A probability-weighted moment test to assess simple scaling

We present a statistically robust approach based on probability weighted moments to assess the presence of simple scaling in geophysical processes. The proposed approach is different from current approaches which rely on estimation of high order moments. High order moments of simple scaling processes (distributions) may not have theoretically defined values and consequently, their empirical estimates are highly variable and do not converge with increasing sample size. They are, therefore, not an appropriate tool for inference. On the other hand we show that 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 presence of scaling. We illustrate this using simulated Levystable processes and then draw inference on the nature of scaling in fluctuations of a spatial rainfall process.