Wpływ wyboru funkcji połączenia na kapitał ekonomiczny - analiza symulacyjna

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(84) 'ROQHLJyUQHRJUDQLF]HQLDZWHM SU]HVWU]HQLEĕGćR]QDF]DQHMDNR . C − (u1 , …, un ) ≤ C(u1 , …, un ) ≤ C + (u1 , …, un ),.

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(86). C + (u1 , …, . un ) = min {ui } ..

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(98) PDIXQNFMĕSRãćF]HQLD&ZWHG\LW\ONRZWHG\JG\ LVWQLHMćQLHPDOHMćFHIXQNFMHKLWDNLHŧHGODSHZQHM]PLHQQHMORVRZHM=VSHãQLRQ\ MHVWZDUXQHN d. . ( X1 , ..., Xn ) = ( h1 (Z ), ..., hn (Z )) ,.

(99). ²ZHNWRU; ;;

(100) PDIXQNFMĕSRãćF]HQLD&ZWHG\LW\ONRZWHG\JG\ LVWQLHMHURVQćFDIXQNFMDKWDNDŧH; K ;

(101) &KDUDNWHU\VW\NDZ\EUDQ\FKIXQNFMLSRïÈF]HQLD (OLSW\F]QHIXQNFMHSRïÈF]HQLD. )XQNFMHSRãćF]HQLD]ZLć]DQH]UR]NãDGDPLHOLSW\F]Q\PLVćQD]\ZDQHHOLS W\F]Q\PLIXQNFMDPLSRãćF]HQLD'ZLHQDMZDŧQLHMV]H]QLFKWRIXQNFMDSRãćF]HQLD *DXVVDL6WXGHQWD )XQNFMDSRãćF]HQLD*DXVVD 1LHFKlR]QDF]DV\PHWU\F]QćGRGDWQLRRNUHŋORQćPDFLHU]RZ\PLDU]HQðQ RUD]GLDJRQDOQHMGLDJl D+l²G\VWU\EXDQWĕZLHORZ\PLDURZHJRVWDQGDU\]R ZDQHJRUR]NãDGXQRUPDOQHJRRPDFLHU]\NRUHODFMLl ZVNUyFLH1 l

(102)

(103) :WHG\ QZ\PLDURZDIXQNFMDSRãćF]HQLD*DXVVDMHVWRNUHŋORQDUyZQDQLHP . (. ). Cρ (u1 , …, un ) = H ρ Φ −1 (u1 ), …, Φ −1 (un ) ..

(104). :]yUJĕVWRŋFLWHMIXQNFMLSRãćF]HQLDPDSRVWDþ cρ (u1 , …, . un ) = . ⎛ 1 ⎞ exp ⎜ − ς T (ρ−1 − I)ς ⎟ , ρ ⎝ 2 ⎠. 1. JG]LH . (. ). T. ς = Φ −1 (u1 ), ..., Φ −1 (un ) .. .

(105).

(106) . 6WDQLVãDZ:DQDW. :VSyãF]\QQLNNRUHODFMLƲ.HQGDOODPLĕG]\]PLHQQ\PL;LL;MZ\QRVL. (. ). τ Xi , X j =. . ( ). 2 arcsin ρij . π.

(107). )XQNFMDSRãćF]HQLD6WXGHQWD 1LHFKlR]QDF]DV\PHWU\F]QćGRGDWQLRRNUHŋORQćPDFLHU]RZ\PLDU]HQðQ RUD]GLDJRQDOQHMGLDJl D7l Ƭ²G\VWU\EXDQWĕZLHORZ\PLDURZHJRVWDQGDU\]R ZDQHJRUR]NãDGX6WXGHQWDRƬVWRSQLDFKVZRERG\LPDFLHU]\NRUHODFMLl:WHG\ QZ\PLDURZDIXQNFMDSRãćF]HQLD6WXGHQWDMHVWRNUHŋORQDUyZQDQLHP. (. ). Cρ, ν (u1 , ..., un ) = Tρ, ν t ν−1 (u1 ), ..., t ν−1 (un ) ,.

