论文标题
单词级别频率关系的两个参数方程
A Two Parameters Equation for Word Rank-Frequency Relation
论文作者
论文摘要
令$ f（\ cdot）$为单词的绝对频率，而$ r $为频率下降顺序的单词等级，那么以下函数可以适合级别频率关系\ [f（r; s，t）= \ left（\ frac {\ frac {r _ {\ tt max}}}} {r}} {r} {r} {r} {1-s} \ left（\ frac {r _ {\ tt max}+t \ cd \ cdot r _ {\ tt exp}}} {r+t \ cdot r _ {\ tt exp}}} \ right）分别对等级的期望； $ s> 0 $和$ t> 0 $是从数据估算的参数。在行为良好的数据上，应该有$ s <1 $和$ s \ cdot t <1 $。
Let $f (\cdot)$ be the absolute frequency of words and $r$ be the rank of words in decreasing order of frequency, then the following function can fit the rank-frequency relation \[ f (r;s,t) = \left(\frac{r_{\tt max}}{r}\right)^{1-s} \left(\frac{r_{\tt max}+t \cdot r_{\tt exp}}{r+t \cdot r_{\tt exp}}\right)^{1+(1+t)s} \] where $r_{\tt max}$ and $r_{\tt exp}$ are the maximum and the expectation of the rank, respectively; $s>0$ and $t>0$ are parameters estimated from data. On well-behaved data, there should be $s<1$ and $s \cdot t < 1$.
