Computation of quantile sets for bivariate data

TL;DR

This paper introduces algorithms for computing set-valued quantiles and the lower cone distribution function in bivariate data, enabling new data analysis methods based on vector orders in two dimensions.

Contribution

It presents novel algorithms specifically designed for bivariate data to compute set-valued quantiles and distribution functions, facilitating analysis with vector order relations.

Findings

Algorithms successfully compute bivariate set-valued quantiles.

Illustrative examples demonstrate practical applications.

New insights into data ordering in two dimensions are provided.

Abstract

Algorithms are proposed for the computation of set-valued quantiles and the values of the lower cone distribution function for bivariate data sets. These new objects make data analysis possible involving an order relation for the data points in form of a vector order in two dimensions. The bivariate case deserves special attention since two-dimensional vector orders are much simpler to handle than such orders in higher dimensions. Several examples illustrate how the algorithms work and what kind of conclusions can be drawn with the proposed approach.