(108) JG]LH t ν−1²IXQNFMDRGZURWQDG\VWU\EXDQW\MHGQRZ\PLDURZHJRUR]NãDGX6WXGHQWD RƬVWRSQLDFKVZRERG\ :]yUJĕVWRŋFLWHMIXQNFMLSRãćF]HQLDPDSRVWDþ. cρ, ν (u1 , ..., u1 ) = ρ . −. 1 2. ⎛ ν + n⎞ ⎛ ⎛ ν⎞ ⎞ n ⎛ ⎞− 1 T −1 ⎟ ⎜ Γ ⎜ ⎟ ⎟ ⎜1 + ς ρ ς⎟ Γ⎜ ⎝ 2 ⎠ ⎝ ⎝ 2⎠⎠ ⎝ ν ⎠ ⎛ ⎛ ν + 1⎞ ⎞ ⎛ ν ⎞ ⎟⎟ Γ⎜ ⎟ ⎜Γ⎜ ⎝ ⎝ 2 ⎠⎠ ⎝ 2⎠ n. ⎛ ⎞ 1 + ⎜ ⎟ ∏ ν⎠ i =1 ⎝ n. ς i2. −. ν+ n 2. ν+1 2. ,.

(109). JG]LH . ς = (ς1 , …, . ς n ) = (t ν−1 (u1 ), …, . t ν−1 (un )). . :VSyãF]\QQLNNRUHODFMLƲ.HQGDOODPLĕG]\]PLHQQ\PL;LL;MMHVWWDNLVDPMDN ZSU]\SDGNXSRãćF]HQLD*DXVVD SRUZ]yU

(110) )XQNFMHSRïÈF]HQLD$UFKLPHGHVD. -HGQć]QDMZDŧQLHMV]\FKNODVIXQNFMLSRãćF]HĸVćSRãćF]HQLD$UFKLPHGHVD $UFKLPHGHDQFRSXODV

(111) =DZLHUDRQDZLHOHURG]LQIXQNFMLSRãćF]HĸNWyUHVWRVXQ NRZRãDWZRVNRQVWUXRZDþL]SUDNW\F]QHJRSXQNWXZLG]HQLDPDMćZDŧQHZãDVQR ŋFL6]F]HJyãRZ\RSLVWHMNODV\MHVW]DZDUW\PLQZSUDFDFK>*HQHVWL0DF.D\ DE0DUVKDOOL2ONLQ-RH1HOVHQ@DLFKDNWXDULDOQH Z\NRU]\VWDQLHSU]HGVWDZLRQRZSUDFDFK>)UHHVL9DOGH].OXJPDQL3DUVD @.

(112) . :Sã\ZZ\ERUXIXQNFML«. 'HILQLFMDIXQNFMLSRãćF]HQLD$UFKLPHGHVD )XQNFMD&MHVWSRãćF]HQLHP$UFKLPHGHVDMHŧHOLPRŧQDMćSU]HGVWDZLþZQDVWĕ SXMćF\VSRVyE . C ( u1 , …, un ) = ψ −1 ( ψ(u1 ) + … + ψ(un )) ,.

(113). JG]LH XLL «Q s²JHQHUDWRUEĕGćF\IXQNFMćFLćJãćPDOHMćFć ŋFLŋOHPDOHMćFć

(114) LZ\SXNãć RGZ]RURZXMćFćSU]HG]LDã>@ZSU]HG]LDOH>@RUD]WDNćŧHs

(115) DIXQN FMDRGZURWQDGRsVSHãQLDQDVWĕSXMćF\ZDUXQHN d n −1 ψ (x) ≥ 0 dla n = 1, 2, 3, … (−1) dx n n. .

(116). =QDF]HQLHIXQNFMLSRãćF]Hĸ$UFKLPHGHVDZJãyZQHMPLHU]HZ\QLND]WHJRŧH ZV]\VWNLHLQIRUPDFMHGRW\F]ćFHZLHORZ\PLDURZHMVWUXNWXU\]DOHŧQRŋFLZHNWRUyZ ORVRZ\FKPRGHORZDQ\FK]DLFKSRPRFćVć]DZDUWHZMHGQRZ\PLDURZ\PJHQH UDWRU]H:LHORZ\PLDURZDZHUVMDZVSyãF]\QQLNDNRUHODFMLƲ.HQGDOODSU]\MPXMH SRQDGWRSRVWDþ SRU>%DUEHHWDO*HQHVW4XHVV\L5pPLOODUG@

(117) . . ⎛ 2 n ⎞ n −1 (−1)i τ = 1 − ⎜ n −1 ⎟ ∑ ⎝ 2 − 1 ⎠ i =1 i!. 1. ∫ ( ψ(t)). i. fi (t)dt ,.

