Product of independent generalised gamma random variables

dc.contributor.advisorBekker, Andriette, 1958-
dc.contributor.advisorMarques, Filipe
dc.contributor.postgraduateBilankulu, Vusi Raphael
dc.date.accessioned2023-12-19T09:03:16Z
dc.date.available2023-12-19T09:03:16Z
dc.date.created2017
dc.date.issued2016-10
dc.descriptionMini Dissertation (MSc (Mathematical Statistics))--University of Pretoria, 2016.en_US
dc.description.abstractThe generalised gamma distribution has received much attention due to its exibility and also for having some well-known distributions as special cases. This study originates from a statistic de ned as the ratio of products of independent generalised gamma random variables and shows that it can be represented as the product of independent generalised gamma random variables with some re-parametrisation. By decomposing the character- istic function of the negative logarithm of the statistic and then using the distribution of the di¤erence of two independent generalized integer gamma random variables as a basis, accurate and computationally appealing near-exact distributions are derived for the statis- tic. In the process, a new exible parameter is introduced in the near-exact distributions which allows to control the degree of precision of these approximations. Furthermore, the performance of the near-exact distributions is assessed using a measure of proximity be- tween cumulative distribution functions; also, by comparison with the exact distribution, empirical distribution and with an approximation developed using a di¤erent method and which can only be applied in some particular cases.en_US
dc.description.availabilityUnrestricteden_US
dc.description.degreeMSc (Mathematical Statistics)en_US
dc.description.departmentStatisticsen_US
dc.description.facultyFaculty of Natural and Agricultural Sciencesen_US
dc.description.sponsorshipNational Research Foundation (NRF)en_US
dc.description.sponsorshipSTATOMETen_US
dc.identifier.citation*en_US
dc.identifier.otherA2017en_US
dc.identifier.urihttp://hdl.handle.net/2263/93805
dc.language.isoenen_US
dc.publisherUniversity of Pretoria
dc.rights© 2021 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.subjectUCTDen_US
dc.subjectGamma random variablesen_US
dc.titleProduct of independent generalised gamma random variablesen_US
dc.typeMini Dissertationen_US

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