Geometric skew-Cauchy distribution as an alternative to the skew-normal and geometric skew-normal distributions

dc.contributor.advisorEhlers, René
dc.contributor.coadvisorBekker, Andriette, 1958-
dc.contributor.emailxan97der@gmail.comen_ZA
dc.contributor.postgraduateHeaney, Xander
dc.date.accessioned2022-01-18T08:01:03Z
dc.date.available2022-01-18T08:01:03Z
dc.date.created2022-05-06
dc.date.issued2021
dc.descriptionMini Dissertation (MSc (Advanced Data Analytics))--University of Pretoria, 2021.en_ZA
dc.description.abstractThe skew-normal distribution was popularised by Azzalini [4] to model skewed data. However, the skew-normal distribution is always unimodal. Kundu [24] recently presented the geometric skew-normal distribution by considering a geometric compounding sum of normal random variables. This distribution is more flexible than the skew-normal distribution since it can be multimodal. In this dissertation we present a new distribution namely the geometric skew-Cauchy distribution. The idea follows a similar approach to that of Kundu's. The difference, however, is that we consider a geometric compounding sum of Cauchy random variables. The inclusion of a simulation and application chapter demonstrates the practical use of this new distribution. It turns out that the geometric skew-Cauchy distribution is also more flexible than the skew-normal distribution. It is concluded that this new distribution can be used as an alternative to the geometric skew-normal distribution since both distributions can be multimodal. The advantage over the geometric skew-normal distribution, is the ability of the geometric skew-Cauchy distribution to model fatter-tailed data.en_ZA
dc.description.availabilityUnrestricteden_ZA
dc.description.degreeMSc (Advanced Data Analytics)en_ZA
dc.description.departmentStatisticsen_ZA
dc.description.sponsorshipNational Research Foundation (NRF) of South Africa, Reference: SRUG190308422768 grant No. 120839; Academic Statistics Funding Instrument grant No. 127946; SARChI Research Chair UID71199.en_ZA
dc.identifier.citation*en_ZA
dc.identifier.otherA2022en_ZA
dc.identifier.urihttp://hdl.handle.net/2263/83345
dc.identifier.uriDOI: 10.25403/UPresearchdata.18319196
dc.language.isoenen_ZA
dc.publisherUniversity of Pretoria
dc.rights© 2019 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria.
dc.subjectStatisticsen_ZA
dc.subjectDistribution Theoryen_ZA
dc.subjectDistributionsen_ZA
dc.subjectMultimodal distributionsen_ZA
dc.subjectData Analyticsen_ZA
dc.subjectData Scienceen_ZA
dc.subjectskewed dataen_ZA
dc.subjectUCTD
dc.titleGeometric skew-Cauchy distribution as an alternative to the skew-normal and geometric skew-normal distributionsen_ZA
dc.typeMini Dissertationen_ZA

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