(118). 0. JG]LH fi (t) = . d i −1 ψ (x) . x = ψ (t ) dx i.

(119). 'ODQ Z]yUWHQUHGXNXMHVLĕGR]QDQHJRZ\UDŧHQLD SRU>*HQHVWL0DF.D\ D1HOVHQ@

(120) 1. . τ = 1+ 4∫ 0. ψ(t) dt . ψ '(t).

(121). .ODVDSRãćF]Hĸ$UFKLPHGHVD]DZLHUDPLQQDVWĕSXMćFHURG]LQ\IXQNFMLSRãćF]Hĸ ²QLH]DOHŧQH n. . C ⊥ (u1 , ..., un ) = ∏ ui ,.

(122). i =1. JG]LHJHQHUDWRUPDSRVWDþs W

(123) ²OQ W

(124) MHŧHOLZHNWRUORVRZ\; ;;Q

(125) PD QLH]DOHŧQćIXQNFMĕSRãćF]HQLDWR]PLHQQH;LVćQLH]DOHŧQH.

(126) . 6WDQLVãDZ:DQDW. ²&OD\WRQD&RRN-RKQVRQD −. 1. ⎛ n ⎞θ C ( u1 , ..., un ) = ⎜ ∑ ui−θ − n + 1⎟ , ⎝ i =1 ⎠. .

(127). t −θ − 1 , θ > 0ZSU]\SDGNXGZXZ\PLDURZ\P θ ZVSyãF]\QQLNƲ.HQGDOODMHVWUyZQ\. JG]LHJHQHUDWRUPDSRVWDþψ(t) =. τ= . θ , τ ∈ ( 0, 1) ; θ+2.

(128). ²*XPEHOD 1 ⎡ ⎤ n θ ⎛ ⎞ θ ⎢ C ( u1 , ..., un ) = exp ⎢ − ⎜ ∑ ( − ln ui ) ⎟ ⎥⎥ , ⎠ ⎥ ⎢⎣ ⎝ i =1 ⎦. .

(129). JG]LHJHQHUDWRUPDSRVWDþs W

(130) ²OQW

(131) ƧƧGODQ ZVSyãF]\QQLNƲ.HQGDOOD MHVWUyZQ\ 1 τ = 1 − , τ ∈ [ 0, 1) ; θ . ²)UDQND. n ⎡ −θu −1 ⎢ ∏ e 1 ⎢ i =1 C ( u1 , ..., un ) = − ln 1 + n −1 θ ⎢ e−θ − 1 ⎢ ⎣. (. (. . i. ). ) ⎤⎥. ⎥, ⎥ ⎥ ⎦.

(132). ⎛ e−θt − 1 ⎞ JG]LHJHQHUDWRUPDSRVWDþψ(t) = − ln ⎜ −θ ⎟ , θ ≠ 0GODQ ZVSyãF]\QQLN ⎝ e −1⎠ Ʋ.HQGDOODMHVWUyZQ\ τ = 1−. θ. JG]LHD1 ( θ ) = ∫. x. θ(e − 1) 0 x. dx.. 4 4D1 (θ) + , θ θ.

(133).

