Merge pull request #1185 from dschmitz89/cauchy_docs

DOC: fix Cauchy CDF formula
boostorg · Aug 23, 2024 · 66b362a · 66b362a
2 parents 8d92f8f + 9862296
commit 66b362a
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diff --git a/doc/distributions/cauchy.qbk b/doc/distributions/cauchy.qbk
@@ -116,7 +116,7 @@ So recall that for `x < 0`:
 
 Substituting into the above we get:
 
-[expression p = -atan(1/x)  ; x < 0]
+[expression p = -atan(1/x) / [pi]  ; x < 0]
 
 So the procedure is to calculate the cdf for -fabs(x)
 using the above formula.  Note that to factor in the location and scale

diff --git a/doc/html/math_toolkit/dist_ref/dists/cauchy_dist.html b/doc/html/math_toolkit/dist_ref/dists/cauchy_dist.html
@@ -221,7 +221,7 @@ <h5>
                     Substituting into the above we get:
                   </p>
                   <div class="blockquote"><blockquote class="blockquote"><p>
-                      <span class="serif_italic">p = -atan(1/x) ; x &lt; 0</span>
+                      <span class="serif_italic">p = -atan(1/x)/π ; x &lt; 0</span>
                     </p></blockquote></div>
                   <p>
                     So the procedure is to calculate the cdf for -fabs(x) using the

diff --git a/include/boost/math/distributions/cauchy.hpp b/include/boost/math/distributions/cauchy.hpp
@@ -57,7 +57,7 @@ BOOST_MATH_GPU_ENABLED RealType cdf_imp(const cauchy_distribution<RealType, Poli
    //
    // Substituting into the above we get:
    //
-   // CDF = -atan(1/x)  ; x < 0
+   // CDF = -atan(1/x)/pi  ; x < 0
    //
    // So the procedure is to calculate the cdf for -fabs(x)
    // using the above formula, and then subtract from 1 when required