Several families of Beta distributions, such as Beta of the first kind, Beta of the second kind, and Beta of the third kind, have been proposed in the literature for modeling random phenomena. This study introduced a new member of the Beta family called the New Beta (NE-Beta) distribution using a logarithmic transformation approach. This new model is highly flexible and capable of analyzing both positive and negative data, making it suitable for a wide range of interdisciplinary applications. The NE-Beta distribution exhibits nearly symmetric, right-skewed, or left-skewed density functions and featured an increasing or decreasing hazard functions, which are crucial for accurately modeling practical scenarios across various fields. Some properties of the new distribution were derived, and the parameter estimation was obtained by utilizing various approaches. To demonstrate the efficacy of the NE-Beta distribution, it was applied to multiple datasets, including exchange rate returns (finance), biomedical data, engineering reliability data, and hydrological data. The results indicate that the proposed NE-Beta model outperforms its competitors across these diverse domains.

In this study, we introduced the log-Lomax distribution, a more versatile probabilistic model for capturing various statistical properties. The study was divided into two sections: Modeling stock price exchange rates with the proposed log-Lomax distribution and incorporating log-Lomax features into machine learning models for prediction. In the modeling section, we introduced the log-Lomax distribution, which employed a logarithmic transformation with an exponent parameter. The model was left- and right-skewed, monotonic, inverted, and bathtub-shaped. Some properties were obtained, and several parameter estimation techniques were evaluated using a simulation study. The model was applied to two Nigerian stock exchange rate datasets: Naira-to-Euro and Naira-to-Riyal, as well as the Worcester heart attack patient dataset. The prediction section used insights from modeling methods and machine learning workflows to improve accuracy and reduce overfitting. The predictions were evaluated in two ways: With raw data and features derived from the log-Lomax model. Employing log-Lomax model features, Random Forest, and XGBoost achieved 99.87% accuracy in the Euro dataset, respectively. Random Forest and XGBoost had accuracy rates of 98.67% and 99.33% on the Riyal dataset, respectively, and 91.25% and 88.75% on the heart attack dataset. Random Forests and XGBoost are the preferred models, as they consistently provide the best prediction performance and stability mix across datasets.