New Opportunity Model Using a Mix of 7 and 8 Gamma Chance Density Functions

Abstract

This research is based on the limitations of classic distributions such as the Normal, Exponential, and Weibull in modeling real-world data with skewness, heavy tails, multimodality, or hazard rate structures, and thus it is necessary to develop a new, more flexible opportunity model. The main objective of this study is to develop a new probability model with a single parameter using a mixed-method approach that specifically employs the 7- and 8 Gamma chance density functions. The research methodology includes the reduction of important characteristics such as the cumulative distribution function, survival function, and hazard function, as well as the use of the Maximum Likelihood method with Newton–Raphson numerical iteration for parameter estimation. The results of this study are expected to prove that the single-parameter 7 and 8 Gamma mixed models have superior performance compared to the previously existing single-parameter models. The contributions of this research include theoretical development in statistical science and the provision of efficient, parsimonious alternative models for application in fields such as biostatistics, finance, and reliability analysis