diff --git a/R/pmt.R b/R/pmt.R
index 845abe3..7e18e0c 100644
--- a/R/pmt.R
+++ b/R/pmt.R
@@ -96,7 +96,7 @@ pmts <- function(
 #' @rdname pmt
 #' 
 #' @param inherit a character string specifying the type of permutation test.
-#' @param statistic definition of the test statistic. See Details.
+#' @param statistic definition of the test statistic. See details.
 #' @param rejection a character string specifying where the rejection region is.
 #' @param scoring one of:
 #'      - a character string in `c("none", "rank", "vw", "expon")` specifying the scoring system
@@ -114,19 +114,25 @@ pmts <- function(
 #' - R: a function returning a closure that returns a double.
 #' - Rcpp: a character string defining a captureless lambda (since C++11) returning another lambda that captures by value, accepts parameters of the same type, and returns a double.
 #' 
-#' When using `Rcpp`, the parameters for different `inherit` are listed as follows. Note that the parameter names are for illustration only.
+#' The purpose of this design is to pre-calculate certain constants that remain invariant during permutation.
 #' 
-#' - `"twosample"`: `(const NumericVector& sample_1, const NumericVector& sample_2)`
-#' - `"ksample"`: `(const NumericVector& combined_sample, const IntegerVector& one_based_group_index)`
-#' - `"paired"`: `(const NumericVector& sample_1, const NumericVector& sample_2)`
-#' - `"rcbd"`: `(const NumericMatrix& block_as_column_data)`
-#' - `"association"`: `(const NumericVector& sample_1, const NumericVector& sample_2)`
-#' - `"table"`: `(const IntegerMatrix& contingency_table)`
+#' When using Rcpp, the parameters for different `inherit` are listed as follows. Note that the names can be customized, and the types can be replaced with `auto` (thanks to the support for generic lambdas in C++14). See examples.
 #' 
-#' Defining the test statistic using R follows a similar approach. The purpose of this design is to pre-calculate certain constants that remain invariant during permutation.
+#' | `inherit`       | Parameter 1                                 | Parameter 2                                  |
+#' |:---------------:|:-------------------------------------------:|:--------------------------------------------:|
+#' | `"twosample"`   | `const NumericVector& sample_1`             | `const NumericVector& sample_2`              |
+#' | `"ksample"`     | `const NumericVector& combined_sample`      | `const IntegerVector& one_based_group_index` |
+#' | `"paired"`      | `const NumericVector& sample_1`             | `const NumericVector& sample_2`              |
+#' | `"rcbd"`        | `const NumericMatrix& block_as_column_data` |                                              |
+#' | `"association"` | `const NumericVector& sample_1`             | `const NumericVector& sample_2`              |
+#' | `"table"`       | `const IntegerMatrix& contingency_table`    |                                              |
+
+#' 
+#' When using R, the parameters should be the R equivalents of these.
 #' 
 #' @note
-#' The data is permuted in-place. Therefore, modifications to the data within `statistic` may lead to incorrect results. Since R has copy-on-modify semantics but C++ does not, it is recommended to pass const references when using Rcpp in `define_pmt`.
+#' - `statistic` should not cause errors or return missing values.
+#' - The data is permuted in-place. Therefore, modifications to the data within `statistic` may lead to incorrect results. Since R has copy-on-modify semantics but C++ does not, it is recommended to pass const references when using Rcpp in `define_pmt`, as shown in the table above.
 #' 
 #' @examples
 #' x <- rnorm(5)
@@ -146,8 +152,7 @@ pmts <- function(
 #' 
 #' \donttest{
 #' r <- define_pmt(
-#'     inherit = "twosample",
-#'     n_permu = 1e5,
+#'     inherit = "twosample", n_permu = 1e5,
 #'     statistic = function(x, y) {
 #'         m <- length(x)
 #'         n <- length(y)
@@ -155,18 +160,30 @@ pmts <- function(
 #'     }
 #' )
 #' 
+#' 
 #' rcpp <- define_pmt(
-#'     inherit = "twosample",
-#'     n_permu = 1e5,
-#'     statistic = "[](const NumericVector& x, const NumericVector& y) {
-#'         R_xlen_t m = x.size();
-#'         R_xlen_t n = y.size();
-#'         return [=](const NumericVector& x, const NumericVector& y) -> double {
+#'     inherit = "twosample", n_permu = 1e5,
+#'     statistic = "[](const auto& x, const auto& y) {
+#'         auto m = x.size();
+#'         auto n = y.size();
+#'         return [=](const auto& x, const auto& y) {
 #'             return sum(x) / m - sum(y) / n;
 #'         };
 #'     }"
 #' )
 #' 
+#' # equivalent
+#' # rcpp <- define_pmt(
+#' #     inherit = "twosample", n_permu = 1e5,
+#' #     statistic = "[](const NumericVector& x, const NumericVector& y) {
+#' #         R_xlen_t m = x.size();
+#' #         R_xlen_t n = y.size();
+#' #         return [=](const NumericVector& x, const NumericVector& y) -> double {
+#' #             return sum(x) / m - sum(y) / n;
+#' #         };
+#' #     }"
+#' # )
+#' 
 #' options(LearnNonparam.pmt_progress = FALSE)
 #' system.time(r$test(x, y))
 #' system.time(rcpp$test(x, y))
diff --git a/man/pmt.Rd b/man/pmt.Rd
index ef20cb9..6da93ce 100644
--- a/man/pmt.Rd
+++ b/man/pmt.Rd
@@ -35,7 +35,7 @@ define_pmt(
 
