▼♦❞❡❧♦s ❞❡ r❡❣r❡ssã♦ ❡stát✐❝♦s
❡ ❞✐♥â♠✐❝♦s ♣❛r❛ t❛①❛s ♦✉ ♣r♦♣♦rçõ❡s❀
✉♠❛ ❛❜♦r❞❛❣❡♠ ❇❛②❡s✐❛♥❛
▲❡❛♥❞r♦ ❚❛✈❛r❡s ❈♦rr❡✐❛
❚❡s❡ ❛♣r❡s❡♥t❛❞❛
❛♦
■♥st✐t✉t♦ ❞❡ ▼❛t❡♠át✐❝❛ ❡ ❊st❛tíst✐❝❛
❞❛
❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦
♣❛r❛
♦❜t❡♥çã♦ ❞♦ tít✉❧♦
❞❡
❉♦✉t♦r ❡♠ ❈✐ê♥❝✐❛s
Pr♦❣r❛♠❛✿ ❊st❛tíst✐❝❛
❖r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❉r✳ ❍❡❧❡♥♦ ❇♦❧❢❛r✐♥❡
❈♦♦r✐❡♥t❛❞♦r✿ Pr♦❢
❛✳ ❉r
❛✳ ❈✐❜❡❧❡ ◗✉❡✐r♦③ ❞❛✲❙✐❧✈❛
❉✉r❛♥t❡ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡st❡ tr❛❜❛❧❤♦ ♦ ❛✉t♦r r❡❝❡❜❡✉ ❛✉①í❧✐♦ ✜♥❛♥❝❡✐r♦ ❞❛ ❈❆P❊❙✴❈◆Pq
▼♦❞❡❧♦s ❞❡ r❡❣r❡ssã♦ ❡stát✐❝♦s
❡ ❞✐♥â♠✐❝♦s ♣❛r❛ t❛①❛s ♦✉ ♣r♦♣♦rçõ❡s❀
✉♠❛ ❛❜♦r❞❛❣❡♠ ❇❛②❡s✐❛♥❛
▼♦❞❡❧♦s ❞❡ r❡❣r❡ssã♦ ❡stát✐❝♦s
❡ ❞✐♥â♠✐❝♦s ♣❛r❛ t❛①❛s ♦✉ ♣r♦♣♦rçõ❡s❀
✉♠❛ ❛❜♦r❞❛❣❡♠ ❇❛②❡s✐❛♥❛
❊st❛ ✈❡rsã♦ ❞❛ t❡s❡ ❝♦♥té♠ ❛s ❝♦rr❡çõ❡s ❡ ❛❧t❡r❛çõ❡s s✉❣❡r✐❞❛s ♣❡❧❛ ❈♦♠✐ssã♦ ❏✉❧❣❛❞♦r❛ ❞✉r❛♥t❡ ❛ ❞❡❢❡s❛ ❞❛ ✈❡rsã♦ ♦r✐❣✐♥❛❧ ❞♦ tr❛❜❛❧❤♦✱ r❡❛❧✐③❛❞❛ ❡♠ ✵✶✴✵✻✴✷✵✶✺✳ ❯♠❛ ❝ó♣✐❛ ❞❛ ✈❡rsã♦ ♦r✐❣✐♥❛❧ ❡stá ❞✐s♣♦♥í✈❡❧ ♥♦ ■♥st✐t✉t♦ ❞❡ ▼❛t❡♠át✐❝❛ ❡ ❊st❛tíst✐❝❛ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦✳
❈♦♠✐ssã♦ ❏✉❧❣❛❞♦r❛✿
• Pr♦❢❛✳ ❉r❛✳ ❈✐❜❡❧❡ ◗✉❡✐r♦③ ❞❛✲❙✐❧✈❛ ✭❝♦♦r✐❡♥t❛❞♦r❛✮ ✲ ❯♥❇ • Pr♦❢✳ ❉r✳ ❍❡❞✐❜❡rt ▲♦♣❡s ✲ ■◆❙P❊❘
• Pr♦❢✳ ❉r✳ ❍❡❧✐♦ ❞♦s ❙❛♥t♦s ▼✐❣♦♥ ✲ ❯❋❘❏ • Pr♦❢✳ ❉r✳ ❏♦s❡♠❛r ❘♦❞r✐❣✉❡s ✲ ■❈▼❈✲❯❙P
❆❣r❛❞❡❝✐♠❡♥t♦s
❆❣r❛❞❡ç♦ ♣r✐♠❡✐r❛♠❡♥t❡ ❛♦s ♠❡✉s ♦r✐❡♥t❛❞♦r❡s ❍❡❧❡♥♦ ❇♦❧❢❛r✐♥❡ ❡ ❈✐❜❡❧❡ ◗✉❡✐r♦③ ❞❛✲❙✐❧✈❛ ♣❡❧❛ ♣❛❝✐ê♥❝✐❛ ❡ t❡♠♣♦ ❞❡❞✐❝❛❞♦ ❛♦ ♠❡✉ tr❛❜❛❧❤♦✳ ❆♦ ♣r♦❢❡ss♦r ❍❡❞✐❜❡rt ▲♦♣❡s q✉❡ ❝♦♥tr✐❜✉✐✉ ❡♠ ❣r❛♥❞❡ ♣❛r❝❡❧❛ ♥♦ ♠❡✉ tr❛❜❛❧❤♦ ❡ s❡♠♣r❡ s❡ ❝♦❧♦❝♦✉ ❝♦♠ ❞✐s♣♦♥✐❜✐❧✐❞❛❞❡ ♣❛r❛ ❡✈❡♥t✉❛✐s ❞✐s❝✉ssõ❡s ❡ ❡s❝❧❛r❡❝✐♠❡♥t♦ ❞❡ ❞ú✈✐❞❛s✳
