diff --git a/CVE_C/R/CVE.R b/CVE_C/R/CVE.R
index 0537bb7..842fe0f 100644
--- a/CVE_C/R/CVE.R
+++ b/CVE_C/R/CVE.R
@@ -43,7 +43,7 @@
 #' supplied.
 #' @param method specifies the CVE method variation as one of
 #' \itemize{
-#'      \item "simple" exact implementation as describet in the paper listed 
+#'      \item "simple" exact implementation as described in the paper listed 
 #'          below.
 #'      \item "weighted" variation with addaptive weighting of slices.
 #' }
@@ -63,7 +63,7 @@
 #' dr <- cve(Y ~ X)
 #' round(dr[[2]]$B, 1)
 #'
-#' @seealso For a detailed description of the formula parameter see
+#' @seealso For a detailed description of \code{formula} see
 #'      [\code{\link{formula}}].
 #' @export
 cve <- function(formula, data, method = "simple", max.dim = 10L, ...) {
@@ -90,16 +90,15 @@ cve <- function(formula, data, method = "simple", max.dim = 10L, ...) {
 #' @param nObs parameter for choosing bandwidth \code{h} using
 #'   \code{\link{estimate.bandwidth}} (ignored if \code{h} is supplied).
 #' @param X data matrix with samples in its rows.
-#' @param Y Responces (1 dimensional).
-#' @param k Dimension of lower dimensional projection, if given only the
-#'      specified dimension is estimated.
+#' @param Y Responses (1 dimensional).
+#' @param k Dimension of lower dimensional projection, if \code{k} is given only the specified dimension \code{B} matrix is estimated.
 #' @param min.dim lower bounds for \code{k}, (ignored if \code{k} is supplied).
 #' @param max.dim upper bounds for \code{k}, (ignored if \code{k} is supplied).
 #' @param tau Initial step-size.
 #' @param tol Tolerance for break condition.
 #' @param epochs maximum number of optimization steps.
 #' @param attempts number of arbitrary different starting points.
-#' @param logger a logger function (only for addvanced user).
+#' @param logger a logger function (only for advanced user, significantly slows down the computation).
 #' @rdname cve
 #' @export
 cve.call <- function(X, Y, method = "simple",
@@ -235,7 +234,7 @@ cve.call <- function(X, Y, method = "simple",
     return(dr)
 }
 
-#' Loss distribution kink plot.
+#' Loss distribution elbow plot.
 #'
 #' @param x Object of class \code{"cve"} (result of [\code{\link{cve}}]).
 #' @param ... Pass through parameters to [\code{\link{plot}}] and
@@ -245,6 +244,7 @@ cve.call <- function(X, Y, method = "simple",
 #'      as well as \code{\link{plot}}, the standard plot utility.
 #' @importFrom graphics plot lines points
 #' @method plot cve
+#' Boxplots of the loss from \code{min.dim} to \code{max.dim} \code{k} values.
 #' @export
 plot.cve <- function(x, ...) {
     L <- c()
@@ -256,7 +256,7 @@ plot.cve <- function(x, ...) {
         }
     }
     L <- matrix(L, ncol = length(k)) / var(x$Y)
-    boxplot(L, main = "Kink plot",
+    boxplot(L, main = "elbow plot",
             xlab = "SDR dimension",
             ylab = "Sample loss distribution",
             names = k)
diff --git a/CVE_C/R/datasets.R b/CVE_C/R/datasets.R
index 1e9380d..0f84299 100644
--- a/CVE_C/R/datasets.R
+++ b/CVE_C/R/datasets.R
@@ -1,7 +1,7 @@
 #' Generates test datasets.
 #'
 #' Provides sample datasets. There are 5 different datasets named
-#' M1, M2, M3, M4 and M5 describet in the paper references below.
+#' M1, M2, M3, M4 and M5 described in the paper references below.
 #' The general model is given by:
 #' \deqn{Y ~ g(B'X) + \epsilon}
 #'
diff --git a/CVE_C/R/estimateBandwidth.R b/CVE_C/R/estimateBandwidth.R
index b03538e..a5a984d 100644
--- a/CVE_C/R/estimateBandwidth.R
+++ b/CVE_C/R/estimateBandwidth.R
@@ -1,16 +1,16 @@
 #' Bandwidth estimation for CVE.
 #'
-#' Estimates a propper bandwidth \code{h} according
+#' Estimates a bandwidth \code{h} according
 #' \deqn{%
 #' h = \chi_{k}^{-1}\left(\frac{nObs - 1}{n-1}\right)\frac{2 tr(\Sigma)}{p}}{%
 #' h = qchisq( (nObs - 1)/(n - 1), k ) * (2 tr(\Sigma) / p)}
-#' with \eqn{n} the number of sample and \eqn{p} its dimension
+#' with \eqn{n} the sample size, \eqn{p} its dimension
 #' (\code{n <- nrow(X); p <- ncol(X)}) and the covariance-matrix \eqn{\Sigma}
-#' which is given by the standard maximum likelihood estimate.
+#' which is \code{(n-1)/n} times the sample covariance estimate.
 #'
-#' @param nObs Expected number of points in a slice, see paper.
 #' @param X data matrix with samples in its rows.
 #' @param k Dimension of lower dimensional projection.
+#' @param nObs number of points in a slice, see \eqn{nObs} in CVE paper.
 #'
 #' @seealso [\code{\link{qchisq}}]
 #' @export
diff --git a/CVE_C/R/util.R b/CVE_C/R/util.R
index b114fc0..3a42ceb 100644
--- a/CVE_C/R/util.R
+++ b/CVE_C/R/util.R
@@ -1,8 +1,8 @@
-#' Samples uniform from the Stiefl Manifold.
+#' Draws a sample from the invariant measure on the Stiefel manifold \eqn{S(p, q)}.
 #'
-#' @param p row dim.
-#' @param q col dim.
-#' @return `(p, q)` semi-orthogonal matrix
+#' @param p row dimension
+#' @param q col dimension
+#' @return \code{p} times \code{q} semi-orthogonal matrix.
 #' @examples
 #'  V <- rStiefel(6, 4)
 #' @export
diff --git a/CVE_C/man/cve.Rd b/CVE_C/man/cve.Rd
index 03674d0..3f71f62 100644
--- a/CVE_C/man/cve.Rd
+++ b/CVE_C/man/cve.Rd
@@ -20,7 +20,7 @@ supplied.}
 
