On a scale-scale plot for comparing multivariate distributions

Pritha Guha; Biman Chakraborty

doi:10.1080/03610926.2020.1759639

On a scale-scale plot for comparing multivariate distributions

Pritha Guha^*, Biman Chakraborty

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

10 Downloads (Pure)

Abstract

In this paper, we propose a scale-scale plot to compare multivariate distributions. These scale-scale plots can be viewed as a multivariate analog of quantile-quantile plots and we illustrate their use as a visualization tool to validate distributional assumptions for multivariate data as well as to compare the distributions of two multivariate samples. We discuss some characterizations of the proposed plots under elliptically symmetric distributions and based on those results, propose some visual tests of location and scale as further applications of these scale-scale plots. For the test of location problem, we present a small power study using simulations.

Original language	English
Pages (from-to)	1270-1289
Number of pages	20
Journal	Communications in Statistics - Theory and Methods
Volume	51
Issue number	5
Early online date	2 May 2020
DOIs	https://doi.org/10.1080/03610926.2020.1759639
Publication status	Published - 4 Mar 2022

Bibliographical note

Funding Information:
This work is part of the first author’s Ph.D. thesis under the guidance of the second author. The thesis was completed at the School of Mathematics, University of Birmingham, UK. The authors would like to thank the referee, associate editor and the School of Mathematics, University of Birmingham, UK for support.

Publisher Copyright:
© 2020 Taylor & Francis Group, LLC.

Keywords

Central rank regions
elliptically symmetric distributions
quantile quantile plots
tests of location
tests of scale

ASJC Scopus subject areas

Statistics and Probability

Access to Document

10.1080/03610926.2020.1759639

On A Scale-Scale Plot
This is an Accepted Manuscript version of the following article, accepted for publication in Communications in Statistics - Theory and Methods. Pritha Guha & Biman Chakraborty (2022) On a scale-scale plot for comparing multivariate distributions, Communications in Statistics - Theory and Methods, 51:5, 1270-1289, DOI: 10.1080/03610926.2020.1759639. It is deposited under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License (http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited, and is not altered, transformed, or built upon in any way.
Accepted author manuscript, 1.03 MBLicence: Creative Commons: Attribution-NonCommercial-NoDerivs (CC BY-NC-ND)

Cite this

@article{6330c01b2cd94a5a8e90f683092a0051,

title = "On a scale-scale plot for comparing multivariate distributions",

abstract = "In this paper, we propose a scale-scale plot to compare multivariate distributions. These scale-scale plots can be viewed as a multivariate analog of quantile-quantile plots and we illustrate their use as a visualization tool to validate distributional assumptions for multivariate data as well as to compare the distributions of two multivariate samples. We discuss some characterizations of the proposed plots under elliptically symmetric distributions and based on those results, propose some visual tests of location and scale as further applications of these scale-scale plots. For the test of location problem, we present a small power study using simulations.",

keywords = "Central rank regions, elliptically symmetric distributions, quantile quantile plots, tests of location, tests of scale",

author = "Pritha Guha and Biman Chakraborty",

note = "Funding Information: This work is part of the first author{\textquoteright}s Ph.D. thesis under the guidance of the second author. The thesis was completed at the School of Mathematics, University of Birmingham, UK. The authors would like to thank the referee, associate editor and the School of Mathematics, University of Birmingham, UK for support. Publisher Copyright: {\textcopyright} 2020 Taylor & Francis Group, LLC.",

year = "2022",

month = mar,

day = "4",

doi = "10.1080/03610926.2020.1759639",

language = "English",

volume = "51",

pages = "1270--1289",

journal = "Communications in Statistics - Theory and Methods",

issn = "0361-0926",

publisher = "Taylor & Francis",

number = "5",

}

TY - JOUR

T1 - On a scale-scale plot for comparing multivariate distributions

AU - Guha, Pritha

AU - Chakraborty, Biman

N1 - Funding Information: This work is part of the first author’s Ph.D. thesis under the guidance of the second author. The thesis was completed at the School of Mathematics, University of Birmingham, UK. The authors would like to thank the referee, associate editor and the School of Mathematics, University of Birmingham, UK for support. Publisher Copyright: © 2020 Taylor & Francis Group, LLC.

PY - 2022/3/4

Y1 - 2022/3/4

N2 - In this paper, we propose a scale-scale plot to compare multivariate distributions. These scale-scale plots can be viewed as a multivariate analog of quantile-quantile plots and we illustrate their use as a visualization tool to validate distributional assumptions for multivariate data as well as to compare the distributions of two multivariate samples. We discuss some characterizations of the proposed plots under elliptically symmetric distributions and based on those results, propose some visual tests of location and scale as further applications of these scale-scale plots. For the test of location problem, we present a small power study using simulations.

AB - In this paper, we propose a scale-scale plot to compare multivariate distributions. These scale-scale plots can be viewed as a multivariate analog of quantile-quantile plots and we illustrate their use as a visualization tool to validate distributional assumptions for multivariate data as well as to compare the distributions of two multivariate samples. We discuss some characterizations of the proposed plots under elliptically symmetric distributions and based on those results, propose some visual tests of location and scale as further applications of these scale-scale plots. For the test of location problem, we present a small power study using simulations.

KW - Central rank regions

KW - elliptically symmetric distributions

KW - quantile quantile plots

KW - tests of location

KW - tests of scale

UR - http://www.scopus.com/inward/record.url?scp=85084352581&partnerID=8YFLogxK

U2 - 10.1080/03610926.2020.1759639

DO - 10.1080/03610926.2020.1759639

M3 - Article

AN - SCOPUS:85084352581

SN - 0361-0926

VL - 51

SP - 1270

EP - 1289

JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

IS - 5

ER -

On a scale-scale plot for comparing multivariate distributions

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Fingerprint

Cite this