Different measures of goodness-of-fit provide information to describe how well models fit the data. However, it's important to note that these measures have shown modest growth in comparison to the emergence of probability distribution models. That said, this research constructed qualitative and quantitative fit measures for Transmuted Inverse Weibull distribution. To develop these Goodness-of-Fit measures, we study some properties of that distribution: we present the Mellin Transform, Log-Moments, and Log-Cumulants. Then, we discuss estimation methods for the model's parameters, such as Moments, Maximum Likelihood, and the one based on the Log-Cumulants method. The last method mentioned is proposed to estimate the parameters of the distribution. We make the Log-Cumulants diagrams and construct the confidence ellipses. The model is applied to three survival datasets to verify the quality of our estimation methods and Goodness-of-Fit measures.