  The estimation of cumulative distribution functions (CDF) and probability
density functions (PDF) is a fundamental practice in applied statistics.
However, challenges often arise when dealing with data arranged in grouped
intervals. In this paper, we discuss a suitable and highly flexible
non-parametric density estimation approach for binned distributions, based on
cubic monotonicity-preserving splines - known as cubic spline interpolation.
Results from simulation studies demonstrate that this approach outperforms many
widely used heuristic methods. Additionally, the application of this method to
a dataset of train delays in Germany and micro census data on distance and
travel time to work yields both meaningful but also some questionable results.
