A New Type of Moment Estimator for the K-distribution Shape Parameter with High Accuracy and Efficiency

The X-Estimator (XE) for the K-distribution shape parameter v based on the zlog(z) expectation can be computed without solving nonlinear equations; thus, it has high estimating efficiency. Nonetheless, its estimating accuracy is lower than many other moment estimators, and occasionally the XE results in odd values. To best use its advantages and avoid its disadvantages, on the basis of derivation and analysis of the XE bias using a set of Monte Carlo experiments, the X-Estimator with a Corrective term (XCE), which overcomes the above shortcomings of the XE, is discussed. Simulations show that the XE and XCE have the same high computational estimating efficiency, whereas the XCE significantly enhances the accuracy of the estimating shape parameter.