A multivariate rank test for comparing mass size distributions

Handle URI:
http://hdl.handle.net/10754/597329
Title:
A multivariate rank test for comparing mass size distributions
Authors:
Lombard, F.; Potgieter, C. J.
Abstract:
Particle size analyses of a raw material are commonplace in the mineral processing industry. Knowledge of particle size distributions is crucial in planning milling operations to enable an optimum degree of liberation of valuable mineral phases, to minimize plant losses due to an excess of oversize or undersize material or to attain a size distribution that fits a contractual specification. The problem addressed in the present paper is how to test the equality of two or more underlying size distributions. A distinguishing feature of these size distributions is that they are not based on counts of individual particles. Rather, they are mass size distributions giving the fractions of the total mass of a sampled material lying in each of a number of size intervals. As such, the data are compositional in nature, using the terminology of Aitchison [1] that is, multivariate vectors the components of which add to 100%. In the literature, various versions of Hotelling's T 2 have been used to compare matched pairs of such compositional data. In this paper, we propose a robust test procedure based on ranks as a competitor to Hotelling's T 2. In contrast to the latter statistic, the power of the rank test is not unduly affected by the presence of outliers or of zeros among the data. © 2012 Copyright Taylor and Francis Group, LLC.
Citation:
Lombard F, Potgieter CJ (2012) A multivariate rank test for comparing mass size distributions. Journal of Applied Statistics 39: 851–865. Available: http://dx.doi.org/10.1080/02664763.2011.623155.
Publisher:
Informa UK Limited
Journal:
Journal of Applied Statistics
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
Apr-2012
DOI:
10.1080/02664763.2011.623155
Type:
Article
ISSN:
0266-4763; 1360-0532
Sponsors:
The first author's work was supported by the National Research Foundation of South Africa. The second author's work was supported byAward No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). The authors thank the two referees for valuable comments that led to a much improved exposition of the work.
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Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorLombard, F.en
dc.contributor.authorPotgieter, C. J.en
dc.date.accessioned2016-02-25T12:30:49Zen
dc.date.available2016-02-25T12:30:49Zen
dc.date.issued2012-04en
dc.identifier.citationLombard F, Potgieter CJ (2012) A multivariate rank test for comparing mass size distributions. Journal of Applied Statistics 39: 851–865. Available: http://dx.doi.org/10.1080/02664763.2011.623155.en
dc.identifier.issn0266-4763en
dc.identifier.issn1360-0532en
dc.identifier.doi10.1080/02664763.2011.623155en
dc.identifier.urihttp://hdl.handle.net/10754/597329en
dc.description.abstractParticle size analyses of a raw material are commonplace in the mineral processing industry. Knowledge of particle size distributions is crucial in planning milling operations to enable an optimum degree of liberation of valuable mineral phases, to minimize plant losses due to an excess of oversize or undersize material or to attain a size distribution that fits a contractual specification. The problem addressed in the present paper is how to test the equality of two or more underlying size distributions. A distinguishing feature of these size distributions is that they are not based on counts of individual particles. Rather, they are mass size distributions giving the fractions of the total mass of a sampled material lying in each of a number of size intervals. As such, the data are compositional in nature, using the terminology of Aitchison [1] that is, multivariate vectors the components of which add to 100%. In the literature, various versions of Hotelling's T 2 have been used to compare matched pairs of such compositional data. In this paper, we propose a robust test procedure based on ranks as a competitor to Hotelling's T 2. In contrast to the latter statistic, the power of the rank test is not unduly affected by the presence of outliers or of zeros among the data. © 2012 Copyright Taylor and Francis Group, LLC.en
dc.description.sponsorshipThe first author's work was supported by the National Research Foundation of South Africa. The second author's work was supported byAward No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). The authors thank the two referees for valuable comments that led to a much improved exposition of the work.en
dc.publisherInforma UK Limiteden
dc.subjectbias testingen
dc.subjectmass size distributionsen
dc.subjectmultivariate rank statisticen
dc.titleA multivariate rank test for comparing mass size distributionsen
dc.typeArticleen
dc.identifier.journalJournal of Applied Statisticsen
dc.contributor.institutionNorth-West University, Potchefstroom, South Africaen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
dc.contributor.institutionUniversity of Johannesburg, Johannesburg, South Africaen
kaust.grant.numberKUS-C1-016-04en
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