Zipf's Law and Benford's Law

Paper Summary:

This paper addresses both Zipf's Law and Benford's Law. It describes the theories of each law in detail and discusses how they can be applied to various situations. It describes Zipf's Law as not a theoretical law, but rather an experimental law. The paper then discusses the significance of these two laws to the field of mathematics.

From the Paper:

"However, there is some lack of precision where this is concerned. Most items have to occur a number of times that is actually an integer (Li, n.d.). In other words, a word that is seen within a document cannot appear in that document 2.5 number of times. It either must appear, in this example, 2 times or three times, since there cannot be an area of the document where only 1/2 of the word appears. Despite the fact that there is some variation and lack of precision, however, when wide ranges are examined and one only desires to have a relatively close approximation, many of the natural phenomena that are seen in this world do obey Zipf's law (Li, n.d.). This is seen to hold true as long as the individual examining the issue is not looking for scientific precision and will accept the slight variation that is seen."

Sample of Sources Used:

• Bogomolny, A. "Benford's Law and Zipf's Law." http://www.cut-the-knot.org/do_you_know /zipfLaw.shtml.
• Hill, T. P. "Base-Invariance Implies Benford's Law." Proc. Amer. Math. Soc. 12, 887-895, 1995.
• Li, W. "Zipf's Law." http://linkage.rockefeller.edu/wli/zipf/.
• Wikipedia. (2006). Benford's Law. http://en.wikipedia.org/wiki/Benford%27s_law.

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