❆❣r❛❞❡ç♦✱ t❛♠❜é♠✱ ❛♦s ❞❡♠❛✐s ♣r♦❢❡ss♦r❡s ❞♦s ✐♥st✐t✉t♦s ■▼❊✲❯❙P ❡ ❊st✲❯♥❇ ♣❡❧♦ ❝♦♥❤❡❝✐✲ ♠❡♥t♦ ❝♦♠♣❛rt✐❧❤❛❞♦ ❡ ♣♦r s❡♠♣r❡ s❡ ♠♦str❛r❡♠ s♦❧í❝✐t♦s ♣❛r❛ q✉❛❧q✉❡r ❞ú✈✐❞❛✳ ❆♦s ❝♦❧❡❣❛s ❞❡ ❝✉rs♦ q✉❡ t❛♠❜é♠ t✐✈❡r❛♠ s✉❛ ♣❛r❝❡❧❛ ❞❡ ❝♦♥tr✐❜✉✐çã♦✳
P♦r ✜♠✱ à ❈❛♣❡s ❡ ❈◆P◗ ♣❡❧♦ ❛♣♦✐♦ ✜♥❛♥❝❡✐r♦✳
❘❡s✉♠♦
❈❖❘❘❊■❆✱ ▲✳ ❚✳ ▼♦❞❡❧♦s ❞❡ r❡❣r❡ssã♦ ❡stát✐❝♦s ❡ ❞✐♥â♠✐❝♦s
♣❛r❛ t❛①❛s ♦✉ ♣r♦♣♦rçõ❡s❀ ✉♠❛ ❛❜♦r❞❛❣❡♠ ❇❛②❡s✐❛♥❛✳ ✷✵✶✺✳ ✶✽✻ ❢✳ ❚❡s❡ ✭❉♦✉t♦r❛❞♦✮ ✲ ■♥s✲ t✐t✉t♦ ❞❡ ▼❛t❡♠át✐❝❛ ❡ ❊st❛tíst✐❝❛✱ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦✱ ❙ã♦ P❛✉❧♦✱ ✷✵✶✺✳
❊st❡ tr❛❜❛❧❤♦ ❛♣r❡s❡♥t❛ ✉♠ ❡st✉❞♦ ❞❡ ❞❛❞♦s ❝♦♠ r❡s♣♦st❛ ❡♠ ✐♥t❡r✈❛❧♦s ❧✐♠✐t❛❞♦s✱ ♠❛✐s ❡s✲ ♣❡❝✐✜❝❛♠❡♥t❡ ♥♦ ✐♥t❡r✈❛❧♦ [0,1]✱ ❝♦♠♦ ♥♦ ❝❛s♦ ❞❡ t❛①❛s ❡ ♣r♦♣♦rçõ❡s✳ ❊♠ ❞✐✈❡rs♦s ❝❛s♦s ♣rát✐❝♦s
❡st❛ ❡str✉t✉r❛ ❞❡ ❞❛❞♦s ❛♣r❡s❡♥t❛ ✉♠❛ q✉❛♥t✐❞❛❞❡ ♥ã♦ ♥❡❣❧✐❣❡♥❝✐á✈❡❧ ❞❡ ✈❛❧♦r❡s ❡①tr❡♠♦s ✭0 ❡ 1✮
❡ q✉❡ ♠♦❞❡❧♦s ✉s✉❛✐s ♥ã♦ sã♦ ❛❞❡q✉❛❞♦s ♣❛r❛ s✉❛ ❛♥á❧✐s❡✳ P❛r❛ ❡st❛ s✐t✉❛çã♦ ♣r♦♣♦♠♦s✱ ♣♦r ♠❡✐♦ ❞❡ ✉♠ ❡♥❢♦q✉❡ ❇❛②❡s✐❛♥♦✱ ♠♦❞❡❧♦s ❞❡ r❡❣r❡ssã♦ ❜❡t❛ ✐♥✢❛❝✐♦♥❛❞♦ ❞❡ ③❡r♦s ❡ ✉♥s ✭❇■❩❯✮ ❡ ♠♦❞❡✲ ❧♦s ❞❡ r❡❣r❡ssã♦ ❚♦❜✐t ❞✉♣❧❛♠❡♥t❡ ❝❡♥s✉r❛❞♦ ❛❞❛♣t❛❞♦s ♥❡ss❡ ✐♥t❡r✈❛❧♦✳ ❚é❝♥✐❝❛s ❞❡ ❞✐❛❣♥óst✐❝♦ ❡ q✉❛❧✐❞❛❞❡ ❞♦ ❛❥✉st❡ t❛♠❜é♠ sã♦ ❞✐s❝✉t✐❞❛s✳ ❆♣r❡s❡♥t❛♠♦s ❛ ❛♥á❧✐s❡ ❞❡st❛ ❡str✉t✉r❛ ❞❡ ❞❛❞♦s ♥♦ ❝♦♥t❡①t♦ ❞❡ sér✐❡ ❞❡ t❡♠♣♦ ♣♦r ♠❡✐♦ ❞❛ ❛❜♦r❞❛❣❡♠ ❇❛②❡s✐❛♥❛ ❞❡ ♠♦❞❡❧♦s ❞✐♥â♠✐❝♦s✳ ❊st✉❞♦s ❞❡ ❝♦♠♣♦rt❛♠❡♥t♦ ❡ ♣r❡✈✐sã♦ ❞❡ sér✐❡s ❞❡ t❡♠♣♦ ❢♦r❛♠ ❡①♣❧♦r❛❞♦s ✉t✐❧✐③❛♥❞♦ té❝♥✐❝❛s ❞❡ ▼♦♥t❡ ❈❛r❧♦ s❡q✉❡♥❝✐❛❧✱ ❝♦♥❤❡❝✐❞❛s ❝♦♠♦ ✜❧tr♦ ❞❡ ♣❛rtí❝✉❧❛s✳ P❛rt✐❝✉❧❛r✐❞❛❞❡s ❡ ❝♦♠♣❡t✐t✐✈✐❞❛❞❡ ❡♥tr❡ ❛s ❞✉❛s ❝❧❛ss❡s ❞❡ ♠♦❞❡❧♦s t❛♠❜é♠ ❢♦r❛♠ ❞✐s❝✉t✐❞❛s✳
P❛❧❛✈r❛s✲❝❤❛✈❡✿ ♣r♦♣♦rçõ❡s✱ r❡❣r❡ssã♦✱ ♠♦❞❡❧♦s ❞✐♥â♠✐❝♦s✱ ❉✐str✐❜✉✐çã♦ ❜❡t❛✱ ▼♦❞❡❧♦ ❜❡t❛ ✐♥✢❛✲ ❝✐♦♥❛❞♦✱ ♠♦❞❡❧♦ ❚♦❜✐t✱ ❛♥á❧✐s❡ ❇❛②❡s✐❛♥❛✱ ✜❧tr♦ ❞❡ ♣❛rtí❝✉❧❛s✳
❆❜str❛❝t
