In this article, a new distribution family called the alpha power transformation of the generalized extreme value distribution with linear normalization (𝐴𝑃 𝑇 − 𝐺𝐸𝑉 𝐿), is proposed and investigated. Since adding a parameter to any baseline distribution enhances its flexibility for better representation of the real data but complicates the process of maximum likelihood estimation (MLE), this problem is addressed using the genetic algorithm (GA). Furthermore, the new parameter adjusts the distribution’s properties, demanding a further examination of its effects. So, both of MLE and Bayesian estimation (BE) for 𝐴𝑃 𝑇 − 𝐺𝐸𝑉 𝐿 parameters are considered under type II progressive censoring for three cases of removals (fixed, binomial, and discrete uniform random removal). Additionally, BE is considered for informative and non-informative priors under both square error and LINEX loss functions using Lindley approximation. To demonstrate the effectiveness of the new parameter to 𝐺𝐸𝑉 𝐿, increased fitting has been noticed for U.S. employment rate data, which is subsequently utilized for forecasting future outcomes using both return level and time series methods.