From 8dbbdff673d717463a951ad9897b07ee423dd4bc Mon Sep 17 00:00:00 2001
From: martinmodrak <modrak.mar@gmail.com>
Date: Wed, 12 May 2021 12:47:10 +0200
Subject: [PATCH] Fix #356 - affine transform docs has the wrong direction of
 transform

---
 src/reference-manual/transforms.Rmd | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/src/reference-manual/transforms.Rmd b/src/reference-manual/transforms.Rmd
index 7ad1c978d..4e3a5bd45 100644
--- a/src/reference-manual/transforms.Rmd
+++ b/src/reference-manual/transforms.Rmd
@@ -292,7 +292,7 @@ Stan uses an affine transform.  Such a variable $X$ is transformed to a new
 variable $Y$, where
 
 $$
-Y = \mu + \sigma * X.
+Y = \frac{X - \mu}{\sigma}.
 $$
 
 The default value for the offset $\mu$ is $0$ and for the multiplier $\sigma$ is
@@ -304,7 +304,7 @@ $1$ in case not both are specified.
 The inverse of this transform is
 
 $$
-X = \frac{Y-\mu}{\sigma}.
+X =  \mu + \sigma \cdot Y.
 $$
 
 ### Absolute derivative of the affine inverse transform
@@ -316,10 +316,10 @@ $$
 \left|
   \frac{d}{dy}
     \left(
-      \frac{y-\mu}{\sigma}
+      \mu + \sigma \cdot y
     \right)
   \right|
-= \frac{1}{\sigma}.
+= \sigma.
 $$
 
 Therefore, the density of the transformed variable $Y$ is
@@ -327,8 +327,8 @@ Therefore, the density of the transformed variable $Y$ is
 $$
 p_Y(y)
 =
- p_X \! \left( \frac{y-\mu}{\sigma} \right)
-    \cdot \frac{1}{\sigma}.
+ p_X \! \left( \mu + \sigma \cdot y \right)
+    \cdot \sigma.
 $$