  We introduce the QuadratiK package that incorporates innovative data analysis
methodologies. The presented software, implemented in both R and Python, offers
a comprehensive set of goodness-of-fit tests and clustering techniques using
kernel-based quadratic distances, thereby bridging the gap between the
statistical and machine learning literatures. Our software implements one, two
and k-sample tests for goodness of fit, providing an efficient and
mathematically sound way to assess the fit of probability distributions.
Expanded capabilities of our software include supporting tests for uniformity
on the d-dimensional Sphere based on Poisson kernel densities. Particularly
noteworthy is the incorporation of a unique clustering algorithm specifically
tailored for spherical data that leverages a mixture of Poisson kernel-based
densities on the sphere. Alongside this, our software includes additional
graphical functions, aiding the users in validating, as well as visualizing and
representing clustering results. This enhances interpretability and usability
of the analysis. In summary, our R and Python packages serve as a powerful
suite of tools, offering researchers and practitioners the means to delve
deeper into their data, draw robust inference, and conduct potentially
impactful analyses and inference across a wide array of disciplines.
