Modified statistics for fitting a new bounded Distribution with Applications

Abstract

Bounded probability functions are very important in life test experiments relating to data on fractions, percentages, survival times from a deadly diseas and other fields, so researchers tried to generate new models with finite support capable to describe such phenomenon. In this work, we propose a new distribution so-called the Unit Generalized Exponential distribution (UGE) defined on (0,1). Unless the increasing and bathtub shaped hazard function, its probability density function can be unimodal, decreasing and left-skewed which enable it to be used in several fields of application. Using different approaches, we propose new powerful test statistics, based on any efficient estimator, capable to fit datasets to this model without regarding any alternative as used in classical selection models. Having the lowest variance and the highest rate of convergence to the limit, they also recover the information lost while grouping data. Thousands of simulated samples of varying sizes were utilized to demonstrate the practicability of the proposed tests. Two real-world data illustrated the flexibility of this model particularly for skewed data, compared to existing distributions, including the Kumaraswamy, Unit Weibull, Unit Generalized Inverse Weibull, Unit Burr III, and Unit Gompertz distributions.