Transmuted power function distribution is generated using the quadratic rank transmutation method based on the mixture of the distributions of two order statistics. The distributions generating via Quadratic rank transmutation map are more flexible than the baseline ones since they have a potential to model various dataset. In this study, we provide some distributional properties and statistical inferences of transmuted power function distribution. We describe several previously unexamined properties, such as density shape, hazard shape, and the transmuted power function distribution measures. We also tackle the problem of point estimation for transmuted power function distribution. In this regard, maximum likelihood, least-squares, weighted least-squares, Anderson-Darling method, and Crámer–Von-Mises method are considered to estimate the two parameters of transmuted power function distribution. A comprehensive Monte Carlo simulation study is performed to compare these methods via bias and mean-squared errors.