Inferential results based on Mellin-type statistics for the transmuted inverse Weibull distribution

Abstract

Different measures of Goodness-of-Fit yield information to describe the fits of models to the data. For example, Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC) measures. The AIC and BIC are not a consistent model selection methods. Also to case AIC and BIC values computed using conditional likelihoods we do not recommend because the conditioning may be different for different 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.