  The momentum distribution of the unpolarized uniform electron gas in its
Fermi-liquid regime, n(k,r_s), with the momenta k measured in units of the
Fermi wave number k_F and with the density parameter r_s, is constructed with
the help of the convex Kulik function G(x). It is assumed that $n(0,r_s),
n(1^\pm, r_s)$, the on-top pair density g(0,r_s) and the kinetic energy t(r_s)
are known (respectively, from effective-potential calculations, from the
solution of the Overhauser model, and from Quantum Monte Carlo calculations via
the virial theorem). Information from the high- and the low-density limit,
corresponding to the random-phase approximation and to the Wigner crystal
limit, is used. The result is an accurate parametrization of n(k,r_s), which
fulfills most of the known exact constraints. It is in agreement with the
effective-potential calculation of Takada and Yasuhara [1991 {\it Phys. Rev.} B
{\bf 44} 7879], is compatible with Quantum Monte Carlo data, and is valid in
the density range $r_s \lesssim 12$. The corresponding cumulant expansions of
the pair density and of the static structure factor are discussed, and some
exact limits are derived.
