Distribution function for the ratio of two normal random variables

Oliveira, Amilcar; Oliveira, Teresa; Seijas-Macias, J. Antonio

Publication

Distribution function for the ratio of two normal random variables

2015-03-10Conference object

dc.contributor.author	Oliveira, Amilcar
dc.contributor.author	Oliveira, Teresa
dc.contributor.author	Seijas-Macias, J. Antonio
dc.date.accessioned	2023-08-01T15:36:22Z
dc.date.available	2023-08-01T15:36:22Z
dc.date.issued	2015-03-10
dc.description.abstract	The distribution of the ratio of two normal random variables X and Y was studied from [1] (the density function) and [2] (the distribution function). The shape of its density function can be unimodal, bimodal, symmetric, asymmetric, following several type of distributions, like Dirac Distribution, Normal Distribution, Cauchy Distribution or Recinormal Distribution. In this paper we study a different approximation for this distribution Z = X /Y , as a function of four parameters: ratio of the means of the two normal variables, ratio of the standard deviations of the two normal variables, the variation coefficient of the normal variable Y , and the correlation between the two variables. A formula for the Distribution function and the density function of Z is given. In addition, using graphical procedures we established singularity points for the parameters where the approximation given for Z has a non normal shape.	pt_PT
dc.description.version	info:eu-repo/semantics/publishedVersion	pt_PT
dc.identifier.doi	10.1063/1.4913045	pt_PT
dc.identifier.uri	http://hdl.handle.net/10400.2/14691
dc.language.iso	eng	pt_PT
dc.peerreviewed	yes	pt_PT
dc.publisher	AIP Publishing	pt_PT
dc.relation	2014 - Strategic Project
dc.rights.uri	http://creativecommons.org/licenses/by/4.0/	pt_PT
dc.subject	Ratio two normal variables	pt_PT
dc.subject	Fieller distribution	pt_PT
dc.subject	Uncorrelated normal variables	pt_PT
dc.subject	Cumulative density distribution	pt_PT
dc.subject	Density function	pt_PT
dc.title	Distribution function for the ratio of two normal random variables	pt_PT
dc.type	conference object
dspace.entity.type	Publication
oaire.awardTitle	2014 - Strategic Project
oaire.awardURI	info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/PEst-OE%2FMAT%2FUI0006%2F2014/PT
oaire.citation.conferencePlace	Rodes	pt_PT
oaire.citation.title	ICNAAM 2014. Proceedings of the international conference on numerical analysis and applied mathematics	pt_PT
oaire.citation.volume	1648	pt_PT
oaire.fundingStream	6817 - DCRRNI ID
person.familyName	Oliveira
person.familyName	Oliveira
person.familyName	Seijas-Macias
person.givenName	Amilcar
person.givenName	Teresa A.
person.givenName	J. Antonio
person.identifier	1155497
person.identifier.ciencia-id	7110-61B4-B87F
person.identifier.ciencia-id	8814-A54B-12DE
person.identifier.ciencia-id	3717-BC82-53C2
person.identifier.orcid	0000-0001-5500-7742
person.identifier.orcid	0000-0003-3283-9946
person.identifier.orcid	0000-0002-6056-3257
person.identifier.rid	J-3077-2019
person.identifier.scopus-author-id	55675222550
person.identifier.scopus-author-id	54403540300
person.identifier.scopus-author-id	57194105655
project.funder.identifier	http://doi.org/10.13039/501100001871
project.funder.name	Fundação para a Ciência e a Tecnologia
rcaap.rights	restrictedAccess	pt_PT
rcaap.type	conferenceObject	pt_PT
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