Estimating the Pareto plus noise distribution parameters using non-integer order moments and [zlog(z)] approaches

Pareto plus noise clutter distribution has been introduced recently as a good candidate model for X-band high resolution maritime clutter returns. In this study, the authors derive a non-integer order moments estimator (NIOME) and [zlog(z)] based estimator to find the parameters of this distribution in the case of non-coherent integration of N-pulses. For this, the authors first develop an asymptotic formula of moments with non-integer order which is expressed in terms of the gamma and the generalised hypergeometric functions. Then, the authors derive [zlog(z)] based approach as a function of the log based moments and the generalised hypergeometric function. By accommodating a non-integer moments and moments of orders one and two, the proposed estimators are given so that non-linear estimates of the shape parameter are achieved using numerical computations. Through synthetic and real data, the authors show numerous examples demonstrating the applicability of the estimation procedures as a function of clutter-plus-noise parameters. The obtained results illustrate that the proposed NIOME method is asymptotically efficient especially for multiple looks case and high sample size.