Ugamma Distribution and Rational Hazard Rate Function: Statistical Properties, Goodness of fit testing and Practical Applications

Ugamma Distribution and Rational Hazard Rate Function

Abstract

This work presents an innovative approach to developing a new continuous distribution, capitalizing
on recent advances in stochastic modeling and weighted distributions. Our approach is based on the
development of an original methodological framework for deriving probability density functions from the
moment r
th of a continuous random variable and its cumulative distribution function.
In this context, we introduce the Ugamma distribution as a concrete illustration of our proposed
methodological framework. We highlight its distinctive features as well as its statistical properties through
an exhaustive analysis. This includes the examination of survival rate and hazard functions, the study of
moments and measures of variability, thus demonstrating the versatility and effectiveness of the Ugamma
distribution in modeling various statistical phenomena. We also develop a modified chi-square goodness
of fit test based on the Nikulin-Rao-Robson statistic for this new model.
To further demonstrate the practical applicability of the Ugamma distribution, we apply it to both
simulated and real-world datasets. This approach enables us to highlight its relevance in a variety of
fields, including internet usage patterns, population dynamics, and pesticide concentration levels. These
concrete applications showcase the Ugamma distribution’s ability to effectively model complex real-world
phenomena, highlighting its versatility and value in various contexts.