How organisms move and disperse is crucial in ecology and random walk (RW) models are typical tools to describe movement patterns. Whether forager movements are better described by Lévy or alternate RW is keenly debated, mostly because of methodological shortcomings. We get around this issue using the Generalized Pareto Distribution (GPD), which includes Brownian, exponential or Lévy as specific cases. We provide a statistically-sound definition of the tail of the move length distribution, and a robust goodness-of-fit test to sustain decision on the nature of the observed movement. Applied to Peruvian anchovy fishing vessels, GPD reveals that fishermen perform mostly Lévy walks in the industrial fleet (super diffusive movement) and light-tailed walks in the artisanal fleet (normally diffusive movement), and suggests this is related to different perceptions of the prey field. Fitting GPD lets the more likely RW model emerge from the data and makes easier analyzing the determinisms of movement strategies.