Exact Likelihood Inference and Robust Filtering for Gauss-Cauchy Convolution Models
高斯—柯西卷积模型的精确似然推断与稳健滤波
The convolution of a Gaussian and a Cauchy distribution, known as the Voigt distribution, is widely used in spectroscopy and provides a natural framework for modeling heavy-tailed measurement noise. We derive analytical expressions for its density, score, Hessian, Fisher information, and conditional moments using the scaled complementary error function, enabling stable maximum likelihood estimation without numerical convolution, finite-difference derivatives, or pseudo-Voigt…