❈❖❘❘❊■❆✱ ▲✳ ❚✳ ❘❡❣r❡ss✐♦♥ ♦❢ st❛t✐❝ ❛♥❞ ❞②♥❛♠✐❝ ♠♦❞❡❧s ❢♦r ♣r♦♣♦rt✐♦♥s ♦r r❛t❡s❀ ❛ ❇❛②❡s✐❛♥ ❛♣♣r♦❛❝❤✳ ✷✵✶✺✳ ✶✽✻ ❢✳ ❚❡s❡ ✭❉♦✉t♦r❛❞♦✮ ✲ ■♥st✐t✉t♦ ❞❡ ▼❛t❡♠át✐❝❛ ❡ ❊st❛tíst✐❝❛✱ ❯♥✐✲ ✈❡rs✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦✱ ❙ã♦ P❛✉❧♦✱ ✷✵✶✺✳
❚❤✐s ♣❛♣❡r ♣r❡s❡♥ts ❛ st✉❞② ❢♦❝✉s❡❞ ♦♥ ♦❜s❡r✈❛t✐♦♥s ✐♥ ❛ ❧✐♠✐t❡❞ ✐♥t❡r✈❛❧ ✱ ♠♦r❡ s♣❡❝✐✜❝❛❧❧② ✐♥
[0,1] ✱ s✉❝❤ ❛s r❛t❡ ❛♥❞ ♣r♦♣♦rt✐♦♥ ❞❛t❛✳ ■♥ ♠❛♥② ♣r❛❝t✐❝❛❧ ❝❛s❡s t❤✐s ❞❛t❛ str✉❝t✉r❡ ❤❛s ❛ ❝♦♥✲
s✐❞❡r❛❜❧❡ ❛♠♦✉♥t ♦❢ ❡①tr❡♠❡ ✈❛❧✉❡s ✭0 ❛♥❞ 1✮ ❛♥❞ ✉s✉❛❧ ❝❧❛ss✐❝❛❧ ♠♦❞❡❧s ❛r❡ ♥♦t s✉✐t❛❜❧❡ ❢♦r t❤✐s
t②♣❡ ♦❢ ❞❛t❛ s❡t✳ ❲❡ ♣r♦♣♦s❡ t✇♦ ❝❧❛ss ♦❢ r❡❣r❡ss✐♦♥ ♠♦❞❡❧s t♦ ❞❡❛❧ ✇✐t❤ t❤✐s ❝♦♥t❡①t✿ ❜❡t❛ ✐♥✢❛t❡❞ ♦❢ ③❡r♦s ❛♥❞ ♦♥❡s (BIZU) ♠♦❞❡❧s ❛♥❞ ❚♦❜✐t ❞♦✉❜❧② ❝❡♥s♦r❡❞ ♠♦❞❡❧s ❛❞❛♣t❡❞ ✐♥ t❤✐s ✐♥t❡r✈❛❧✳ ❋✐t
q✉❛❧✐t② ❛♥❞ ❞✐❛❣♥♦st✐❝ t❡❝❤♥✐q✉❡s ❛r❡ ❛❧s♦ ❞✐s❝✉ss❡❞✳ ❚✐♠❡ s❡r✐❡s ♦❢ ♣r♦♣♦rt✐♦♥s ❛r❡ ❛❧s♦ ❞❡✈❡❧♦♣❡❞ t❤r♦✉❣❤ ❇❛②❡s✐❛♥ ❞②♥❛♠✐❝ ♠♦❞❡❧s✳ ❋♦r❡❝❛st✐♥❣ ❛♥❞ ❜❡❤❛✈✐♦r❛❧ ❛♥❛❧②s✐s ✇❡r❡ ❡①♣❧♦r❡❞ ✉s✐♥❣ s❡q✉❡♥✲ t✐❛❧ ▼♦♥t❡ ❈❛r❧♦ t❡❝❤♥✐q✉❡s✱ ❦♥♦✇♥ ❛s ♣❛rt✐❝❧❡ ✜❧t❡rs✳ P❛rt✐❝✉❧❛r✐t✐❡s ❛♥❞ ❝♦♠♣❡t✐t✐✈❡♥❡ss ❜❡t✇❡❡♥ t❤❡ t✇♦ ❝❧❛ss❡s ♦❢ ♠♦❞❡❧s ✇❡r❡ ❛❧s♦ ❞✐s❝✉ss❡❞ ❛s ✇❡❧❧✳
❑❡②✇♦r❞s✿ ♣r♦♣♦rt✐♦♥s✱ r❡❣r❡ss✐♦♥✱ ❞②♥❛♠✐❝ ♠♦❞❡❧s✱ ❜❡t❛ ❞✐str✐❜✉t✐♦♥✱ ❜❡t❛ ✐♥✢❛t❡❞ ♠♦❞❡❧✱ ❚♦❜✐t ♠♦❞❡❧✱ ❇❛②❡s✐❛♥ ❛♥❛❧②s✐s✱ ♣❛rt✐❝❧❡ ✜❧t❡rs✳
❙✉♠ár✐♦
▲✐st❛ ❞❡ ❋✐❣✉r❛s ①✐
▲✐st❛ ❞❡ ❚❛❜❡❧❛s ①✈
✶ ■♥tr♦❞✉çã♦ ✶
✶✳✶ ❖❜❥❡t✐✈♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸
✶✳✷ ❖r❣❛♥✐③❛çã♦ ❞♦ ❚r❛❜❛❧❤♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸
✷ ▼✐st✉r❛ ❞❡ ❞✐str✐❜✉✐çõ❡s ✺
✷✳✶ ❈❛s♦ ❣❡r❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺
✷✳✷ ❉✐str✐❜✉✐çã♦ ❇❡t❛ ✐♥✢❛❝✐♦♥❛❞❛ ❞❡ ③❡r♦s ❡✴♦✉ ✉♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻
✷✳✸ ❉✐str✐❜✉✐çã♦ ❚♦❜✐t ♥♦r♠❛❧ ❞✉♣❧❛♠❡♥t❡ ❝❡♥s✉r❛❞❛ ❡ ✐♥✢❛❝✐♦♥❛❞❛ ❞❡ ③❡r♦s ❡✴♦✉ ✉♥s ✳ ✳ ✶✵
