diff --git a/src/functions-reference/bounded_discrete_distributions.Rmd b/src/functions-reference/bounded_discrete_distributions.Rmd
index a97d9bb39..152694ed0 100644
--- a/src/functions-reference/bounded_discrete_distributions.Rmd
+++ b/src/functions-reference/bounded_discrete_distributions.Rmd
@@ -158,7 +158,7 @@ logit-scaled chance of success alpha dropping constant additive terms
## Binomial-logit generalized linear model (Logistic Regression) {#binomial-logit-glm}
Stan also supplies a single function for a generalized linear model
-with Binomial likelihood and logit link function, i.e. a function
+with binomial likelihood and logit link function, i.e., a function
for logistic regression with aggregated outcomes. This provides a more efficient
implementation of logistic regression than a manually written
regression in terms of a Binomial likelihood and matrix
@@ -167,10 +167,11 @@ multiplication.
### Probability mass function
Suppose $N \in \mathbb{N}$, $x\in \mathbb{R}^{n\cdot m}, \alpha \in \mathbb{R}^n, \beta \in \mathbb{R}^m$, and $n \in
-\{0,\ldots,N\}$. Then \begin{align*}
-&\text{BinomialLogitGLM}(n~|~N, x, \alpha, \beta) = \text{Binomial}(n~|~N,\text{logit}^{-1}(\alpha_i + x_i\cdot
-\beta)) \\ &= \binom{N}{n} \left( \text{logit}^{-1}(\alpha_i + \sum_{1\leq j\leq m}x_{ij}\cdot \beta_j) \right)^{n} \left( 1 -
-\text{logit}^{-1}(\alpha_i + \sum_{1\leq j\leq m}x_{ij}\cdot \beta_j) \right)^{N - n}. \end{align*}
+\{0,\ldots,N\}$. Then
+\begin{align*}
+ &\text{BinomialLogitGLM}(n~|~N, x, \alpha, \beta) = \text{Binomial}(n~|~N,\text{logit}^{-1}(\alpha_i + x_i \cdot \beta)) \\
+ &= \binom{N}{n} \left( \text{logit}^{-1}(\alpha_i + \sum_{1\leq j\leq m}x_{ij}\cdot \beta_j) \right)^{n} \left( 1 - \text{logit}^{-1}(\alpha_i + \sum_{1\leq j\leq m}x_{ij}\cdot \beta_j) \right)^{N - n}.
+\end{align*}
### Sampling statement
@@ -188,7 +189,7 @@ Increment target log probability density with `binomial_logit_glm_lupmf(n | N, x
\index{{\tt \bfseries binomial\_logit\_glm\_lpmf }!{\tt (int n \textbar\ int N, matrix x, real alpha, vector beta): real}|hyperpage}
`real` **`binomial_logit_glm_lpmf`**`(int n | int N, matrix x, real alpha, vector beta)`
\newline
-The log Binomial probability mass of n given N trials and chance of success
+The log binomial probability mass of n given N trials and chance of success
`inv_logit(alpha + x * beta)`.
`r since("2.34")`
@@ -196,7 +197,7 @@ The log Binomial probability mass of n given N trials and chance of success
\index{{\tt \bfseries binomial\_logit\_glm\_lupmf }!{\tt (int n \textbar\ int N, matrix x, real alpha, vector beta): real}|hyperpage}
`real` **`binomial_logit_glm_lupmf`**`(int n | int N, matrix x, real alpha, vector beta)`
\newline
-The log Binomial probability mass of n given N trials and chance of success
+The log binomial probability mass of n given N trials and chance of success
`inv_logit(alpha + x * beta)` dropping constant additive terms.
`r since("2.34")`
@@ -204,7 +205,7 @@ The log Binomial probability mass of n given N trials and chance of success
\index{{\tt \bfseries binomial\_logit\_glm\_lpmf }!{\tt (int n \textbar\ int N, matrix x, vector alpha, vector beta): real}|hyperpage}
`real` **`binomial_logit_glm_lpmf`**`(int n | int N, matrix x, vector alpha, vector beta)`
\newline
-The log Binomial probability mass of n given N trials and chance of success
+The log binomial probability mass of n given N trials and chance of success
`inv_logit(alpha + x * beta)`.
`r since("2.34")`
@@ -212,7 +213,7 @@ The log Binomial probability mass of n given N trials and chance of success
\index{{\tt \bfseries binomial\_logit\_glm\_lupmf }!{\tt (int n \textbar\ int N, matrix x, vector alpha, vector beta): real}|hyperpage}
`real` **`binomial_logit_glm_lupmf`**`(int n | int N, matrix x, vector alpha, vector beta)`
\newline
-The log Binomial probability mass of n given N trials and chance of success
+The log binomial probability mass of n given N trials and chance of success
`inv_logit(alpha + x * beta)` dropping constant additive terms.
