Modeling Image Pixel Intensities Using Continuous Probability Distributions

Abstract

This paper presents a comprehensive analysis of five fundamental continuous probability distributions—Normal, Gamma, Weibull, Beta, and Exponential—applied to five image datasets. We estimate parameters using Maximum Likelihood Estimation (MLE) and evaluate the goodness-of-fit using Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). The results consistently demonstrate that the Weibull distribution provides the best fit across all image datasets, outperforming other distributions based on information criteria. Visual assessments through histograms, fitted plots, and probability density function comparisons support these findings. Additionally, we provide R code implementations for plotting probability density and cumulative distribution functions for all five distributions. The findings highlight the importance of selecting appropriate distributions for image data analysis and the versatility of the Weibull distribution in modeling image pixel intensity distributions.