  Topological Data Analysis (TDA) is an approach to handle with big data by
studying its shape. A main tool of TDA is the persistence diagram, and one can
use it to compare data sets. One approach to learn on the similarity between
two persistence diagrams is to use the Bottleneck and the Wasserstein
distances. Another approach is to fit a parametric model for each diagram, and
then to compare the model coefficients. We study the behaviour of both distance
measures and the RST parametric model. The theoretical behaviour of the
distance measures is difficult to be developed, and therefore we study their
behaviour numerically. We conclude that the RST model has an advantage over the
Bottleneck and the Wasserstein distances in sense that it can give a definite
conclusion regarding the similarity between two persistence diagrams. More of
that, a great advantage of the RST is its ability to distinguish between two
data sets that are geometrically different but topologically are the same,
which is impossible to have by the two distance measures.
