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The momentum distribution of the unpolarized uniform electron gas in itsFermi-liquid regime, n(k,r_s), with the momenta k measured in units of theFermi wave number k_F and with the density parameter r_s, is constructed withthe 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 thesolution of the Overhauser model, and from Quantum Monte Carlo calculations viathe virial theorem). Information from the high- and the low-density limit,corresponding to the random-phase approximation and to the Wigner crystallimit, is used. The result is an accurate parametrization of n(k,r_s), whichfulfills most of the known exact constraints. It is in agreement with theeffective-potential calculation of Takada and Yasuhara [1991 {\it Phys. Rev.} B{\bf 44} 7879], is compatible with Quantum Monte Carlo data, and is valid inthe density range $r_s \lesssim 12$. The corresponding cumulant expansions ofthe pair density and of the static structure factor are discussed, and someexact limits are derived

Momentum distribution of the uniform electron gas: Improved parametrization and exact limits of the cumulant expansion