caa a22 4500 605519633 CHVBK 20210128100731.0 cr unu---uuuuu 210128e20150901xx s 000 0 eng 10.1007/s11009-013-9386-z doi (NATIONALLICENCE)springer-10.1007/s11009-013-9386-z Methods and Algorithms to Test the Hausdorff and Simplex Dispersion Orders with an R Package [Elektronische Daten] [Guillermo Ayala, María López-Díaz, Miguel López-Díaz, Lucía Martínez-Costa] Stochastic orders aim to order probability distributions in accordance with an appropriate criterion. Dispersion orderings are particular cases of stochastic orderings. Essentially, given two random vectors, a dispersion ordering attempts to determine which vector induces a more dispersive probability distribution. The Hausdorff and simplex dispersion orderings are two particular cases of such a kind of orders. Although they satisfy suitable properties from a theoretical point of view, the application to real problems is very complex since the study of such orders implies to determine sample values of Hausdorff distances between random convex hulls. The paper proposes two exact algorithms to test the Hausdorff and simplex dispersion orderings. A software implementation using R is provided and evaluated using a simulation study. An ophthalmological application concerned with the diabetes evaluation using the mean calibers of arteries and veins in fundus images is considered. The Hausdorff and simplex dispersion orderings are applied to the study of the effects produced by diabetes in the retinal vessels. The possible differences in dispersion that could exist between the groups defined using some categorical covariables are tested. The comparison between homogeneous groups will produce accurate results in medical research. Springer Science+Business Media New York, 2013 Dispersive ordering nationallicence Hausdorff dispersion ordering nationallicence Diabetes nationallicence Retinal vessel diameter nationallicence Simplex dispersion ordering nationallicence Stochastic order nationallicence Ayala Guillermo Departamento de Estadística e I.O., Universidad de Valencia, Avda. Vicent Andrés Estellés 1, Burjasot, 46100, Valencia, Spain aut López-Díaz María Departamento de Matemáticas, Universidad de Oviedo, C/Calvo Sotelo s/n, 33007, Oviedo, Spain aut López-Díaz Miguel Departamento de Estadística e I.O. y D.M., Universidad de Oviedo, C/Calvo Sotelo s/n, 33007, Oviedo, Spain aut Martínez-Costa Lucía Servicio de Oftalmología, Hospital Dr. Peset, Av. Gaspar Aguilar 90, 46017, Valencia, Spain aut Methodology and Computing in Applied Probability Springer US; http://www.springer-ny.com 17/3(2015-09-01), 661-675 1387-5841 17:3<661 2015 17 11009 https://doi.org/10.1007/s11009-013-9386-z text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s11009-013-9386-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Ayala Guillermo Departamento de Estadística e I.O., Universidad de Valencia, Avda. Vicent Andrés Estellés 1, Burjasot, 46100, Valencia, Spain aut NATIONALLICENCE 700 1- López-Díaz María Departamento de Matemáticas, Universidad de Oviedo, C/Calvo Sotelo s/n, 33007, Oviedo, Spain aut NATIONALLICENCE 700 1- López-Díaz Miguel Departamento de Estadística e I.O. y D.M., Universidad de Oviedo, C/Calvo Sotelo s/n, 33007, Oviedo, Spain aut NATIONALLICENCE 700 1- Martínez-Costa Lucía Servicio de Oftalmología, Hospital Dr. Peset, Av. Gaspar Aguilar 90, 46017, Valencia, Spain aut NATIONALLICENCE 773 0- Methodology and Computing in Applied Probability Springer US; http://www.springer-ny.com 17/3(2015-09-01), 661-675 1387-5841 17:3<661 2015 17 11009