(134) :Sã\ZZ\ERUXIXQNFML«. . :Sï\ZZ\EUDQ\FKVWUXNWXU]DOHĝQRĂFLQDUR]NïDG DJUHJRZDQ\FKURG]DMöZU\]\NDLNDSLWDïHNRQRPLF]Q\ļ Z\QLNLEDGDñV\PXODF\MQ\FK :EDGDQLXV\PXODF\MQ\PXZ]JOĕGQLRQRGZDURG]DMHU\]\NDLDQDOL]RZDQR ZMDNLPVWRSQLX]DOHŧQRŋþPLĕG]\QLPLZSã\ZDQDUR]NãDGLZ\PRJLNDSLWDãRZH GODÅãćF]QHJRU\]\NDµRWU]\PDQHJRZZ\QLNXLFKDJUHJDFML3U]HDQDOL]RZDQR MDN]PLHQLDVLĕUR]NãDG]DJUHJRZDQHJRU\]\NDMHŧHOLVWUXNWXUD]DOHŧQRŋFLPLĕG]\ DJUHJRZDQ\PLF]\QQLNDPLU\]\NDMHVWRSLV\ZDQDIXQNFMćSRãćF]HQLD*DXVVD *XPEHODL)UDQND)XQNFMHWHZ\EUDQR]HZ]JOĕGXQDLFKZãDVQRŋFLLPRŧOL ZRŋþSUDNW\F]QHJRZ\NRU]\VWDQLDZPRGHORZDQLXU\]\NDZXEH]SLHF]HQLDFK )XQNFMDSRãćF]HQLD*DXVVDMHVWQDMF]ĕŋFLHMZ\NRU]\VW\ZDQDZSUDNW\FH]DUyZQR ZPRGHORZDQLXU\]\NDZXEH]SLHF]HQLDFKMDNLZILQDQVDFK6WUXNWXUD]DOHŧ QRŋFLX]\VNLZDQD]DMHMSRPRFćMHVWZSHãQL]GHWHUPLQRZDQDPDFLHU]ćNRUHODFML DJUHJRZDQ\FKURG]DMyZU\]\ND-HVWRQDVWDQGDUGRZRZ\NRU]\VW\ZDQDZPRGH ORZDQLXU\]\NDNUHG\WRZHJR=NROHLIXQNFMDSRãćF]HQLD*XPEHODMHVWQDMF]ĕŋFLHM VWRVRZDQDZPRGHORZDQLXU\]\NDXEH]SLHF]HQLRZHJRNWyUHFKDUDNWHU\]XMHVLĕ PRŧOLZRŋFLćZ\VWćSLHQLDZDUWRŋFLHNVWUHPDOQ\FK'ROQHLJyUQHRJUDQLF]HQLH MHMSDUDPHWUyZNRUHVSRQGXMHRGSRZLHGQLR]QLH]DOHŧQćIXQNFMćSRãćF]HQLD L]JyUQ\PRJUDQLF]HQLHP)UpFKHWD-HVWZ\JRGQ\PQDU]ĕG]LHPXPRŧOLZLDMćF\P PRGHORZDQLHURG]DMyZU\]\NDFKDUDNWHU\]XMćF\FKVLĕQLH]DOHŧQćRUD]GRGDWQLć VWUXNWXUć]DOHŧQRŋFL'\VWU\EXDQWDãćF]QHJRUR]NãDGXRWU]\PDQD]DSRPRFćWHM IXQNFMLSRãćF]HQLDMHVWG\VWU\EXDQWćZDUWRŋFLHNVWUHPDOQ\FKW\SX%DMHMG\VWU\ EXDQW\EU]HJRZHVćWRUR]NãDG\ZDUWRŋFLHNVWUHPDOQ\FKW\SX,5RG]LQDIXQNFML SRãćF]HQLD)UDQND]DZLHUDMDNRJUDQLFHGROQHLJyUQHRJUDQLF]HQLH)UpFKHWDRUD] QLH]DOHŧQćIXQNFMĕSRãćF]HQLD8PRŧOLZLDWRPRGHORZDQLH]DUyZQRGRGDWQLFK MDNLXMHPQ\FKVWUXNWXU]DOHŧQRŋFL:RGUyŧQLHQLXMHGQDNRGIXQNFMLSRãćF]HQLD *XPEHODQLHPRŧQDMHMZ\NRU]\VWDþGRPRGHORZDQLDURG]DMyZU\]\NDFKDUDNWH U\]XMćF\FKVLĕPRŧOLZRŋFLćZ\VWćSLHQLDZDUWRŋFLHNVWUHPDOQ\FK3DUDPHWU\W\FK IXQNFMLGREUDQRWDNDE\ZVSyãF]\QQLNNRUHODFMLƲ.HQGDOODPLĕG]\F]\QQLNDPL U\]\NDE\ãUyZQ\ :Z\SDGNXNDŧGHM]IXQNFMLSRãćF]HQLDSU]\MĕWRŧHUR]NãDG\DJUHJRZDQ\FK F]\QQLNyZU\]\NDVćWDNLHVDPH5R]ZDŧDQRWU]\SU]\SDGNLZNWyU\FK]PLHQQH ORVRZHPRGHOXMćFHREDF]\QQLNLU\]\NDPLDã\UR]NãDGQRUPDOQ\UR]NãDGJDPPD LUR]NãDGORJDU\WPLF]QRQRUPDOQ\5R]NãDG\WHZ\EUDQR]HZ]JOĕGXQDZãDVQRŋFL XPRŧOLZLDMćFHZ\NRU]\VWDQLHLFKZPRGHORZDQLXU\]\NDZXEH]SLHF]HQLDFK]Dŋ SDUDPHWU\XVWDORQRWDNDE\LFKZDUWRŋþRF]HNLZDQDLZDULDQFMDE\ã\UyZQHMHGHQ &HOHPDQDOL]\E\ãREDGDQLHZMDNLPVWRSQLXSRVWDþIXQNFMLSRãćF]HQLDZSã\ZD QDNDSLWDãHNRQRPLF]Q\DWDNLZ\EyUSDUDPHWUyZJZDUDQWRZDãRJUDQLF]HQLH ZSã\ZXQDWHQNDSLWDãZDUWRŋFLDJUHJRZDQ\FKURG]DMyZU\]\ND.

