Can you determine from the history of x,y coordinates of the mover whether he's employing the levy walk?

Question

I have a movement model that is creating traces much like the traces of a Levy walk. I would like to statistically justify that the movement model is indeed a levy model. For that, I believe I need to show that it follows a power law distribution. Can I use the history of x,y coordinates to check if the movement is a levy walk/flight? If so, how?

Answer 1

The important part is the step length; if you can find those from the history of coordinates, then the rest falls into place: to detect a power law distribution you can take a power law regression, which is essentially taking, for each index and matching value $k$, $x_k$, their logarithms $\log(k)$ and $\log(x_k)$, and taking a linear regression through those values. A power-law distribution will correlate well in this situation.