Of the four parameters defining the family, most attention has been focused on the stability parameter, α (see panel). Stable distributions have 0 < α ≤ 2, with the upper bound corresponding to the normal distribution, and α = 1 to the Cauchy distribution. The distributions have undefined variance for α < 2, and undefined mean for α ≤ 1. The importance of stable probability distributions is that they are "attractors" for properly normed sums of independent and identically distributed (iid) random variables. The normal distribution defines a family of stable distributions. By the classical central limit theorem the properly normed sum of a set of random variables, each with finite variance, will tend toward a normal distribution as the number of variables increases. Without the finite variance assumption, the limit may be a stable distribution that is not normal. Mandelbrot referred to such distributions as "stable Paretian distributions", after Vilfredo Pareto. In particular, he referred to those maximally skewed in the positive direction with 1 < α < 2 as "Pareto–Lévy distributions", which he regarded as better descriptions of stock and commodity prices than normal distributions.