`r since("2.34")`
@@ -220,7 +221,7 @@ The log Binomial probability mass of n given N trials and chance of success
\index{{\tt \bfseries binomial\_logit\_glm\_lpmf }!{\tt (array[] int n \textbar\ array[] int N, row\_vector x, real alpha, vector beta): real}|hyperpage}
`real` **`binomial_logit_glm_lpmf`**`(array[] int n | array[] int N, row_vector x, real alpha, vector beta)`
\newline
-The log Binomial probability mass of n given N trials and chance of success
+The log binomial probability mass of n given N trials and chance of success
`inv_logit(alpha + x * beta)`.
`r since("2.34")`
@@ -228,7 +229,7 @@ The log Binomial probability mass of n given N trials and chance of success
\index{{\tt \bfseries binomial\_logit\_glm\_lupmf }!{\tt (array[] int n \textbar\ array[] int N, row\_vector x, real alpha, vector beta): real}|hyperpage}
`real` **`binomial_logit_glm_lupmf`**`(array[] int n | array[] int N, row_vector x, real alpha, vector beta)`
\newline
-The log Binomial probability mass of n given N trials and chance of success
+The log binomial probability mass of n given N trials and chance of success
`inv_logit(alpha + x * beta)` dropping constant additive terms.
`r since("2.34")`
@@ -236,7 +237,7 @@ The log Binomial probability mass of n given N trials and chance of success
\index{{\tt \bfseries binomial\_logit\_glm\_lpmf }!{\tt (array[] int n \textbar\ array[] int N, row\_vector x, vector alpha, vector beta): real}|hyperpage}
`real` **`binomial_logit_glm_lpmf`**`(array[] int n | array[] int N, row_vector x, vector alpha, vector beta)`
\newline
-The log Binomial probability mass of n given N trials and chance of success
+The log binomial probability mass of n given N trials and chance of success
`inv_logit(alpha + x * beta)`.
`r since("2.34")`
@@ -244,7 +245,7 @@ The log Binomial probability mass of n given N trials and chance of success
\index{{\tt \bfseries binomial\_logit\_glm\_lupmf }!{\tt (array[] int n \textbar\ array[] int N, row\_vector x, vector alpha, vector beta): real}|hyperpage}
`real` **`binomial_logit_glm_lupmf`**`(array[] int n | array[] int N, row_vector x, vector alpha, vector beta)`
\newline
-The log Binomial probability mass of n given N trials and chance of success
+The log binomial probability mass of n given N trials and chance of success
`inv_logit(alpha + x * beta)` dropping constant additive terms.
`r since("2.34")`
@@ -253,7 +254,7 @@ The log Binomial probability mass of n given N trials and chance of success
\index{{\tt \bfseries binomial\_logit\_glm\_lpmf }!{\tt (array[] int n \textbar\ array[] int N, matrix x, real alpha, vector beta): real}|hyperpage}
`real` **`binomial_logit_glm_lpmf`**`(array[] int n | array[] int N, matrix x, real alpha, vector beta)`
\newline
-The log Binomial probability mass of n given N trials and chance of success
+The log binomial probability mass of n given N trials and chance of success
`inv_logit(alpha + x * beta)`.
`r since("2.34")`
@@ -261,7 +262,7 @@ The log Binomial probability mass of n given N trials and chance of success
\index{{\tt \bfseries binomial\_logit\_glm\_lupmf }!{\tt (array[] int n \textbar\ array[] int N, matrix x, real alpha, vector beta): real}|hyperpage}
`real` **`binomial_logit_glm_lupmf`**`(array[] int n | array[] int N, matrix x, real alpha, vector beta)`
\newline
-The log Binomial probability mass of n given N trials and chance of success
+The log binomial probability mass of n given N trials and chance of success
`inv_logit(alpha + x * beta)` dropping constant additive terms.
`r since("2.34")`
@@ -269,7 +270,7 @@ The log Binomial probability mass of n given N trials and chance of success
\index{{\tt \bfseries binomial\_logit\_glm\_lpmf }!{\tt (array[] int n \textbar\ array[] int N, matrix x, vector alpha, vector beta): real}|hyperpage}
`real` **`binomial_logit_glm_lpmf`**`(array[] int n | array[] int N, matrix x, vector alpha, vector beta)`
\newline
-The log Binomial probability mass of n given N trials and chance of success
+The log binomial probability mass of n given N trials and chance of success
`inv_logit(alpha + x * beta)`.
`r since("2.34")`
@@ -277,7 +278,7 @@ The log Binomial probability mass of n given N trials and chance of success
\index{{\tt \bfseries binomial\_logit\_glm\_lupmf }!{\tt (array[] int n \textbar\ array[] int N, matrix x, vector alpha, vector beta): real}|hyperpage}
`real` **`binomial_logit_glm_lupmf`**`(array[] int n | array[] int N, matrix x, vector alpha, vector beta)`
\newline
-The log Binomial probability mass of n given N trials and chance of success
+The log binomial probability mass of n given N trials and chance of success
`inv_logit(alpha + x * beta)` dropping constant additive terms.
`r since("2.34")`