Whether Gaussian Nucleus Entropy Helps? Case in Point is Prediction of Number of Cesarean Births

In this article, entropy in the collected data about the Gaussian population mean is traced from its embryonic stage as new data are periodically collected. The traditional Shannon's entropy has shortcomings from the data analytics point of view and it creates a necessity to refine the Shannon's entropy. Its refined version is named Gaussian Nucleus Entropy in this article. Advantages of the refined version are pointed out. The Prior, likelihood, Posterior and predictive nucleus entropies are derived, interconnected and interpreted. The results are illustrated using data on cesarean births in thirteen countries in the period [1987, 2007]. The medical communities and families are alarmed, as the cesarean births are increasing not due to emergency or necessity basis but rather for monetary or convenience basis. Nucleus entropy based data analysis answers whether their alarm is baseless.