  This paper delves into the significance of the tomographic probability
density function (pdf) representation of quantum states, shedding light on the
special classes of pdfs that can be tomograms. Instead of using wave functions
or density operators on Hilbert spaces, tomograms, which are the true pdfs, are
used to completely describe the states of quantum systems. Unlike quasi-pdfs,
like the Wigner function, tomograms can be analysed using all the tools of
classical probability theory for pdf estimation, which can allow a better
quality of state reconstruction. This is particularly useful when dealing with
non-Gaussian states where the pdfs are multi-mode. The knowledge of the family
of distributions plays an important role in the application of both parametric
and non-parametric density estimation methods. We show that not all pdfs can
play the role of tomograms of quantum states and introduce the conditions that
must be fulfilled by pdfs to be "quantum".
