Real-life sciences rely heavily on statistical modeling because new applications and phenomena pop up constantly, increasing the demand for new distributions.

In this article, the exponentiated generalized Weibull exponential (EGWE) distribution is proposed and studied. The density can exhibit decreasing, increasing, right-skewed, and left-skewed shapes. The hazard rate function shows decreasing, J-shaped, bathtub, and upside-down bathtub shapes. Statistical properties such as asymptotic behavior, quantile function, moment and incomplete moments, mean and median deviations, inequality measures, moment generating function, and order statistics are studied. The estimation of the parameters of the EGWE distribution using six frequentist estimation methods, namely maximum likelihood, least squares, maximum product spacing, weighted least squares, Anderson-Darling, and Cramer-von Mises are discussed. Monte Carlo simulation study to ascertain the behavior of the estimators in terms of average absolute biases and mean square error is carried out. All the estimators performed very well since the average absolute biases and mean square errors decrease as the sample size increases. The usefulness of the EGWE distribution is illustrated with two datasets. The results show that the EGWE distribution provides better parametric fit compared with the competing distributions. Also, in estimating the EGWE parameters with the six estimation methods, the results show that the performance of the six estimation methods is good.