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Zipf’s law: Brief

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Added on  2020-01-16

Zipf’s law: Brief

   Added on 2020-01-16

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(a)Zipf’s law:It states that given some corpus of natural language utterances, the frequency of any word is inversely proportional to its rank in the frequency table.Zipf’s law states that rank (r) of a word times its frequency (f) is approximately a constant (k) assuming words are ranked in order of decreasing frequency.r.f ≈ k or r.Pr ≈ c where,Pr is probability of word occurrence and c ≈ 0.1 for English.Zipf’s law is very important application in Information Retrieval. The whole data on the internet satisfies the zipf’s law.(b)Zipf’s law: Pr = A/rSince the probability of seeing any of the first m words must be 60% or greater, we would like to find the minimal m such that: A1+ A2 + .. + Am ≥ 0.6Here, we add up the terms for most common words manually to find minimal m: p1 = 0.21 = 0.2
Zipf’s law: Brief_1
p2 = 0.22 = 0.1 p3 = 0.23 = 0.07p4 = 0.24 = 0.05p5 = 0.25 = 0.04p6 = 0.26 = 0.033p7 = 0.27 = 0.028p8 = 0.28 = 0.025p9 = 0.29 = 0.022p10 = 0.210 = 0.02
Zipf’s law: Brief_2
p11 = 0.211 = 0.018p1 + p2 +p3 +p4 +p5 +p6 +p7 +p8 +p9 +p10 =0.588while,p1 + p2 +p3 +p4 +p5 +p6 +p7 +p8 +p9 +p10 +p11=0.606 > 0.6Therefore,m=11
Zipf’s law: Brief_3

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