The higher-order statistics (HOS) of the channel capacity $μ_n=\mathbb{E}[\log^n(1+γ_{end})]$, where $n\in\mathbb{N}$ denotes the order of the statistics, has received relatively little attention in the literature, due in part to the intractability of its analysis. In this letter, we propose a novel and unified analysis, which is based on the moment generating function (MGF) technique, to exactly compute the HOS of the channel capacity. More precisely, our mathematical formalism can be readily applied to maximal-ratio-combining (MRC) receivers operating in generalized fading environments (i.e., the sum of the correlated noncentral chi-squared distributions / the correlated generalized Rician distributions). The mathematical formalism is illustrated by some numerical examples focussing on the correlated generalized fading environments.