 \item{inherit}{a character string specifying the type of permutation test.}
 
-\item{statistic}{definition of the test statistic. See Details.}
+\item{statistic}{definition of the test statistic. See details.}
 
 \item{rejection}{a character string specifying where the rejection region is.}
 
@@ -68,20 +68,26 @@ The test statistic can be defined using either R or Rcpp, with the \code{statist
 \item Rcpp: a character string defining a captureless lambda (since C++11) returning another lambda that captures by value, accepts parameters of the same type, and returns a double.
 }
 
-When using \code{Rcpp}, the parameters for different \code{inherit} are listed as follows. Note that the parameter names are for illustration only.
-\itemize{
-\item \code{"twosample"}: \verb{(const NumericVector& sample_1, const NumericVector& sample_2)}
-\item \code{"ksample"}: \verb{(const NumericVector& combined_sample, const IntegerVector& one_based_group_index)}
-\item \code{"paired"}: \verb{(const NumericVector& sample_1, const NumericVector& sample_2)}
-\item \code{"rcbd"}: \verb{(const NumericMatrix& block_as_column_data)}
-\item \code{"association"}: \verb{(const NumericVector& sample_1, const NumericVector& sample_2)}
-\item \code{"table"}: \verb{(const IntegerMatrix& contingency_table)}
+The purpose of this design is to pre-calculate certain constants that remain invariant during permutation.
+
+When using Rcpp, the parameters for different \code{inherit} are listed as follows. Note that the names can be customized, and the types can be replaced with \code{auto} (thanks to the support for generic lambdas in C++14). See examples.\tabular{ccc}{
+   \code{inherit} \tab Parameter 1 \tab Parameter 2 \cr
+   \code{"twosample"} \tab \verb{const NumericVector& sample_1} \tab \verb{const NumericVector& sample_2} \cr
+   \code{"ksample"} \tab \verb{const NumericVector& combined_sample} \tab \verb{const IntegerVector& one_based_group_index} \cr
+   \code{"paired"} \tab \verb{const NumericVector& sample_1} \tab \verb{const NumericVector& sample_2} \cr
+   \code{"rcbd"} \tab \verb{const NumericMatrix& block_as_column_data} \tab  \cr
+   \code{"association"} \tab \verb{const NumericVector& sample_1} \tab \verb{const NumericVector& sample_2} \cr
+   \code{"table"} \tab \verb{const IntegerMatrix& contingency_table} \tab  \cr
 }
 
-Defining the test statistic using R follows a similar approach. The purpose of this design is to pre-calculate certain constants that remain invariant during permutation.
+
+When using R, the parameters should be the R equivalents of these.
 }
 \note{
-The data is permuted in-place. Therefore, modifications to the data within \code{statistic} may lead to incorrect results. Since R has copy-on-modify semantics but C++ does not, it is recommended to pass const references when using Rcpp in \code{define_pmt}.
+\itemize{
+\item \code{statistic} should not cause errors or return missing values.
+\item The data is permuted in-place. Therefore, modifications to the data within \code{statistic} may lead to incorrect results. Since R has copy-on-modify semantics but C++ does not, it is recommended to pass const references when using Rcpp in \code{define_pmt}, as shown in the table above.
+}
 }
 \examples{
 pmt("twosample.wilcoxon")
@@ -105,8 +111,7 @@ t$print()
 
 \donttest{
 r <- define_pmt(
-    inherit = "twosample",
-    n_permu = 1e5,
+    inherit = "twosample", n_permu = 1e5,
     statistic = function(x, y) {
         m <- length(x)
         n <- length(y)
@@ -114,18 +119,30 @@ r <- define_pmt(
     }
 )
 
+
 rcpp <- define_pmt(
-    inherit = "twosample",
-    n_permu = 1e5,
-    statistic = "[](const NumericVector& x, const NumericVector& y) {
-        R_xlen_t m = x.size();
-        R_xlen_t n = y.size();
-        return [=](const NumericVector& x, const NumericVector& y) -> double {
+    inherit = "twosample", n_permu = 1e5,
+    statistic = "[](const auto& x, const auto& y) {
+        auto m = x.size();
+        auto n = y.size();
+        return [=](const auto& x, const auto& y) {
             return sum(x) / m - sum(y) / n;
         };
     }"
 )
 
+# equivalent
+# rcpp <- define_pmt(
+#     inherit = "twosample", n_permu = 1e5,
+#     statistic = "[](const NumericVector& x, const NumericVector& y) {
+#         R_xlen_t m = x.size();
+#         R_xlen_t n = y.size();
+#         return [=](const NumericVector& x, const NumericVector& y) -> double {
+#             return sum(x) / m - sum(y) / n;
+#         };
+#     }"
+# )
+
 options(LearnNonparam.pmt_progress = FALSE)
 system.time(r$test(x, y))
 system.time(rcpp$test(x, y))