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a.Norm.0} Weighted Inverse Ga.ssia. Distribution for Skewed a.d Hea.y-Ta.led Da.a

a.plied m.0}hem.0}ics 2022年第2期13卷 163-177页

作者： Ca.vin B. m.0}na.Pa.rick G. O. Weke Ca.olyne a. Ogutu joseph a. m. ottieno Depa.tm.nt of m.0}hem.0}ics a.d a.tua.ia. Science Kisii University Kisii Kenya School of m.0}hem.0}ics University of Nairobi Nairobi Kenya

High frequency fina.cia. da.a.is cha.a.terized by non-norm.0}ity: a.ym.etric, leptokurtic a.d fa.-ta.led beha.iour. The norm.0} distribution is therefore ina.equa.e in ca.turing these cha.a.teristics. To this end, va.ious flexible distributions ha.e been proposed. It is well known tha. m.xture distributions produce flexible m.dels with good sta.istica. a.d proba.ilistic properties. In this work, a.finite m.xture of two specia. ca.es of Genera.ized Inverse Ga.ssia. distribution ha. been constructed. Using this finite m.xture a. a.m.xing distribution to the Norm.0} Va.ia.ce m.a. m.xture we get a.Norm.0} Weighted Inverse Ga.ssia. (NWIG) distribution. The second objective, therefore, is to construct a.d obta.n properties of the NWIG distribution. The m.0}im.m.likelihood pa.a.eter estim.0}es of the proposed m.del a.e estim.0}ed via.Em.a.gorithm.a.d three da.a.sets a.e used for a.plica.ion. The result shows tha. the proposed m.del is flexible a.d fits the da.a.well.

关键词： Inverse Ga.ssia. Finite m.xture Weighted Distribution m.xed m.del Em.a.gorithm

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Ga.m.0}Genera.ized Inverse Ga.ssia. Cla.s of Distributions

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Open Journa. of Sta.istics 2021年第6期11卷 1026-1043页

作者： Richa.d L. K. Tinega.Joa.h m. Kerongo joseph a. m. ottieno Kisii University Kisii Kenya

Ga.m.0}distribution nests exponentia., chi-squa.ed a.d Erla.g distributions;while genera.ized Inverse Ga.ssia. distribution nests quite a.num.er of distributions. The a.m.of this pa.er is to construct a.ga.m.0}m.xture using Genera.ized inverse Ga.ssia. m.xing distribution. The a.>rth moment of the mixture is obtained via the rtha. style="font-fa.ily:Verda.a."> m.m.nt of the m.xing distribution. Specia. ca.es a.d lim.ting ca.es of the m.xture a.e deduced.

关键词： GIG m.xture Specia. Ca.es Lim.ting Ca.es Ga.m. m.xing Distribution

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a.Finite m.xture of Genera.ised Inverse Ga.ssia. with Indexes -1/2 a.d -3/2 a. m.xing Distribution for Norm.0} Va.ia.ce m.a. m.xture with a.plica.ion

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Open Journa. of Sta.istics 2021年第6期11卷 963-976页

m.xture m.dels ha.e becom. m.re popula. in m.delling com.a.ed to sta.da.d distributions. The m.xing distributions pla. a.role in ca.turing the va.ia.ility of the ra.dom.va.ia.le in the conditiona. distribution. Studies ha.e la.ely focused on finite m.xture m.dels a. m.xing distributions in the m.xing m.cha.ism. In the present work, we consider a.Norm.0} Va.ia.ce m.a. m.xture model. The mixing distribution is a finite mixture of two special cases of Generalised Inverse Gaussian distribution with indexes -1/2 and -3/2. The a.>parameters of the mixed model are obtained via the Expectation-Maximizationa.> (Em. a.gorithm. The itera.ive schem. is ba.ed on a.presenta.ion of the norm.0} equa.ions. a. a.plica.ion to som. fina.cia. da.a.ha. been done.

关键词： Finite m.xture Weighted Distribution m.xed m.del Em.a.gorithm

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a.Specia. Weight for Inverse Ga.ssia. m.xing Distribution in Norm.0} Va.ia.ce m.a. m.xture with a.plica.ion

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Open Journa. of Sta.istics 2021年第6期11卷 977-992页

Norm.0} Va.ia.ce-m.a. m.xture (NVm.) provides a.genera. fra.ework for deriving m.dels with desira.le properties for m.delling fina.cia. m.0}ket va.ia.les such a. excha.ge ra.es, equity prices, a.d interest ra.es m.a.ur... 详细信息

Normal Variance-Mean Mixture (NVMM) providea.>sa.>a.> a general framework for deriving models with desirable properties for modelling financial market variables such as exchange rates, equity prices, and interest rates measured over short time intervals, i.e. daily or weekly. Such data sets are characterized by non-normality and are usually skewed, fat-tailed and exhibit excess kurtosis. The Generalised Hyperbolic distribution (GHD) introduced by Barndorff-Nielsen a.>a.>a.>(1977)a.>a.> which act as Normal variance-mean mixtures with Generalised Inverse Gaussian (GIG) mixing distribution nest a number of special and limiting case distributions. The Normal Inverse Gaussian (NIG) distribution is obtained when the Inverse Gaussian is the mixing distribution, i.ea.>a.>a.>.a.>a.>, the index parameter of the GIG is . The NIG is very popular because of its analytical tractability. In the mixing mechanisma.>a.>a.>,a.>a.>a.>a.>a.>a.>a. style="color:#000000;"> the m.x

关键词： Finite m.xture Weighted Distribution m.xed m.del Em.a.gorithm

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