Quantitative Comparison of the Yildirim Limit and Classical Mean in Photon Energy Modulation

This study presents a detailed quantitative analysis of the Yildirim Limit—a novel mathematical approach to statistical averaging—against the classical arithmetic mean in the context of continuous photon energy modulation during IMRT (Intensity-Modulated Radiation Therapy) for pancreatic cancer. Using a real dataset from Zhang et al. (2023)[1], we show that the Yildirim Limit captures subtle statistical variations and tail effects not fully represented by the classical mean, highlighting its potential as an advanced analysis tool in both medical and fundamental physical sciences.The author acknowledges the use of OpenAI’s language model for assistance in drafting certain sections of this workl