✷✳✹ ❉✐str✐❜✉✐çã♦ ❚♦❜✐t ♥♦r♠❛❧✲♣♦tê♥❝✐❛ ❞✉♣❧❛♠❡♥t❡ ❝❡♥s✉r❛❞❛ ❡ ✐♥✢❛❝✐♦♥❛❞❛ ❞❡ ③❡r♦s ❡✴♦✉ ✉♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻
✸ ▼♦❞❡❧♦s ❞❡ ❘❡❣r❡ssã♦ ✶✾
✸✳✶ ▼♦❞❡❧♦s ❞❡ r❡❣r❡ssã♦ ❜❡t❛ ✐♥✢❛❝✐♦♥❛❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾
✸✳✷ ▼♦❞❡❧♦s ❞❡ r❡❣r❡ssã♦ ❚♦❜✐t ♥♦r♠❛❧ ❞✉♣❧❛♠❡♥t❡ ❝❡♥s✉r❛❞♦ ❡ ✐♥✢❛❝✐♦♥❛❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷
✸✳✸ ▼♦❞❡❧♦s ❞❡ r❡❣r❡ssã♦ ❚♦❜✐t ♥♦r♠❛❧✲♣♦tê♥❝✐❛ ❞✉♣❧❛♠❡♥t❡ ❝❡♥s✉r❛❞♦ ❡ ✐♥✢❛❝✐♦♥❛❞♦ ✳ ✳ ✷✹
✸✳✹ ■♥❢❡rê♥❝✐❛ ❇❛②❡s✐❛♥❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻
✸✳✹✳✶ Pr✐♦r✐s ♣❛r❛ ♦s ♣❛râ♠❡tr♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻
✸✳✹✳✷ ❖❜t❡♥çã♦ ❞❛s ❞✐str✐❜✉✐çõ❡s ❛ ♣♦st❡r✐♦r✐ ♣❛r❛ ♦s ♣❛râ♠❡tr♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽
✸✳✺ ▼❡❞✐❞❛s ❞❡ ❞✐❛❣♥óst✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾
✸✳✺✳✶ ❈r✐tér✐♦s ❞❡ ❡s❝♦❧❤❛ ❞♦ ♠♦❞❡❧♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾
✸✳✺✳✷ ❘❡sí❞✉♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵
✸✳✺✳✸ P♦♥t♦s ✐♥✢✉❡♥t❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶
✸✳✻ ❊st✉❞♦ ❞❡ s✐♠✉❧❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸
✸✳✻✳✶ ❊st✉❞♦ ✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸
✸✳✻✳✷ ❊st✉❞♦ ✷✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽
✸✳✻✳✸ ❈♦♥❝❧✉sã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸
✸✳✼ ❆♣❧✐❝❛çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸
✸✳✼✳✶ Pr♦♣♦rçõ❡s ❞❡ ❡♠♣r❡❣❛❞♦s ❞♦ s❡①♦ ❢❡♠✐♥✐♥♦ ♥♦ s❡t♦r ❞❡ ✐♥❞ústr✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸
✸✳✼✳✷ Pr♦♣♦rçõ❡s ❞❡ ❝❛♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵
✈✐✐✐ ❙❯▼➪❘■❖