(135) . 6WDQLVãDZ:DQDW. ) f(x 1, x 2. Gumbela. ) f(x 1, x 2. Normalny. Gaussa. x2. x2 x1. ) f(x 1, x 2. ) f(x 1, x 2. Gamma. x1. x2. x2 x1. ) f(x 1, x 2. ) f(x 1, x 2. Logarytmiczno-normalny. x1. x2. x2 x1. x1. 5\V )XQNFMH JĕVWRŋFL SRVWDFL

(136) GZXZ\PLDURZHJR ZHNWRUD ORVRZHJR GOD SRãćF]Hĸ *DXVVDL*XPEHODRUD]UR]NãDGyZEU]HJRZ\FKQRUPDOQHJRJDPPDLORJDU\WPLF]QRQRU PDOQHJRRSUDFRZDQH]]DãRŧHQLHPŧHZVSyãF]\QQLNƲ.HQGDOODPLĕG]\DJUHJRZDQ\PL URG]DMDPLU\]\NDZ\QRVL ŤUyGãRRSUDFRZDQLHZãDVQH.

(137) . :Sã\ZZ\ERUXIXQNFML«. ) f(x 1, x 2. Gumbela. ) f(x 1, x 2. Normalny. Gaussa. x2. x2 x1. ) f(x 1, x 2. ) f(x 1, x 2. Gamma. x1. x2 x2. x1. ) f(x 1, x 2. ) f(x 1, x 2. Logarytmiczno-normalny. x1. x2. x2 x1. x1. 5\V )XQNFMH JĕVWRŋFL SRVWDFL

(138) GZXZ\PLDURZHJR ZHNWRUD ORVRZHJR GOD SRãćF]Hĸ *DXVVDL*XPEHODRUD]UR]NãDGyZEU]HJRZ\FKQRUPDOQHJRJDPPDLORJDU\WPLF]QRQRU PDOQHJRRSUDFRZDQH]]DãRŧHQLHPŧHZVSyãF]\QQLNƲ.HQGDOODPLĕG]\DJUHJRZDQ\PL URG]DMDPLU\]\NDZ\QRVL ŤUyGãRRSUDFRZDQLHZãDVQH.

