A generalization of the Málaga atmospheric optical communications links treated as a finite number of generalized-K distributed sub-channels is analyzed in terms of outage probability and outage rate when its β parameter belongs to the set of real numbers. To the best of the author’s knowledge, this is the first time that β ∈ ℜ is considered. The new analytical expressions derived in this paper lead to a new physical and more realistic interpretation of atmospheric optical links, especially in terms of performance