Cumulative Probability Distribution Function of Absorption Coefficient with MATLAB Implementation

This section discusses the cumulative probability distribution function of absorption coefficients and the utilization of MATLAB for curve fitting applications. We will elaborate on these concepts in detail. The absorption coefficient represents a medium's capacity to absorb electromagnetic waves, serving as a crucial optical parameter. The cumulative probability distribution function is a fundamental statistical concept that describes the probability of a random variable being less than or equal to a specific value. By integrating these two concepts, we investigate medium absorption phenomena and their impact on light propagation. For enhanced data analysis, we employ MATLAB, a powerful computational tool for numerical fitting. The implementation typically involves using MATLAB's Distribution Fitting Tool (dfittool) or programming approaches with key functions like: - ecdf() for empirical cumulative distribution calculation - fitdist() for probability distribution fitting - nlinfit() for nonlinear curve fitting algorithms Through fitting the cumulative probability distribution function of absorption coefficients, we gain deeper insights into optical properties of media. This analysis provides fundamental support for subsequent research by enabling: 1. Parameter estimation using maximum likelihood methods 2. Goodness-of-fit evaluation with metrics like R-squared and RMSE 3. Predictive modeling of light-matter interactions The MATLAB implementation allows for automated processing of experimental data, visualization of fitting results, and statistical validation of optical models, establishing a robust foundation for advanced photonics research.