My apologies if this is a naive question but does anyone happen to know if the equation below (and/or the distribution it describes) is commonly know by a specific name?
$f(i) = ( a / i^k ) b^i$
(where $a$, $b$ and $k$ are constants; and, FWIW, for my purposes $i$ should be a positive integer denoting rank according to frequency)
This equation appears in Simon (1955), but he doesn't give it a specific name and always refers to it by its example number in his paper.
This is not my field so I'm not familiar with the relevant literature so I don't know how often this particular distribution crops up and if it is common enough to warrant a specific name (pointers to places where it does appear would also be appreciated though!).
The same formula is also mentioned in Tambovtsev & Martindale (2007), who call it a "Yule distribution" but, as far as I can glean, this seems wrong since it appears "Yule(-Simon)" refers to a different distribution; T&M seem to have mislabelled it based on a careless reading of Simon, who does indeed mention the above equation in the proximity of a discussion of Yule (1924).
Instead, Simon cites Champernowne (1953) for this equation; however, calling it a "Champernowne distribution" doesn't seem appropriate either since, isn't that already the name for a different distribution?
Help, comments and corrections would be gratefully appreciated!
Champernowne, D. G. 1953. A Model of Income Distribution. The Economic Journal 63(250): 318–51
Simon, H. A. 1955. On a class of skew distribution functions. Biometrika 42(3–4). 425–40.
Tambovtsev, Y. A. & C. Martindale. 2007. Phoneme frequencies follow a Yule distribution. SKASE Journal of Theoretical Linguistics 4(2). 1–11.
Yule, G. U. 1924. A mathematical theory of evolution, based on the conclusions of Dr J. C. Willis, F.R.S. Philosophical Transactions B 213(21).