The exponentiated new exponential-gamma distribution: Properties and applications

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