The article presents a new method to accurately estimate the proportion of false null hypotheses in statistical modeling. Existing methods have limitations, but the new approach uses Lebesgue-Stieltjes integral equations to create consistent estimators. These estimators work well for various types of distributions and provide reliable results. The researchers also determined the speed of convergence and uniform consistency for each estimator under certain conditions. This method can be applied to a wide range of statistical scenarios, improving the accuracy of hypothesis testing and data analysis.