  } The main goal of this note is to provide new, mostly multidimensional
densities, compactly supported and list many of its properties that enable
effective calculations. The idea of obtaining such densities is firstly to
build some one-dimensional densities depending on many parameters and then
treat the constructed in this way distributions as conditional ones. Then of
course by imposing certain distribution on the parameters and multiplying the
two distributions we arrive at new multivariate distribution. To enable
effective calculations, we utilize nice, simple and widely known properties of
Chebyshev polynomials. Thus, in particular, the one-dimensional distribution
mentioned above will have a form of arcsine distribution multiplied by some
rational function. The fact that we use Chebyshev polynomials allows us to
calculate all moments of this one-dimensional distribution as well as to find a
family of polynomials that are orthogonal with respect to this distribution.
