  In the recently proposed two-parameter $\tilde{\mu},q$-deformed Bose gas
model [Ukr. J. Phys. {\bf 58}, 1171 (2013), arXiv:1312.1573] aimed to take
effectively into account both compositeness of particles and their interaction,
the $\tilde{\mu},q$-deformed virial expansion of the equation of state (EOS)
was obtained. In this paper we further explore the $\tilde{\mu},q$-deformation,
namely the version of $\tilde{\mu},q$-Bose gas model involving deformed
distributions and correlation functions. In the model, we explicitly derive the
one- and two-particle deformed distribution functions and the intercept of
two-particle momentum correlation function. The results are illustrated by
plots, and the comparison with known experimental data on two-pion correlation
function intercepts extracted in RHIC/STAR experiments is given.
