  We show that the F-signature of an F-finite local ring R of characteristic p
>0 exists when R is either the localization of an $\mathbf{N}$-graded ring at
its irrelevant ideal or $\mathbf{Q}$-Gorenstein on its punctured spectrum. This
extends results by Huneke, Leuschke, Yao and Singh and proves the existence of
the F-signature in the cases where weak F-regularity is known to be equivalent
to strong F-regularity.
