Alpha Power One-Parameter Weibull Distribution: Its Properties, Simulations and Applications to Real-Life Data

In this paper, we introduce a new lifetime distribution called alpha power one-parameter Weibull (APOPW) distribution based on the alpha power transformation method has been defined and studied. Various statistical properties of the newly proposed distribution including moments, moment generating function, quantile function, Rényi and Shannon entropy, stress-strength reliability, mean deviations, and extreme order statistics have been obtained. Several estimation techniques are studied, including maximum likelihood estimation (MLE), Anderson–Darling (AD), least squares estimation (LSE), Cramér–von Mises (CVM), and maximum product of spacings (MPS). The estimators compared their efficiency based on average absolute bias (BIAS), mean squared error (MSE), and mean absolute relative error (MRE), identifying that MLE as the most robust method across various sample sizes increase. The efficiency and flexibility of the new distribution are illustrated by analysing two real-live data sets, and compare its goodness-of-fit against several existing lifetime distributions.