Statistical Modeling of Pixel Intensities Using a Novel Generalized Probability Distribution Family

This study proposes a new family of continuous probability distributions, called the Continuous Bernoulli-G (CB-G), which is constructed using the T–X framework by adopting the Continuous Bernoulli (CB) distribution as the generator. Defined on a positive and continuous interval, this family provides a flexible modeling framework by combining the structural properties of the CB distribution with various baseline distributions. The primary motivation behind developing this new family is to generate alternative distributions that are particularly suitable for modeling pixel intensities in grayscale image analysis.Fundamental statistical properties of the proposed family—such as the probability density and cumulative distribution functions, quantile function, moments, entropy, reliability measures, and maximum likelihood estimation—are derived. Three special submodels of the CB-G family, based respectively on the Beta, Uniform, and Weibull distributions, are examined in detail due to their mathematical tractability and practical relevance. The proposed models are applied to grayscale image data extracted from the CIFAR-100 dataset, and their performance is evaluated using log-likelihood values and information criteria (such as AIC). The results show that, in particular, the CB-B and CB-W distributions outperform the classical Beta and CB distributions in modeling pixel intensity distributionsThis study demonstrates the potential of the proposed family to contribute to real-world data modeling problems and provides a foundation for a wide range of future theoretical and applied research efforts.