table 5 Table 6 Table 7 Table 8 Table 9 Table 10 Table 11 


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