 \item{method}{specifies the CVE method variation as one of
 \itemize{
-     \item "simple" exact implementation as describet in the paper listed 
+     \item "simple" exact implementation as described in the paper listed 
          below.
      \item "weighted" variation with addaptive weighting of slices.
 }}
diff --git a/CVE_C/man/dataset.Rd b/CVE_C/man/dataset.Rd
index d68db13..9ce9e6e 100644
--- a/CVE_C/man/dataset.Rd
+++ b/CVE_C/man/dataset.Rd
@@ -28,7 +28,7 @@ List with elements
 }
 \description{
 Provides sample datasets. There are 5 different datasets named
-M1, M2, M3, M4 and M5 describet in the paper references below.
+M1, M2, M3, M4 and M5 described in the paper references below.
 The general model is given by:
 \deqn{Y ~ g(B'X) + \epsilon}
 }
diff --git a/CVE_C/man/plot.cve.Rd b/CVE_C/man/plot.cve.Rd
index 1fd71b2..16d511e 100644
--- a/CVE_C/man/plot.cve.Rd
+++ b/CVE_C/man/plot.cve.Rd
@@ -2,7 +2,7 @@
 % Please edit documentation in R/CVE.R
 \name{plot.cve}
 \alias{plot.cve}
-\title{Creates a kink plot of the sample loss distribution over SDR dimensions.}
+\title{Loss distribution elbow plot.}
 \usage{
 \method{plot}{cve}(x, ...)
 }
@@ -13,7 +13,7 @@
 [\code{\link{lines}}]}
 }
 \description{
-Creates a kink plot of the sample loss distribution over SDR dimensions.
+Loss distribution elbow plot.
 }
 \seealso{
 see \code{\link{par}} for graphical parameters to pass through
diff --git a/CVE_R/R/CVE.R b/CVE_R/R/CVE.R
index df42ed6..c0ec00a 100644
--- a/CVE_R/R/CVE.R
+++ b/CVE_R/R/CVE.R
@@ -76,7 +76,7 @@ cve <- function(formula, data, method = "simple", max.dim = 10L, ...) {
     return(dr)
 }
 
-#' @param nObs as describet in the Paper.
+#' @param nObs as described in the Paper.
 #' @param X Data
 #' @param Y Responces
 #' @param nObs Like in the paper.
diff --git a/CVE_R/R/cve_rcg.R b/CVE_R/R/cve_rcg.R
index f1cc8fa..0a459f5 100644
--- a/CVE_R/R/cve_rcg.R
+++ b/CVE_R/R/cve_rcg.R
@@ -142,7 +142,7 @@ cve_rcg <- function(X, Y, k,
 
             # Reset beta if needed.
             if (loss.prime < 0) {
-                # Compute `beta` as describet in paper.
+                # Compute `beta` as described in paper.
                 beta.FR <- (norm(A, type = 'F') / norm(A.last, type = 'F'))^2
                 beta.PR <- sum(A * (A - A.last)) / norm(A.last, type = 'F')^2
                 if (beta.PR < -beta.FR) {
diff --git a/CVE_R/R/datasets.R b/CVE_R/R/datasets.R
index 68af0f4..70e08b5 100644
--- a/CVE_R/R/datasets.R
+++ b/CVE_R/R/datasets.R
@@ -1,7 +1,7 @@
 #' Generates test datasets.
 #'
 #' Provides sample datasets. There are 5 different datasets named
-#' M1, M2, M3, M4 and M5 describet in the paper references below.
+#' M1, M2, M3, M4 and M5 described in the paper references below.
 #' The general model is given by:
 #' \deqn{Y ~ g(B'X) + \epsilon}
 #'
diff --git a/CVE_R/man/cve.Rd b/CVE_R/man/cve.Rd
index d3e0d05..07d86a2 100644
--- a/CVE_R/man/cve.Rd
+++ b/CVE_R/man/cve.Rd
@@ -30,7 +30,7 @@ See: \code{\link{formula}}.}
 
 \item{Y}{Responces}
 
-\item{nObs}{as describet in the Paper.}
+\item{nObs}{as described in the Paper.}
 
 \item{k}{guess for SDR dimension.}
 
diff --git a/CVE_R/man/dataset.Rd b/CVE_R/man/dataset.Rd
index da7be5b..8e65402 100644
--- a/CVE_R/man/dataset.Rd
+++ b/CVE_R/man/dataset.Rd
@@ -28,7 +28,7 @@ List with elements
 }
 \description{
 Provides sample datasets. There are 5 different datasets named
-M1, M2, M3, M4 and M5 describet in the paper references below.
+M1, M2, M3, M4 and M5 described in the paper references below.
 The general model is given by:
 \deqn{Y ~ g(B'X) + \epsilon}
 }