<p dir="auto">I'm using scipy's Fisk distribution. The <a href="https://github.com/scipy/scipy/blob/v1.6.3/scipy/stats/_continuous_distns.py">documentation</a> says the pdf is:</p>
<p dir="auto"><code class="notranslate">f(x, c) = c x^{-c-1} (1 + x^{-c})^{-2}</code>,</p>
<p dir="auto">but it should be:</p>
<p dir="auto"><code class="notranslate">f(x, c) = c x^{c-1} (1 + x^{c})^{-2}</code>.</p>
<p dir="auto">I think the same applies to the documentation of the Burr distribution. I'm not sure if this is worthy of an issue, just wanted to mention it because it could potentially confuse users.</p>
<p dir="auto">In <code class="notranslate">_continuous_distns.py</code> [1] the method <code class="notranslate">burr_gen._pdf()</code> specifies the PDF of the Burr distribution, which is also used by the Fisk distribution (<code class="notranslate">fisk_gen._pdf()</code>).</p>
<p dir="auto">The current PDF is <code class="notranslate">c*d*(x**(-c-1.0))*((1+x**(-c*1.0))**(-d-1.0))</code>, however, the sign of the first <code class="notranslate">c</code> is wrong.</p>
<p dir="auto">The PDF should be: <code class="notranslate">c*d*(x**(c-1.0))*((1+x**(-c*1.0))**(-d-1.0))</code>.</p>
<p dir="auto">This can be verified in Equation 53 of the paper referenced in the class documentation [2].</p>
<p dir="auto">[1] scipy/scipy/stats/_continuous_distns.py<br>
[2] Burr, I. W. "Cumulative frequency functions", Annals of Mathematical Statistics, 13(2), pp 215-232 (1942).</p>