Essays on Stochastic Comparisons and Goodness-of-Fit Measures Based on The Mellin Transform
Goodness-of-Fit, Hotelling’s T2 Statistic, Log-Cumulants, Majorization, Order statistics, Parameters Estimation.
Distributions functions and Goodness-of-Fit techniques are being developed from different perspectives and applications in the world. In this thesis document we provide results in those fields. In the first one, the main idea is to do stochastic comparisons by using majorization theory. We investigate conditions on the parameters of the Exponentiated Generalized class with equal and different baseline. In second one, to describe the fits of models to the data by using Goodness-of-Fit measures, we use the Transmuted Inverse Weibull distribution and derive the Mellin Transform from that model. We estimate the parameters by Moments, Likelihhod and Log-Cumulants methods and we do an interesting analysis with T 2 statistic and confidence ellipses. The data used in this part was based on survival datasets.