(139) . 6WDQLVãDZ:DQDW. Gaussa. Gumbela. Normalny. 0,5. tau = 0 tau = 0,10 tau = 0,25 tau = 0,50 tau = 0,75 tau = 0,95. 0,4 0,3. 0,1. 0,1. 0,0. 0,0 5. 0,5. 0,3. –5. 10. tau = 0 tau = 0,10 tau = 0,25 tau = 0,50 tau = 0,75 tau = 0,95. 0,4 Gamma. 0,3 0,2. 0. 0,1. 0,0. 0,0 6. 0,5. 8. 0,4 0,3. 2. 4. 6. 8. 0,5. 0,3 0,2. 0,1. 0,1. 10. tau = 0 tau = 0,10 tau = 0,25 tau = 0,50 tau = 0,75 tau = 0,95. 0,4. 0,2. 0,0. tau = 0 tau = 0,10 tau = 0,25 tau = 0,50 tau = 0,75 tau = 0,95. 0. 10. tau = 0 tau = 0,10 tau = 0,25 tau = 0,50 tau = 0,75 tau = 0,95. 10. 0,3. 0,1. 4. 5. 0,4. 0,2. 2. 0. 0,5. 0,2. 0. tau = 0 tau = 0,10 tau = 0,25 tau = 0,50 tau = 0,75 tau = 0,95. 0,4. 0,2. –5. Logarytmiczno-normalny. 0,5. 0,0 0. 2. 4. 6. 8. 10. 0. 2. 4. 6. 8. 5\V)XQNFMHJĕVWRŋFLUR]NãDGXVXP\GZyFKURG]DMyZU\]\NDZ]DOHŧQRŋFL RGSU]\MĕWHMVWUXNWXU\]DOHŧQRŋFLLUR]NãDGyZDJUHJRZDQ\FKF]\QQLNyZU\]\ND ŤUyGãRRSUDFRZDQLHZãDVQH. 10.

(140) . :Sã\ZZ\ERUXIXQNFML«. :\PRJLNDSLWDãRZHGRW\F]ćFHUR]ZDŧDQ\FKF]\QQLNyZU\]\NDZ\]QDF]RQR ]DSRPRFćNDSLWDãXHNRQRPLF]QHJRRNUHŋORQHJRMDNRUyŧQLFHNZDQW\ODU]ĕGXT UR]NãDGX]PLHQQHMORVRZHM;LPRGHOXMćFHMLW\F]\QQLNU\]\ND L

(141) LZDUWRŋFL RF]HNLZDQHMWHM]PLHQQHMF]\OL SRUQS>'KDHQHHWDO@

(142) κ ( Xi ) = FX−1 (q) − E(Xi ),. .

(143). i. JG]LH FX ²G\VWU\EXDQWD]PLHQQHM;L i. :WHQVDPVSRVyEZ\]QDF]RQRNDSLWDãHNRQRPLF]Q\GOD]DJUHJRZDQHJRU\]\ND = ;; κ ( Z ) = FZ−1 (q) − E(Z ),. .

(144). JG]LHUR]NãDG=]DOHŧDãRGSU]\MĕWHMIXQNFMLSRãćF]HQLD ]DãRŧRQHMVWUXNWXU\]DOHŧ QRŋFL

(145) RUD]UR]NãDGX]PLHQQ\FK;L; 1DU\VLSU]HGVWDZLRQRZ\NUHV\IXQNFMLJĕVWRŋFLSRVWDFL

(146) GZXZ\PLDUR ZHJRZHNWRUDORVRZHJRSRãćF]Hĸ*DXVVDL*XPEHODRUD]UR]NãDGyZEU]HJRZ\FK QRUPDOQHJRJDPPDLORJDU\WPLF]QRQRUPDOQHJR]]DãRŧHQLHPŧHZVSyãF]\Q QLNƲ.HQGDOODPLĕG]\DJUHJRZDQ\PLURG]DMDPLU\]\NDZ\QRVLRUD] :\NUHV\IXQNFMLJĕVWRŋFLUR]NãDGXVXP\ZDUWRŋFLU\]\ND;L;SRGOHJDMćF\FK RSLVDQ\PZ\ŧHMGZXZ\PLDURZ\PUR]NãDGRPZ\]QDF]RQH]]DãRŧHQLHPŧH ZVSyãF]\QQLNƲ.HQGDOODMHVWUyZQ\]DSUH]HQWR ZDQRQDU\V)XQNFMHWHX]\VNDQRZZ\QLNXV\PXODFMLUHDOL]DFMLZHN WRUD; ;;

(147) L]DVWRVRZDQLXHVW\PDWRUyZMćGURZ\FK REOLF]HQLDSURZDG]RQR ]Z\NRU]\VWDQLHPSDNLHWXÅ5µ

(148) 7DEHOD.DSLWDãHNRQRPLF]Q\]XZ]JOĕGQLHQLHP]DJUHJRZDQHJRU\]\NDZ\]QDF]RQ\ QDSRGVWDZLHZ]RUX

(149) ]]DãRŧHQLHPUR]ZDŧDQ\FKVWUXNWXU]DOHŧQRŋFL .ZDQW\O. 5R]NãDG EU]HJRZ\. 1RUPDOQ\. . Ʋ. *DXVVD . . *XPEHOD . . . . . . . . . . . . . . . . . . . . . . )UDQND. . . . . . 1DU\VXQNDFKSUH]HQWRZDQHVćW\ONRZ\QLNLGODIXQNFMLSRãćF]HQLD*DXVVDL*XPEHOD.

