A Flexible Probability Model for Proportion Data: Unit Gumbel Type-II Distribution, Development, Properties, Different Method of Estimations and Applications

In explaining and forecasting real life scenarios, statistical distributions are very helpful. It is very important to select the best fitting statistical distribution for modelling data. In analysis of real world phenomena like in reliability and economics, we may find distributions for bounded data observed as percentages, proportions or fractions (see, for example, Marshall and Olkin (2007)). In this context, in view of pertinent transformation on the Gumbel Type-II model, we suggest and study the unit Gumbel Type-II (UG-TII) model and explore few of its statistical characteristics. We also consider various methods of estimating the unknown parameters of UG-TII model from the frequentist perspective. Monte Carlo simulations are worked out in order to compare efficiency of suggested estimation methods for small as well as large samples. The efficiency of estimators is measured using simulated samples in terms of their bias and mean square error. In the end, two datasets have been examined in attempt to validate the realistic possibilities of new model. In comparison to the six severe competitors.