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In this study, we have focused to propose a flexible model that demonstrates increasing, decreasing and upside-down bathtubshaped density and failure rate functions. The proposed model refers to as the exponentiated power function (EPF) distribution. Some mathematical and reliability measures are developed and derived. We develop explicit expressions for the moments, quantile function and order statistics. Some shapes of the density and the reliability functions are sketched out and discussed. We suggest the method to estimate the unknown parameters of EPF by the maximum likelihood estimation. Two suitable lifetime datasets from engineering sector are used to explore the dominance of the EPF distribution.

This study presents an innovative model that utilizes a newly developed logarithmic transformation method for the examination of data obtained from lifetime studies in the fields of medicine and engineering. Several fundamental distributional features are established, such as reliability measures, quantiles, moments, probability moments, and order statistics. The primary emphasis is directed towards the power function distribution, which functions as a sub-model within the newly introduced logarithmic transformation. Diverse forms of the recently developed density and hazard rate functions are explored, demonstrating their applicability in modeling an extensive range of data. The study explores and analyzes several entropy measures, specifically Rényi, Havrda and Charvat, Awad et al.*, Awad et al., Arimoto, and Tsallis. A comprehensive examination of these measures is provided, accompanied by numerical findings that allow for an evaluation of their respective characteristics. Additionally, risk indicators, including value at risk, tail value at risk, tail variance, and tail variance premium, are investigated. To obtain estimates for the parameters of the proposed model, seven established classical estimating methods are analyzed, and their effectiveness is evaluated in terms of absolute bias, mean squared error, and mean relative error. Ultimately, the novel model is implemented on three distinct lifespan datasets sourced from the domains of medical science and engineering. To assess its efficacy, a comparative analysis of its performance versus many established models is conducted, utilizing goodness-of-fit criteria as the basis for evaluation. The findings of the study suggest that the proposed model exhibits superior performance in terms of fit compared to the other models examined.