✹ ▼♦❞❡❧♦s ❉✐♥â♠✐❝♦s ✺✺
✹✳✶ ❆❜♦r❞❛❣❡♠ ❇❛②❡s✐❛♥❛ ❡♠ ▼♦❞❡❧♦s ❉✐♥â♠✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺
✹✳✷ ▼♦❞❡❧♦ ❞✐♥â♠✐❝♦ ❜❡t❛ ✐♥✢❛❝✐♦♥❛❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻
✹✳✷✳✶ ❆♥á❧✐s❡ ❇❛②❡s✐❛♥❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼
✹✳✷✳✷ Pr✐♠❡✐r♦ r❡s✉❧t❛❞♦ ❝♦♠ s✐♠✉❧❛çõ❡s ✈✐❛ ▼❈▼❈ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾
✹✳✸ ▼♦❞❡❧♦ ❞✐♥â♠✐❝♦ ❚♦❜✐t✲♥♦r♠❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸
✹✳✸✳✶ ▼♦❞❡❧♦ ❞✐♥â♠✐❝♦ ❚♦❜✐t ♥♦r♠❛❧ ❞✉♣❧❛♠❡♥t❡ ❝❡♥s✉r❛❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻
✺ ❋✐❧tr♦ ❞❡ P❛rtí❝✉❧❛s ✻✾
✺✳✶ ❈❛s♦ ❣❡r❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾
✺✳✶✳✶ ❋✐❧tr♦ ♥♦ ❝♦♥t❡①t♦ ❞❛ ♠♦❞❡❧❛❣❡♠ ❇❛②❡s✐❛♥❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶
✺✳✷ ❚✐♣♦s ❞❡ ✜❧tr♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷
✺✳✷✳✶ ❋✐❧tr♦ ❞❡ ♣❛rt✐❝✉❧❛s ❜♦♦tstr❛♣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷
✺✳✷✳✷ ❋✐❧tr♦ ❞❡ ♣❛rtí❝✉❧❛s ❛✉①✐❧✐❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸
✺✳✸ ❊st✐♠❛çã♦ ❞♦s ♣❛râ♠❡tr♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻
✺✳✸✳✶ ❋✐❧tr♦ ▲✐✉ ❡ ❲❡st ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻
✺✳✸✳✷ ❋✐❧tr♦ ❙t♦r✈✐❦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✼
✺✳✸✳✸ ❋✐❧tr♦ ♣❛r❛♠❡t❡r ❧❡❛r♥✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✽
✺✳✹ ❙✉❛✈✐③❛çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✽
✻ ❙✐♠✉❧❛çã♦ ❡ ❛♣❧✐❝❛çã♦ ✽✶
✻✳✶ ❊st✉❞♦ ❞❡ s✐♠✉❧❛çã♦ ♣❛r❛ ♦ ♠♦❞❡❧♦ ❞✐♥â♠✐❝♦ ❇■❩❯ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶
✻✳✶✳✶ ▼♦❞❡❧♦ ❞❡ ♣❛ss❡✐♦ ❛❧❡❛tór✐♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷
