  We propose kernel-type smoothed Kolmogorov-Smirnov and Cram\'{e}r-von Mises
tests for data on general interval, using bijective transformations. Though not
as severe as in the kernel density estimation, utilizing naive kernel method
directly to those particular tests will result in boundary problem as well.
This happens mostly because the value of the naive kernel distribution function
estimator is still larger than $0$ (or less than $1$) when it is evaluated at
the boundary points. This situation can increase the errors of the tests
especially the second-type error. In this article, we use bijective
transformations to eliminate the boundary problem. Some simulation results
illustrating the estimator and the tests' performances will be presented in the
last part of this article.
