Rényi extropy revisited: Enhanced framework for cryptocurrency risk analysis with machine learning

.This article extends the theoretical framework of Rényi extropy by establishing new properties, including its convergence to information extropy under limiting parameter conditions and its ability to assume both positive and negative values. Furthermore, it explores the interrelationships among Rényi, information, and Tsallis extropies, providing a unified perspective on these uncertainty measures. To demonstrate its practical utility, we apply Rényi extropy to analyze uncertainty in cryptocurrency markets, specifically Bitcoin (BTC) and Ethereum (ETH). Our findings reveal its superior capability in capturing non Gaussian dynamics and assessing risk compared to traditional entropy-based methods. Furthermore, we integrate machine learning techniques, including Extreme Gradient Boosting (XGBoost) and k-Nearest Neighbors (kNN) to predict BTC and ETH prices, validating the synergy between advanced statistical measures and computational forecasting. The predictive performance is evaluated using advanced XGBoost and k-NN models, assessed through RMSE and R2 metrics. The results demonstrate a significant improvement over traditional benchmarks, including Shannon entropy and ARIMA, in forecasting risk-adjusted returns. The empirical results underscore Rényi extropy’s potential as a robust tool for financial market analysis and risk management.