✻✳✶✳✷ ▼♦❞❡❧♦ ❝♦♠ ♥í✈❡❧✱ t❡♥❞ê♥❝✐❛ ❡ s❛③♦♥❛❧✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✻
✻✳✶✳✸ ▼♦❞❡❧♦ ❝♦♠ ❝♦✈❛r✐á✈❡✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✹
✻✳✷ ❊st✉❞♦ ❞❡ s✐♠✉❧❛çã♦ ♣❛r❛ ♦ ♠♦❞❡❧♦ ❞✐♥â♠✐❝♦ ❚♦❜✐t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✷
✻✳✷✳✶ ▼♦❞❡❧♦ ❝♦♠ t❡♥❞ê♥❝✐❛ ❡ s❛③♦♥❛❧✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✷
✻✳✷✳✷ ▼♦❞❡❧♦ ❝♦♠ ❝♦✈❛r✐á✈❡✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✾
✻✳✸ ❆♣❧✐❝❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✻
✼ ❈♦♥❝❧✉sõ❡s ✶✹✸
✼✳✶ ❈♦♥s✐❞❡r❛çõ❡s ❋✐♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✸
✼✳✷ ❙✉❣❡stõ❡s ♣❛r❛ P❡sq✉✐s❛s ❋✉t✉r❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✸
❆ ▼étr✐❝❛s ✶✹✺
❇ ■♥t❡r✈❡♥çã♦ ❡①t❡r♥❛ ✶✹✼
❇✳✶ ■❣♥♦r❛r ♦❜s❡r✈❛çã♦ Yt ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✼
❇✳✷ ❘✉í❞♦ ❞❡ ❡✈♦❧✉çã♦ ❛❞✐❝✐♦♥❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✼
❇✳✸ ■♥t❡r✈❡♥çã♦ s✉❜❥❡t✐✈❛ ❛r❜✐trár✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✼
❇✳✹ ■♥❝❧✉sã♦ ❞❡ ❡❢❡✐t♦ ❞❡ ✐♥t❡r✈❡♥çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✽
❙❯▼➪❘■❖ ✐①
❉ Pr✐♥❝✐♣❛✐s ♣r♦❣r❛♠❛çõ❡s ❡♠ ❘ ✶✺✶
❉✳✶ ❙✐♠✉❧❛çã♦ ❞♦s ❞❛❞♦s ❇■❩❯ ❞✐♥â♠✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✶
❉✳✷ ❙✐♠✉❧❛çã♦ ❞♦s ❞❛❞♦s ❚♦❜✐t ❞✐♥â♠✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✸
❉✳✸ ❋✐❧tr♦ P▲ ♣❛r❛ ♦ ♠♦❞❡❧♦ ❞✐♥â♠✐❝♦ ❇■❩❯ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✺
❉✳✹ ❋✐❧tr♦ P▲ ♣❛r❛ ♦ ♠♦❞❡❧♦ ❞✐♥â♠✐❝♦ ❚♦❜✐t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✽
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✷✳✶ ●rá✜❝♦ ❞❛s ❞❡♥s✐❞❛❞❡s ❜❡t❛ ♣❛r❛ ❞✐❢❡r❡♥t❡s ✈❛❧♦r❡s ❞❡ (µ, φ)✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽
