Minimum Variance Unbiased Estimators of Generalized Gaussian Distribution With an H-Proper Quaternion Random Variable

This paper presents a comprehensive approach to parameter estimation in generalized Gaussian distributions (GGD) with -proper quaternion random variables, utilizing Maximum Likelihood Estimation (MLE) and the Minimum Variance Unbiased Estimator (MVUE). These estimators provide a means to accurately capture the shape and scale parameters of quaternion-valued GGDs, which are increasingly relevant in multidimensional signal processing applications such as radar, sonar, and communications. By incorporating the Cramér-Rao Lower Bound (CRLB) as a performance benchmark, we assess the efficiency and effectiveness of MLE and MVUE in estimating GGD parameters within quaternion contexts. Our findings show that MLE achieves lower bias, especially with large sample sizes, while MVUE offers minimal variance, aligning with the CRLB. This study contributes to the development of robust statistical tools for quaternion-based data modeling, providing insights into efficient estimation techniques that support advanced signal processing tasks involving complex data structures.