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DOC: fix Cauchy CDF formula

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dschmitz89
2024-08-23 20:34:35 +02:00
parent 8d92f8fe0a
commit 98622966ec
3 changed files with 3 additions and 3 deletions
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2
doc/distributions/cauchy.qbk
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@@ -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

2
doc/html/math_toolkit/dist_ref/dists/cauchy_dist.html
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@@ -221,7 +221,7 @@
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

2
include/boost/math/distributions/cauchy.hpp
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@@ -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