From a total of $N$ words i have the following dataset where the first column represents the ranks and the second the frequency. For example $$\begin{array}{cc} 1 & 4300 \\ 2 & 3100 \\ 3 & 2500 \\ 4 & 1900 \\ \vdots & \vdots \end{array} $$ I want to find the constant where satisfies $$cf_i =\frac{\text{const}}{i}$$ where $i$ is the rank and $cf_i$ the frequency. I have plotted the loglog plot of the data and found the fitting line through regression but i cannot understand how to found $\text{const}$. Any ideas?
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You have $\displaystyle cf_i = \frac{\text{const}} i.$ Dividing both sides by $c$ you get$\vphantom{\displaystyle\frac{\displaystyle\int}{\displaystyle\int}}$$$ f_i = \frac{\text{const}/c} i = \frac{\text{a different constant}} i, $$ so only one constant is involved. In other words, your way of writing it makes it appear slightly more complicated than it is. $\qquad$ – Michael Hardy May 31 '23 at 16:55