  Nowadays, data analysis in the world of Big Data is connected typically to
data mining, descriptive or exploratory statistics, e.~g.\ cluster analysis,
classification or regression analysis. Aside these techniques there is a huge
area of methods from inferential statistics that are rarely considered in
connection with Big Data. Nevertheless, inferential methods are also of use for
Big Data analysis, especially for quantifying uncertainty. The article at hand
will provide some insights to methodological and technical issues referring
inferential methods in the Big Data area in order to bring together Big Data
and inferential statistics, as it comes along with its difficulties. We present
an approach that allows testing goodness-of-fit without model assumptions and
relying on the empirical distribution. Especially, the method is able to
utilize information from large datasets. Thereby, the approach is based on a
clear theoretical background. We concentrate on the widely-used
Kolmogorov-Smirnov test that is applied for testing goodness-of-fit in
statistics. Our approach can be parallelized easily, which makes it applicable
to distributed datasets particularly on a compute cluster. By this
contribution, we turn to an audience that is interested in the technical and
methodological backgrounds while implementing especially inferential
statistical methods with Big Data tools as e. g. Spark.