(150) . 6WDQLVãDZ:DQDW. FGWDEHOL .ZDQW\O. 5R]NãDG EU]HJRZ\. *DPPD. /RJDU\WPLF]QR QRUPDOQ\. Ʋ. *DXVVD . . *XPEHOD . . . )UDQND . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ŤUyGãRREOLF]HQLDZãDVQH. :WDEHOLSU]HGVWDZLRQRZ\VRNRŋþNDSLWDãXHNRQRPLF]QHJR Z\]QDF]RQHJRQD SRGVWDZLHZ]RUX

(151) GODNZDQW\OL

(152) XZ]JOĕGQLDMćF]DJUHJRZDQH U\]\NRLUR]ZDŧDQHVWUXNWXU\]DOHŧQRŋFL ZDUWRŋþWHJRNDSLWDãXGODNZDQW\OD L]DSUH]HQWRZDQRWDNŧHQDU\V

(153) 'OD]DJUHJRZDQHJRU\]\ND= ;; Z\]QDF]RQRNDSLWDãHNRQRPLF]Q\ZVSRVyEVWDQGDUGRZ\W]Q]Z\NRU]\VWDQLHP Z]RUX κ'(Z ) = FZ−1 (q) − μ Z = ERE',. .

(154). JG]LH E = κ ( X1 ) , κ ( X 2 ) ²ZHNWRU]DZLHUDMćF\NDSLWDãHNRQRPLF]Q\GODDJUHJRZD. (. ). Q\FKF]\QQLNyZU\]\ND;F]\OLκ ( Xi ) = FX−1 (q) − μ i , 5²PDFLHU]NRUHODFMLOLQLRZHMPLĕG]\F]\QQLNDPLU\]\ND i. :FHOXSRUyZQDQLDZ\VRNRŋFLNDSLWDãXHNRQRPLF]QHJRRNUHŋORQHM]XZ]JOĕG QLHQLHP]DJUHJRZDQHJRU\]\NDZ\]QDF]RQHJR]]DãRŧHQLHPUR]ZDŧDQ\FKVWUXN WXU]DOHŧQRŋFLL]DSRPRFćSRGHMŋFLDVWDQGDUGRZHJRREOLF]RQRZ]JOĕGQHUyŧQLFHG LFKZDUWRŋFLZSU]HGVWDZLRQRZWDEHOL

(155) d= . κ(Z ) − κ'(Z ) . κ'(Z ).

(156).

(157) . :Sã\ZZ\ERUXIXQNFML«. κ(Z ). a). 8,00 7,50 7,00 6,50 6,00 5,50 5,00 4,50 4,00 3,50 3,00 2,50 2,00 1,50 1,00 0,50 0,00 Gaussa normalny. Gumbela normalny. τ=0. κ(Z ). b). 8,00 7,50 7,00 6,50 6,00 5,50 5,00 4,50 4,00 3,50 3,00 2,50 2,00 1,50 1,00 0,50 0,00. Gaussa normalny. Gumbela normalny. τ=0. Franka normalny. τ = 0,10. Franka normalny. τ = 0,10. Gaussa gamma. Gumbela gamma. τ = 0,25. Gaussa gamma. τ = 0,50. Gumbela gamma. τ = 0,25. Franka gamma. Gaussa Gumbela Franka log.-normalny log.-normalny log.-normalny. τ = 0,75. Franka gamma. τ = 0,50. τ = 0,95. Gaussa Gumbela Franka log.-normalny log.-normalny log.-normalny. τ = 0,75. τ = 0,95. 5\V.DSLWDãHNRQRPLF]Q\Z\]QDF]RQ\QDSRGVWDZLHNZDQW\OD D

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