File:Zipf-engl-0_English_-_Culpeper_herbal_and_War_of_the_Worlds.svg · Wikimedia Commons · See Wikimedia Commons
In the Vinony graph
Vinony's link graph records 349 inbound references to Zipf's law, and connects out to Torah, continuous uniform distribution and discrete uniform distribution.
It is catalogued under topics including 1949 introductions, Bibliometrics and Computational linguistics.
Vinony links it to 40 Wikipedia language editions.
Key facts
- Parameters
- s ≥ 0 {\displaystyle s\geq 0\,} ( real ) N ∈ { 1 , 2 , 3 … } {\displaystyle N\in \{1,2,3\ldots \}} ( integer )
- Support
- k ∈ { 1 , 2 , … , N } {\displaystyle k\in \{1,2,\ldots ,N\}}
- Pmf
- 1 / k s H N , s {\displaystyle {\frac {1/k^{s}}{H_{N,s}}}} where H N,s is the N th generalized harmonic number
- Cdf
- H k , s H N , s {\displaystyle {\frac {H_{k,s}}{H_{N,s}}}}
- Mean
- H N , s − 1 H N , s {\displaystyle {\frac {H_{N,s-1}}{H_{N,s}}}}
- Mode
- 1 {\displaystyle 1\,}
- Variance
- H N , s − 2 H N , s − H N , s − 1 2 H N , s 2 {\displaystyle {\frac {H_{N,s-2}}{H_{N,s}}}-{\frac {H_{N,s-1}^{2}}{H_{N,s}^{2}}}}
- Entropy
- s H N , s ∑ k = 1 N ln ( k ) k s + ln ( H N , s ) {\displaystyle {\frac {s}{H_{N,s}}}\sum \limits _{k=1}^{N}{\frac {\ln(k)}{k^{s}}}+\ln(H_{N,s})}
- Mgf
- 1 H N , s ∑ n = 1 N e n t n s {\displaystyle {\frac {1}{H_{N,s}}}\sum \limits _{n=1}^{N}{\frac {e^{nt}}{n^{s}}}}
- Cf
- 1 H N , s ∑ n = 1 N e i n t n s {\displaystyle {\frac {1}{H_{N,s}}}\sum \limits _{n=1}^{N}{\frac {e^{int}}{n^{s}}}}
via Wikipedia infobox
~20 min read
Encyclopedic overview
A plot of the frequency of each word as a function of its frequency rank for two English language texts: Culpeper's Complete Herbal (1652) and H. G. Wells's The War of the Worlds (1898) in a log-log scale. The dashed line is the ideal law
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Excerpted from Wikipedia’s “Zipf's law” article, available under the CC BY-SA 4.0 licence.