added latex equation to percentage_change_trans and updated bivariate…

… transformations user guide in sphinx docs

docs/user_guide/percentage_change.rst

@@ -1,7 +1,50 @@
-Percentage Change
-=============
+=========================
+Bivariate Transformations
+=========================
 
-Currently percentage change is implemented in two ways. You can either provide raw data in the form
-of observations from 2 separate, equally sized samples (as you would have from an experiment) or
-raw counts with the separate, not necessarily equal sample sizes (as you would have from incidence
-counts at two separate times)
+There are currently 2 bivariate transformations implemented in distrx:
+    * percentage change
+    * ratio
+
+These transformations are implemented using the first order delta method. See INSERT CONCEPTS for
+derivation if desired. Note that all functions are in terms of sample statistics (e.g. mean), not
+raw counts, even though some functions do take counts as input.
+
+Example: Percentage Change
+--------------------------
+
+Suppose we have samples in 2 different years measuring the incidence of cancer cases in each year
+in various state counties. The data may look something like the following,
+
+.. csv-table::
+   :header: county, cases_1, sample_1, cases_2, sample_2
+   :widths: 10, 10, 10, 10, 10
+   :align: center
+
+   "King", 252, 400, 258, 250
+   "Snohomish", 12, 300, 90, 500
+   "Pierce", 505, 1000, 219, 1000
+   "Kitsap", 88, 124, 67, 204
+
+and our goal is to find the percentage change in the prevalence of cancer with its appropriate SE.
+
+The first step is to import the required function from the distrx package.
+
+.. code-block:: python
+
+    from distrx import transform_univariate
+
+Different transformation functions can be chosen through specifying a string parameter of which
+transform you would like to apply to your data. In this case, it is the following.
+
+.. code-block:: python
+
+    mu_tx, sigma_tx = transform_bivariate(c_x=df["cases_1"],
+                                          n_x=df["sample_1"],
+                                          c_y=df["cases_2"],
+                                          n_y=df["sample_2"],
+                                          transform="percentage_change")
+
+``mu_tx`` and ``sigma_tx`` are simply the percentage change for each county and their corresponding
+standard errors, respectively. ``sigma_tx`` has already been scaled the appropriate sample size so
+we **should not** scale it additionally to obtain a confidence interval.

docs/user_guide/simple_transformations.rst

@@ -16,7 +16,7 @@ order Taylor expansion of the transformation function.
 Example: Log Transform
 ----------------------
 
-Assume that we have some means and standard errors (SEs) of systolic blood pressure (SBP) from
+Suppose that we have some means and standard errors (SEs) of systolic blood pressure (SBP) from
 several different samples. The data may look something like the following,
 
 .. csv-table::

src/distrx/transforms.py

@@ -192,7 +192,7 @@ def percentage_change_trans(
 
         .. math::
 
-            \frac{p_y}{p_x} - 1, \sigma * \exp(\mu)
+            \frac{p_y}{p_x} - 1, \sqrt{\frac{\sigma_y^2}{n_y\mu_x^2} + \frac{\mu_y^2\sigma_x^2}{n_x\mu_x^4}}
 
         Parameters
         ----------