Statistical Modeling and Analysis Using F-Ratio Continuous Distribution

For the comparison of variances, we take a continuous F-ratio distribution . Strong statistical models in several fields underlying it include theoretical modeling, biological science, engineering science, and environmental science applications. The first three numerical examples of it are its resilience and adaptability to the fields of biological treatment effects, engineering process control, and ecological variability. The full results including tables and graphs for clarity.\r\nThe first example shows biological treatment differences represented by the F-ratio. The second one shows how F-ratio controls industrial operations through determining batch variability. The third case has F-ratio regulating environmental science rainfall patterns. The examples show the usefulness of the distribution in variance analysis and making decisions across fields.\r\n