diff --git a/R/lpcde/R/lpcde.R b/R/lpcde/R/lpcde.R
index d510269..11837bb 100644
--- a/R/lpcde/R/lpcde.R
+++ b/R/lpcde/R/lpcde.R
@@ -89,6 +89,17 @@
 #' \code{\link{plot.lpcde}}, \code{\link{print.lpcde}},
 #' \code{\link{summary.lpcde}}, \code{\link{vcov.lpcde}}
 #'
+#'
+#' @examples
+#' #Density estimation example
+#' n=500
+#' x_data = matrix(rnorm(n, mean=0, sd=1))
+#' y_data = matrix(rnorm(n, mean=x_data, sd=1))
+#' y_grid = seq(from=-1, to=1, length.out=5)
+#' model1 = lpcde::lpcde(x_data=x_data, y_data=y_data, y_grid=y_grid, x=0, bw=0.5)
+#' #summary of estimation
+#' summary(model1)
+#'
 #' @references
 #' \insertRef{bernoulli}{lpcde}\cr
 #' \insertRef{JASA}{lpcde}\cr
diff --git a/R/lpcde/man/lpcde.Rd b/R/lpcde/man/lpcde.Rd
index 7fd57f7..6113523 100644
--- a/R/lpcde/man/lpcde.Rd
+++ b/R/lpcde/man/lpcde.Rd
@@ -116,6 +116,17 @@ Sometimes the density point estimates may lie outside
 of the confidence intervals/bands, which can happen if the underlying distribution exhibits
 high curvature at some evaluation point(s). One possible solution in this case is to
 increase the polynomial order \code{p} or to employ a smaller bandwidth.
+}
+\examples{
+#Density estimation example
+n=500
+x_data = matrix(rnorm(n, mean=0, sd=1))
+y_data = matrix(rnorm(n, mean=x_data, sd=1))
+y_grid = seq(from=-1, to=1, length.out=5)
+model1 = lpcde::lpcde(x_data=x_data, y_data=y_data, y_grid=y_grid, x=0, bw=0.5)
+#summary of estimation
+summary(model1)
+
 }
 \references{
 \insertRef{bernoulli}{lpcde}\cr
diff --git a/R/lpcde/tests/testthat/test-lpbwcde.R b/R/lpcde/tests/testthat/test-lpbwcde.R
index 8cd3633..d66f831 100644
--- a/R/lpcde/tests/testthat/test-lpbwcde.R
+++ b/R/lpcde/tests/testthat/test-lpbwcde.R
@@ -12,9 +12,6 @@ test_that("lpbwcde default output", {
   coef(model1)
   expect_equal(model1$opt$ng, 19)
 
-  expect_error(vcov(model1), regexp="The vcov method does not support \"lpbwcde\" objects.")
-  expect_error(confint(model1), regexp="The confint method does not support \"lpbwcde\" objects.")
-
   model1 = lpbwcde(x_data=x_data, y_data=y_data, x=0, bw_type = "mse-rot")
   expect_equal(model1$opt$bw_type, "mse-rot")
   model1 = lpbwcde(x_data=x_data, y_data=y_data, y_grid=y_grid, x=0, bw_type = "mse-dpi")
diff --git a/R/lpcde_0.1.2.pdf b/R/lpcde_0.1.2.pdf
index 824706c..bf2f3fa 100644
Binary files a/R/lpcde_0.1.2.pdf and b/R/lpcde_0.1.2.pdf differ