Refined gamma kernel estimator outperforms standard methods for positive random variables.
Standard kernel density estimators struggle with positive random variables close to zero. Asymmetric gamma kernel estimators perform better but depend on the shape of the density near zero and the chosen kernel. A refined gamma kernel with an extra parameter based on the density shape near the boundary improves estimation. Comparing different estimators in simulations, the refined gamma kernel outperforms others in all scenarios. Real-world applications in stock trading volumes and volatility forecasts show the practical benefits of this new approach.