LIMIT DISTRIBUTIONS OF DIFFERENCES AND QUOTIENTS OF
NON-ADJACENT 
-TH RECORD VALUES
Mariusz Bieniek
Dominik Szynal
Abstract: Let 
denote the sequence of 
-th record values of the sequence
of i.i.d. random variables with an absolutely continuous distribution function
Fix 
We show that, for some very broad class of distributions 
the limit
distribution of the sequence
is
the gamma distribution with pdf
where
is a parameter which depends on
We prove the similar result for
-th
lower record values
Moreover, we discuss the asymptotic behaviour of quotients of
these quantities.
2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -
