Cramer-Rao Lower Bound Computation Via the Characteristic Function

The Cramer-Rao Lower Bound is widely used in statistical signal processing as a benchmark to evaluate unbiased estimators. However, for some random variables, the probability density function has no closed analytical form. Therefore, it is very hard or impossible to evaluate the Cramer-Rao Lower Bound directly. In these cases the characteristic function may still have a closed and even simple form. In this paper, we propose a method to evaluate the Cramer-Rao Lower Bound via the characteristic function. As an example, the Cramer-Rao Lower Bound of the scale parameter and the shape parameter of the K-distribution is accurately evaluated with the proposed method. Finally it is shown that for probability density functions with a scale parameter, the Cramer-Rao Lower Bound for the remaining parameters do not depend on the scale parameter.