Detecting random sets by samplings from their values

TL;DR

This paper investigates how well random samples from a set reveal its underlying distribution, exploring methods to detect the distribution from sampling statistics, with positive results, counterexamples, and open questions.

Contribution

It introduces new methods for identifying the distribution of a random set from its samples, including positive results and counterexamples.

Findings

Methods successfully detect distributions in some cases

Counterexamples show limitations of sampling-based detection

Open problems suggest directions for future research

Abstract

We examine the extent to which random samplings from the values of a random set, determine the distribution of the random set itself. We also comment on how, given the statistics of the sampling, to detect the distribution. Several methods are displayed, leading to positive results, counter-examples, and open problems.