zipf’s law and heaps’ law

• Heaps’ Law
• Zip’s Law

Heaps’ Law

Heaps’ law can also be applied in characterizing natural language processing, according to which the vocabulary size grows in a sublinear function with document size, say $N(t) sim t^{lamda}$ with $% <![CDATA[ lamda<1 %]]>$, where t denotes the total number of words and N(t) is the number of distinct words.

Heap法则描述的是词的个数是整个文章长度的函数。即多次出现的词仅算一次的次数是所有单词（文档长度）的函数。

$$N(t) = Kt^{lamda} lamda approx 0.5 30 leq K leq 100$$

Zip’s Law

Ranking all the words in descending order of occurrence frequency and denoting by z(r) the frequency of the word with rank r, the Zipf’s law reads $z(r)=z_{max}r^{-alpha}$ , where $z_{max}$ is the maximal frequency and $alpha$ is the so-called Zipf’s exponent.

Zip法则指出一个词出现的频率是它频率降序排名的倒数。$y = kx^c, c=-1$ 也代表频率，x代表排名。