Weighted Laws of Large Numbers for a Class of
This paper obtains a necessary and sufficient condition for a weak law of large numbers for weighted averages
of positive-valued independent random variables whose distributions belong to a class which includes
the \(F^\alpha\)-scheme of record theory. Additional general conditions
are found under which the weak law extends to a strong law with the same norming. Examples show
these conditions can be fulfilled, and that if they are not, then the weighted averages exhibit multiple growth rates.
2010 AMS Mathematics Subject Classification: Primary 60F05, 60F15; Secondary 60E10.
Keywords and phrases: weak and strong laws of large numbers, weighted sums, relative stability,