Applications of the Difference of Successes Continuous Distribution in Modeling Variability Between Dependent Success Rates

The Difference of Successes Continuous (DoSC) distribution is a novel approach for analyzing the variability between two continuous success rates. While traditional probability models for success/failure data, such as binomial or Poisson distributions, are frequently used in discrete settings, many real-world applications require a continuous framework for modeling the differences between success rates over time or in large populations. This study presents the application of the DoSC distribution in modeling interdependent success rates across fields such as healthcare, finance, quality control, and engineering. We provide an overview of the DoSC distribution\'s theoretical underpinnings and its use in representing continuous differences in success measurements. Through five numerical examples, we demonstrate the distribution’s adaptability to various scenarios, including dependent trials with continuous outcomes and variability in dependent success rates. Our findings show that the DoSC distribution can effectively capture shifts in mean difference, variance, and tail behavior across different applications, providing a nuanced tool for probabilistic analysis of continuous success differences. This work highlights the DoSC distribution as a flexible model for enhancing the accuracy of statistical predictions where continuous success differences are of primary interest.