Finite sequences representing expected order statistics

TL;DR

This paper characterizes finite sequences that can represent the expected order statistics from a sample, and as a by-product, it describes binomial mixtures supported in (0,1) and their convex hulls.

Contribution

It provides new characterizations of sequences representing expected order statistics and describes the convex hull of open binomial and moment curves.

Findings

Characterization of finite sequences as expected order statistics.

Exact description of the convex hull of the open binomial curve.

Analysis of binomial mixtures supported in (0,1).

Abstract

Characterizations of finite sequences $\beta_{1}<\cdots<\beta_{n}$ representing expected values of order statistics from a random sample of size $n$ are given. As a by-product, a characterization of binomial mixtures, when the mixing random variable is supported in the open interval $(0,1)$, is presented; this enables the exact description of the convex hull of the open binomial curve, as well as the open moment curve.