Estimation Accuracy of Partial Q-Q Plot of Log-Weibull Distribution

Abstract

In stormy weather due to typhoon approaching the Kanto district, I have observed sea clutter containing a target (ship) using an X-band radar with a frequency of 9.41GHz, a beamwidth of 1.0°, a pulsewidth of 0.5µs, and a pulse-repetition frequency of 1,600Hz. To estimate the sea clutter amplitude statistics, I have used partial Q-Q plot. The partial Q-Q plot is as follows : locate the maximum value on the histogram of observed data and find the point on Q-Q plot corresponding to the maximum value. Fit the approximate line to this point and the nearest ones on both sides by least squares method. Adding a neighbor point on the right side of these ones, fit it similarly, and then adding a neighbor point on the left side of these ones, fit it similarly. Repeat them and select the approximate line giving the smallest RMSE (Root Mean Square Error). I have found that the sea clutter amplitudes obey the log-Weibull distribution with the shape parameters of c=21.13 for entire data and c=17.80 to 32.26 for data within the beam width of an antenna. When sea clutter contains a target, it is found that the partial Q-Q plot is more rigorous fit of the distribution to the data than maximum log-likelihood method.