By analyzing the reduced density matrices derived from a generalized $W$-class state under any partition, we present new analytical monogamy inequalities satisfied

 by the $\alpha$-th ($\alpha\geq\gamma,~\gamma\geq2$) power and $\beta$-th ($0\leq\beta\leq\frac{\gamma}{2},~\gamma\geq2$) power of the concurrence of

 assistance for multi-qudit generalized $W$-class states, which are demonstrated to be tighter than previous studies through detailed examples. Furthermore, using the 

Tsallis-$q$ entanglement of assistance, we also establish new monogamy and polygamy relations, which are shown to be valid even for multipartite higher-dimensional

 states that the CKW inequality is violated.