(untitled) (Contemporary Mathematics, 2025)
Probability distributions are widespread across various fields, such as economics, science, and engineering. These distributions offer a way to represent complex occurrences in everyday life. The increasing complexity of these occurrences has led researchers to develop new techniques for creating probability distributions. This paper introduces several generalized methods for transforming probability distributions using generalized and dual generalized order statistics. These methods yield transmuted distributions and record-based transmuted distributions in particular. Important properties of these methods, including moments, quantiles, hazard rate, and entropy, have been investigated. The paper also delves into discussing maximum likelihood estimation of the parameters. The proposed generalized transmuted distributions have been analyzed based on the Weibull distribution as a baseline probability distribution, and real-data applications have also been included.