THE LIMITING BEHAVIOUR OF SUMS AND MAXIMUMS OF IID
RANDOM VARIABLES FROM THE VIEWPOINT OF DIFFERENT
OBSERVERS
Tomasz K. Krajka
Zdzisław Rychlik
Abstract: The limiting behaviour of observed and all random variables in the max limit schema
was considered by Mladenović and Piterbarg (2006) and Krajka (2011). Here those results
are generalised in two directions:
- we allow more than one observer and one superobserver;
- we consider the max limit schema as well as the sum limit schema.
2000 AMS Mathematics Subject Classification: Primary: 60F05; Secondary:
60G70.
Keywords and phrases: Central limit theorem, extreme value theory, observed and
unobserved random variables.