In this article, the effect of the parameters in the properties of a well-known distribution called q-extended extreme value with linear normalization is discussed. Moreover, these parameters are estimated by both maximum likelihood and Bayesian approaches using type-II progressive censoring. The removals of type-II progressive censoring are considered under three well-known random removals (Fixed, discrete uniform, and binomial). Finding effective numerical techniques is a typical challenge for statisticians when estimating MLE parameters for distributions with many parameters. So one of our aims in this article is to show how the metaheuristic optimization like the particle swarm optimization, can handle this problem. Furthermore, the interval estimation for the parameters is calculated using the Fisher information matrix. The Bayesian approach is utilized for both the informative and non-informative under two different loss functions (square error and Linex loss functions) using Lindley’s approximation. Moreover, home price data in California represent a good fit for the q-extended extreme value distribution with linear normalization. By using this fitting some of California’s future home prices are predicted by using the return level function.