<p>The normalising constant is fairly easy to calculate. See the <a href="http://arxiv.org/abs/0706.1062" rel="nofollow"><em>Clauset et al's</em></a> powerlaw paper (in particular table 2.1). For the continuous case, <em>C = (alpha-1) xmin^(alpha-1)</em>, the discrete case involves calculating the diagamma function.</p>

<p>You can also examine the R code:</p>

<ul>
<li><a href="https://github.com/csgillespie/poweRlaw/blob/master/pkg/R/pldis.R" rel="nofollow">Discrete</a></li>
<li><a href="https://github.com/csgillespie/poweRlaw/blob/master/pkg/R/plcon.R" rel="nofollow">Continuous</a></li>
</ul>
Fitting power-law distributions with poweRlaw package in R
<p>With poweRlaw library, and once computed <code>alpha</code> and <code>xmin</code> with <code>estimate_xmin</code>, which formula the script uses to compute the fitted values?
I mean, assuming that y=C·x^(-alpha), my question is how the script computes the <em>normalization constant</em> from <code>alpha</code> and <code>xmin</code>.</p>