Cumulative Probability Distribution Function of Absorption Coefficient

The cumulative probability distribution function of absorption coefficient serves as a statistical tool describing how the probability of photon or particle absorption in a medium varies with changing absorption coefficients. Its core lies in constructing probability distribution models through experimental or simulated data, reflecting the cumulative likelihood of different absorption intensities occurring.

Implementing this distribution function in MATLAB typically involves the following steps: First, prepare experimental absorption coefficient datasets and generate raw probability distributions using histogram or ksdensity functions. Then call the cdf function to compute cumulative probability values. For theoretical fitting, select appropriate models (such as lognormal distribution, Weibull distribution, etc.) based on data characteristics, use fitdist for parameter estimation, and finally visualize results through probability plots (probplot) or custom fitting curves.

The key aspects include model selection and goodness-of-fit testing: Compare AIC/BIC values of different distribution functions or perform K-S tests using kstest to ensure the selected model accurately reflects data characteristics. For strongly nonlinear distributions, combine with Curve Fitting Toolbox for custom equation fitting to optimize physical interpretation of parameters. This methodology finds widespread application in data analysis for atmospheric optics, biological tissue imaging, and related fields.