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dc.contributor.authorAlzaatreh, Ayman
dc.contributor.authorKazempoor, Jaber
dc.contributor.authorNadi, Adel Ahmadi
dc.date.accessioned2021-04-14T07:43:28Z
dc.date.available2021-04-14T07:43:28Z
dc.date.issued2020
dc.identifier.citationAlzaatreh, A., Kazempoor, J., & Nadi, A. A. (2020). Weighted multimodal family of distributions with sine and cosine weight functions. Heliyon, 6(8), e04757. https://doi.org/10.1016/j.heliyon.2020.e04757en_US
dc.identifier.issn2405-8440
dc.identifier.urihttp://hdl.handle.net/11073/21410
dc.description.abstractIn this paper, the moment of various types of sine and cosine functions are derived for any random variable. For an arbitrary even probability density function, the sine and cosine moments are used to define new families of univariate multimodal probability density and their corresponding characteristic functions. For illustration, two weighted multimodal generalizations of the t distribution are investigated. Furthermore, a method of calculating some interesting improper integrals is also presented. Finally, an explicit expression of the probability density function of the sum of independent t-distributed random variables with odd degrees of freedom is derived.en_US
dc.description.sponsorshipAmerican University of Sharjahen_US
dc.language.isoen_USen_US
dc.publisherCell Pressen_US
dc.relation.urihttps://doi.org/10.1016/j.heliyon.2020.e04757en_US
dc.subjectMathematicsen_US
dc.subjectMomentsen_US
dc.subjectCharacteristic functionen_US
dc.subjectEven probability density functionen_US
dc.subjectParseval's identityen_US
dc.titleWeighted multimodal family of distributions with sine and cosine weight functionsen_US
dc.typePeer-Revieweden_US
dc.typeArticleen_US
dc.typePublished versionen_US
dc.identifier.doi10.1016/j.heliyon.2020.e04757


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