INTERVAL KREDIBEL BAYESIAN OBYEKTIF DARI PARAMETER POPULASI BERDISTRIBUSI POISSON DAN EKSPONENSIAL

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1 INTERVAL KREDIBEL BAYESIAN OBYEKTIF DARI PARAMETER POPULASI BERDISTRIBUSI POISSON DAN EKSPONENSIAL A Sawa Program S Mamaka Isr a Saska Faklas Sas a Mamaka Uvrsas Krs Saya Wacaa Jl Dpogoro 5-6 Salaga 57 Iosa Emal korspos : [email protected] ABSTRAK Mo sask Baysa obyk masarka paa pmlha pror a gs krga r shgga mghaslka smas rval krbl yag haya rgag paa aa a poplas aggapa. Dalam makalah aka jlaska pa rval krbl baysa obyk ar paramr bla sampl aggap brasal ar poplas yag brsrbs Posso aa yag brsrbs ksposal. Kywors: pror Jry loss co srbs posror rsc scrpacy loss co crbl rval Baysa obyk. PENDAHULUAN Irval krbl crbl rval lah jlaska alam makalah Sawa 9 paa kass srbs Broll. Dalam makalah aka jlaska k kass srbs Posso a srbs ksposal. DASAR TEORI Dalam paaga Baysa srbs posror mrpaka gabga ar ormas yag saka olh aa a ormas pror rlva yag rsa. Aka ap apabla ak rsa ormas pror maka plh gs ormav pror arya gs pror yag brpgarh mmm paa gs posror. Rrc pror apa gaka sbaga pror yag brpgarh mmal paa srbs posror. Dalam kass ms sa rrc pror mrpaka pror Jry. Dga mggaka pror maka pylsaa masalah smas haya rgag paa mol aggapa a aa pgamaa shgga smas k yag mggaka mo amaka sbaga smas k Baysa obyk. Msalka sampl =... rr ar pgamaa ar M { p X } a msalka { } aalah gs krga skrpas rsk rsc scrpacy loss yag ra jka gaka sbaga proy k. Dalam hal paramr mrpaka paramr sac. Esmas k rsk k paramr aalah * arg m ya aalah la paramr yag mmmalka harapa gs krga skrpas rsk ar rrc posror ya ga { } p a aalah rrc pror brsama ar ga mrpaka kaas yag mja prhaa Braro a Jarz 3. 73

2 74 Irval krbl rsk rsc crbl rgo ska sbaga rval krbl yag mmpya lows posror loss yag brkaa ga pggaa gs krga posror rkcl skrpas rsk a rrc pror yag brssaa. Irval krbl rsk q% q-crbl rgo rsc aalah hmpa baga R* q = R* q ar rag paramr shgga mmh q R q * k sap R* q a k sap j R* q rsk saskya mmpya sa j ga aalah harapa gs krga rrc posror sbaga proy k la ar paramr yag brka paa prsamaa Braro 5. Prsamaa mmpya bk yag prhgaya scara aalk aklah mah am ga mggaka gras mrk hal ga mah apa lakka. Poplas Posso Msalka mlk sampl... ar poplas brsrbs Posso ga gs probablas probably co k =... a >. Dskrpas rsk ar srbs ksposal aalah ] m[ ga l l l l l = l. Kara gs kpaaa probablas aalah maka l l l shgga

3 75 a. Akbaya ormas Fshr yag prolh aalah ] [ ] [ ] [ X E X E E I a sampg rrc pror ar paramr aalah = -/. Fgs lklhoo ar sampl... aalah L. Hal brar bahwa L /... shgga rrc posror yag rka aalah /... ga. Akbaya prolh sask rsk /.... Poplas Eksposal Msalka mlk sampl... ar poplas brsrbs ksposal ga gs kpaaa probablas probably sy co k > a >. Dalam hal skrpas rsk ar srbs ksposal aalah ] m[ ga l = l. Dapa bkka bahwa rrc pror ar paramr yag mja prhaa aalah = - a rrc posror yag rka aalah.... Akbaya prolh sask rsk... ga Braro 9. HASIL DAN DISKUSI Kass Dsrbs Posso Apabla brka kra sampl a sask ckp ga sampl aggap brasal ar poplas Posso maka apa ka rval krbl k paramr ya rval hmpa baga ar rag paramr yag mmh. Paa Gambar brka gambar yag mrpaka hasl prhga rsk sask jka brka bbrapa la a yag

