Levy distributions are the natural limiting class whenever independent price increments converge at all.

Evidence

First, Levy distributions had been shown mathematically to occupy a certain privileged position. A generalization of the central limit theorem that was known well enough to be found in the more advanced textbooks of probability theory was that “if a sum of independent random variables with common distribution tends toward any limiting distribution, that distribution will be a member of the [Levy] class” (Roll 1970, p. 63, summarizing Feller 1966, p. 168). The random-walk hypothesis suggested that price changes were indeed sums of independent random variables, so this theorem might well apply. — Donald MacKenzie, An Engine, Not a Camera, 490

Categorization

• DEFINE: Explains the privileged mathematical status of Levy distributions via the generalized central limit theorem — central to why Mandelbrot’s claim was theoretically attractive.