Infinite variance plays havoc with standard statistical procedures. Levy distributions with values of alpha other than 2 could thus seem to be theorists' oddities, of little or no value to practical statisticians. I was taught statistics as an undergraduate in 1970-1972. Levy distributions were never mentioned explicitly, though one member of the family the "Cauchy distribution," for which a = 1 was described briefly, perhaps as a warning to students not unthinkingly to assume that a distribution's "moments" its mean, its variance, and so on always exist.

Donald MacKenzie, An Engine, Not a Camera, loc. 481