✷✳✷ ●rá✜❝♦ ❞❛s ❢✉♥çõ❡s ❞❡ ❞✐str✐❜✉✐çã♦ ❛❝✉♠✉❧❛❞❛ ❞❛s ✈❛r✐á✈❡✐sBI0 ✭❡sq✉❡r❞❛✮ ❡BIZU
✭❞✐r❡✐t❛✮✱ ❝♦♥s✐❞❡r❛♥❞♦ ♦s ♣❛râ♠❡tr♦s (α = 0.24, µ = 0.6, φ = 5) ❡ (α = 0.39, γ = 0.38, µ= 0.6, φ= 5)✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾
✷✳✸ ●rá✜❝♦ ❞❛s ❢✉♥çõ❡s ❞❡ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ❞❛s ✈❛r✐á✈❡✐s BI0 ✭❡sq✉❡r❞❛✮ ❡ BIZU ✭❞✐✲
r❡✐t❛✮✱ ❝♦♥s✐❞❡r❛♥❞♦ ♦s ♣❛râ♠❡tr♦s (α = 0.24, µ = 0.6, φ = 5) ❡ (α = 0.39, γ = 0.38, µ= 0.6, φ= 5)✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾
✷✳✹ ●rá✜❝♦ ❞❛s ❞❡♥s✐❞❛❞❡s ❚♦❜✐t ♥♦r♠❛❧ ✐♥✢❛❝✐♦♥❛❞❛ ♣❛r❛ ❞✐❢❡r❡♥t❡s ✈❛❧♦r❡s ❞❡ (µ, σ)✳ ✳ ✶✹
✷✳✺ ●rá✜❝♦ ❞❛s ❢✉♥çõ❡s ❞❡ ❞✐str✐❜✉✐çã♦ ❛❝✉♠✉❧❛❞❛ ❞❛s ✈❛r✐á✈❡✐s t♦❜✐t ♥♦r♠❛❧ ✐♥✢❛❝✐♦♥❛❞❛ ❞❡ ③❡r♦s ✭❡sq✉❡r❞❛✮ ❡ t♦❜✐t ♥♦r♠❛❧ ✐♥✢❛❝✐♦♥❛❞❛ ❞❡ ③❡r♦s ❡ ✉♥s ✭❞✐r❡✐t❛✮✱ ❝♦♥s✐❞❡r❛♥❞♦ ♦s ♣❛râ♠❡tr♦s(δ = 0.24, µ = 0.6, σ= 0.3)❡ (δ0 = 0.24, δ1 = 0.15, µ= 0.6, σ= 0.3)✱
r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹
✷✳✻ ●rá✜❝♦ ❞❛s ❢✉♥çõ❡s ❞❡ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ❞❛s ✈❛r✐á✈❡✐s ❚♦❜✐t ♥♦r♠❛❧ ✐♥✢❛❝✐♦♥❛❞❛ ❞❡ ③❡r♦s ✭❡sq✉❡r❞❛✮ ❡ t♦❜✐t ♥♦r♠❛❧ ✐♥✢❛❝✐♦♥❛❞❛ ❞❡ ③❡r♦s ❡ ✉♥s ✭❞✐r❡✐t❛✮✱ ❝♦♥s✐❞❡r❛♥❞♦ ♦s ♣❛râ♠❡tr♦s(δ = 0.24, µ = 0.6, σ= 0.3)❡ (δ0 = 0.24, δ1 = 0.15, µ= 0.6, σ= 0.3)✱
r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺
✷✳✼ ●rá✜❝♦ ❞❛s ❞❡♥s✐❞❛❞❡s ❚♦❜✐t ♥♦r♠❛❧✲♣♦tê♥❝✐❛ ✐♥✢❛❝✐♦♥❛❞❛ ♣❛r❛ ❞✐❢❡r❡♥t❡s ✈❛❧♦r❡s ❞❡
(α, µ, σ)✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼
✷✳✽ ●rá✜❝♦ ❞❛s ❢✉♥çõ❡s ❞❡ ❞✐str✐❜✉✐çã♦ ❛❝✉♠✉❧❛❞❛ ❞❛s ✈❛r✐á✈❡✐s ❚♦❜✐t ♥♦r♠❛❧✲♣♦tê♥❝✐❛ ✐♥✢❛❝✐♦♥❛❞❛ ❞❡ ③❡r♦s ✭❡sq✉❡r❞❛✮ ❡ ❚♦❜✐t ♥♦r♠❛❧✲♣♦tê♥❝✐❛ ✐♥✢❛❝✐♦♥❛❞❛ ❞❡ ③❡r♦s ❡ ✉♥s ✭❞✐r❡✐t❛✮✱ ❝♦♥s✐❞❡r❛♥❞♦ ♦s ♣❛râ♠❡tr♦s (δ = 0.24, α = 0.5, µ = 0.6, σ = 0.3) ❡ (δ0= 0.24, δ1 = 0.15, α= 0.5, µ= 0.6, σ= 0.3)✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼
