On sequences of expected maxima and expected ranges

TL;DR

This paper establishes a new necessary and sufficient condition to determine if a sequence of real numbers can be interpreted as expected maxima or ranges, linking it to Bernstein functions and Lévy-Khintchine representation.

Contribution

It introduces a novel criterion connecting expected maxima sequences to Bernstein functions via Lévy-Khintchine representation, advancing the theoretical understanding of order statistics.

Findings

Provides a necessary and sufficient condition for expected maxima sequences.

Links expected maxima to Bernstein functions and Lévy-Khintchine representation.

Enhances theoretical framework for analyzing order statistics.

Abstract

We investigate conditions in order to decide whether a given sequence of real numbers represents expected maxima or expected ranges. The main result provides a novel necessary and sufficient condition, relating an expected maxima sequence to a translation of a Bernstein function through its L\'{e}vy-Khintchine representation. Key words and phrases: expected maxima; expected ranges; Bernstein functions, L\'{e}vy-Khintchine representation, order statistics.