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Bayesian Estimation of NIG-parameters by Markov Chain Monte Carlo Methods

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(10)

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Simulated NIG(2,1,2,1)

0 2 4 6

x

0 0.1 0.2 0.3 0.4 0.5 0.6

FTA returns

-20 0 20 40 60

return

0 0.02 0.04 0.06

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(12)

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í î ê ì

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m ^OvWY‘•Qƒ±Ï4^Op{^$giYlU7Ylp9YhT7UVsgi^OU7YhT

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Z$[‹Z$U n í ^$Sb î-^OpYd_lvWZrTYlpiU7ZÌU n YhVWp%U7p{X+Y´O^$v]X+YhTµQ~ÖU n V]T¥g¥YlU n Zkb¼U n ^$S¼U n Y

ceÔw€‚g¥YlU n Zkb)}q.VWU n î ^O*ZrX+UAZrSÖU^Opf$YlUl‡ m2n Y%YhTUV]gi^OU7YŽZ$[9ìzVsTA^$v]TZ©Vsg¥¬pZž$Yhb

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(13)

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n

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n

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n

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Posterior density alpha

1.5 2

alpha

0 0.5 1 1.5

Posterior density mu

2 2.1 2.2 2.3

mu

1.4 1.5 1.6 1.7 1.8

Posterior density beta

0.5 1 1.5

beta

0 0.5 1 1.5

Posterior density delta

0.4 0.5 0.6 0.7 0.8

delta

0.5 1 1.5 2 2.5 3

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U n Y™U7p{X+Y™¬^Op{^$giYlU7Ylp¥Ù^$v]XYhT‘[°Z$pµîØVsT“^OU“U n Y´_`YhSuU7p{^$v'¬^OpU“Z$[.U n YŽbV]T7U7p§VWX+UVWZrSw}

q n V]vWY´U n YzU7p§X+Ydê-^$Sb»íá^OpYeZrX+U¦VsS¼U n YdU^$Vsv]Tl‡ \+Z$pzìtqY n ^$Ye*YlYhS p§^OU n Ylp

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(14)

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U n Ya¬^Op§^$g¥YlU7Ylpì!‡

m2n YŽTg¥ZQZ$U n Yhb n V]T7U7Z$f$p§^$giT‘Z$[9T^$g¥¬vWYhb¬*ZrT7U7Ylp{VWZ$p“b+YhSTV]UVWYhTa[°Z$p¥\ m |Œ.x m

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Posterior density alpha

0.5 1

alpha

0 0.5 1 1.5 2

Posterior density mu

0 0.5 1 1.5 2 2.5

mu

0 0.2 0.4 0.6 0.8

Posterior density beta

0.5 1

beta

0 0.5 1 1.5 2

Posterior density delta

1.8 2 2.2 2.4

delta

0 0.5 1 1.5 2 2.5

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