Effect of Non-Integer Order Moments on Parameter Estimation of Pareto Distributed Clutter plus Noise

In this paper, accurate estimate of the Pareto plus noise shape parameter using a modified non-integer positive and negative order moment estimator is investigated. Closed form of the NIPNOME is derived in a previous work [16]. In single pulse case with a fixed value of the order moment, undesirable shape parameter estimates are obtained for high shape parameter values. In the prospect of improving the estimation performance, the NelderMead algorithm is used to optimize two parameters fitness function involving the shape and the non-integer order moment of the considered model. The impact of the order moment on the NIPNOME is examined firstly using simulated Pareto plus noise data. Then, via IPIX database, fitting comparisons are carried out using Pareto plus noise PDFs and CCDFs where [zlog(z)] and NIPNOME are employed to elucidate the robustness of the proposed estimator