4 mghaslka MLE yag sama k paramr ya 4 bsra ga rval krbl 95 % k paramr. Hal brar lbar rval krbl 95 % k masg-masg kass brr-r aalah a. Dmka jga paa Gambar brka gambar yag mrpaka hasl prhga rsk sask yag mghaslka MLE k paramr ya 5. Lbar rval krbl 95 % k masg-masg kass brrr aalah a 48. Akbaya spr yag harapka mak bsar kra sampl aka mak smp rval krbl yag prolh. a = =4 rval krbl : 9 84 b =5 = rval krbl : rsc sascs rsc sascs ha ha c = =4 rval krbl : =5 = rval krbl : rsc sascs 3 rsc sascs ha ha Gambar. Sask rsk k ap-ap kmgka a rval krbl yag prolh jka brka a k masg-masg kmgka. Dalam hal smaya mmpya MLE = 4. a = = rval krbl : b =5 = rval krbl : 6 43 rsc sascs 5 5 rsc sascs ha 3 4 ha c = = rval krbl : 78 8 =5 = rval krbl : rsc sascs 5 5 rsc sascs ha ha Gambar. Sask rsk k ap-ap kmgka a rval krbl yag prolh jka brka a k masg-masg kmgka. Dalam hal smaya mmpya MLE =. 76

5 Kass Dsrbs Eksposal Uk kra sampl a sask ckp yag brka ga sampl aggap brasal ar poplas ksposal maka apa ka rval krbl k paramr. Paa Gambar 3 myaaka hasl prhga rsk sask jka brka bbrapa la a yag mghaslka MLE yag sama k paramr ya. Hal brar lbar rval krbl 95 % k masg-masg kass brr-r aalah a 6 Dmka jga paa Gambar 4 brka gambar yag mrpaka hasl prhga rsk sask yag mghaslka MLE k paramr ya 5. Lbar rval krbl 95 % k masg-masg kass brr-r aalah 64 3 a 55. Dalam kass jga brlak sa bahwa mak bsar kra sampl aka mak smp rval krbl yag prolh. a = =5 shgga rval krbl : 3.58 b =4 = shgga rval krbl : IrskSask 3 4 IrskSask Tha Tha c =8 =4 shgga rval krbl : =6 =8 shgga rval krbl : 7.3 IrskSask 3 4 IrskSask Tha Tha Gambar 3. Sask rsk k ap-ap kmgka a rval krbl yag prolh jka brka a k masg-masg kmgka. Dalam hal smaya mmpya MLE =. a = = shgga rval krbl : 5 89 b =4 =8 shgga rval krbl : Irsk Sask Irsk Sask Tha Tha c =8 =6 shgga rval krbl : =6 =3 shgga rval krbl : Irsk Sask Irsk Sask Tha Tha 77

6 Gambar 4. Sask rsk k ap-ap kmgka a rval krbl yag prolh jka brka a k masg-masg kmgka. Dalam hal smaya mmpya MLE = 5. KESIMPULAN Irval krbl ga mo Baysa obyk apa ka k paramr poplas bla sampl aggap brasal ar poplas yag brsrbs Posso aa yag brsrbs ksposal. Pla apa jga kmbagka k kass srbs-srbs poplas yag la map sa asmpokya. DAFTAR PUSTAKA [] Braro J. M. 5 Irsc Crbl Rgos : A objcv Baysa Approach o Irval Esmao Ts 4 : [] Braro J. M. a M. A. Jarz 3 Irsc Esmao Baysa Sascs 7 Oor : Uvrsy Prss. [3] Sawa A. 9 Crbl Irval Baysa Obyk Prosg Smar Nasoal Mamaka Uvrsas Kaolk Parahyaga Bag. 78