A PROBABILITY-WEIGHTED MOMENT TEST TO ASSESS SIMPLE SCALING

We present a statistically robust approach based on probability weight ed moments to assess the presence of simple scaling in geophysical pro cesses. The proposed approach is different from current approaches whi ch rely on estimation of high order moments. High order moments of sim ple scaling processes (distributions) may not have theoretically defin ed values and consequently, their empirical estimates are highly varia ble and do not converge with increasing sample size. They are, therefo re, not an appropriate tool for inference. On the other hand we show t hat the probability weighted moments of such processes (distributions) do exist and hence, their empirical estimates are more robust. These moments, therefore, provide an appropriate tool for inferring the pres ence of scaling. We illustrate this using simulated Levy-stable proces ses and then draw inference on the nature of scaling in fluctuations o f a spatial rainfall process.