✷✳✾ ●rá✜❝♦ ❞❛s ❢✉♥çõ❡s ❞❡ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ❞❛s ✈❛r✐á✈❡✐s ❚♦❜✐t ♥♦r♠❛❧✲♣♦tê♥❝✐❛ ✐♥✢❛✲ ❝✐♦♥❛❞❛ ❞❡ ③❡r♦s ✭❡sq✉❡r❞❛✮ ❡ ❚♦❜✐t ♥♦r♠❛❧✲♣♦tê♥❝✐❛ ✐♥✢❛❝✐♦♥❛❞❛ ❞❡ ③❡r♦s ❡ ✉♥s ✭❞✐r❡✐t❛✮✱ ❝♦♥s✐❞❡r❛♥❞♦ ♦s ♣❛râ♠❡tr♦s(δ = 0.24, µ= 0.6, σ= 0.3)❡ (δ0 = 0.24, δ1 = 0.15, α= 0.5, µ= 0.6, σ= 0.3)✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽
✸✳✶ ●rá✜❝♦ ❞♦s r❡sí❞✉♦s ❇❛②❡s✐❛♥♦s ♣❛❞r♦♥✐③❛❞♦s ♣❡❧❛s ♦❜s❡r✈❛çõ❡s ♣❛r❛ ♦s ♠♦❞❡❧♦s ❇■❩❯ ✭❡sq✉❡r❞❛✮ ❡ ❚♦❜✐t ✐♥✢❛❝✐♦♥❛❞♦ ✭❞✐r❡✐t❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻
✸✳✷ ●rá✜❝♦ ❞♦s r❡sí❞✉♦s ❇❛②❡s✐❛♥♦s ❝♦♥❞✐❝✐♦♥❛✐s ♣❛❞r♦♥✐③❛❞♦s ♣❡❧❛s ♦❜s❡r✈❛çõ❡s ♣❛r❛ ♦s ♠♦❞❡❧♦s ❇■❩❯ ✭❡sq✉❡r❞❛✮ ❡ ❚♦❜✐t ✐♥✢❛❝✐♦♥❛❞♦ ✭❞✐r❡✐t❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻
✸✳✸ ●rá✜❝♦ ❞❛ ❞✐✈❡r❣ê♥❝✐❛ ❞❡ ❑✲▲ ♣❛r❛ ♦ ♠♦❞❡❧♦ ❇■❩❯ ✭❡sq✉❡r❞❛✮ ❡ ❚♦❜✐t ✐♥✢❛❝✐♦♥❛❞♦ ✭❞✐r❡✐t❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼
①✐✐ ▲■❙❚❆ ❉❊ ❋■●❯❘❆❙
✸✳✹ ●rá✜❝♦ ❞♦s r❡sí❞✉♦s ❇❛②❡s✐❛♥♦s ♣❛❞r♦♥✐③❛❞♦s ♣❡❧❛s ♦❜s❡r✈❛çõ❡s ♣❛r❛ ♦s ♠♦❞❡❧♦s ❇■❩❯ ✭❡sq✉❡r❞❛✮ ❡ ❚♦❜✐t ✐♥✢❛❝✐♦♥❛❞♦ ✭❞✐r❡✐t❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶
✸✳✺ ●rá✜❝♦ ❞♦s r❡sí❞✉♦s ❇❛②❡s✐❛♥♦s ❝♦♥❞✐❝✐♦♥❛✐s ♣❛❞r♦♥✐③❛❞♦s ♣❡❧❛s ♦❜s❡r✈❛çõ❡s ♣❛r❛ ♦s ♠♦❞❡❧♦s ❇■❩❯ ✭❡sq✉❡r❞❛✮ ❡ ❚♦❜✐t ✐♥✢❛❝✐♦♥❛❞♦ ✭❞✐r❡✐t❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶
✸✳✻ ●rá✜❝♦ ❞❛ ❞✐✈❡r❣ê♥❝✐❛ ❞❡ ❑✲▲ ♣❛r❛ ♦ ♠♦❞❡❧♦ ❇■❩❯ ✭❡sq✉❡r❞❛✮ ❡ ❚♦❜✐t ✐♥✢❛❝✐♦♥❛❞♦ ✭❞✐r❡✐t❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷
✸✳✼ ●rá✜❝♦ ❞♦s r❡sí❞✉♦s ❇❛②❡s✐❛♥♦s ♣❛❞r♦♥✐③❛❞♦s ♣❡❧❛s ♦❜s❡r✈❛çõ❡s ♣❛r❛ ♦s ♠♦❞❡❧♦s ❇■❩❯ ✭❡sq✉❡r❞❛ s✉♣❡r✐♦r✮✱ ❚♦❜✐t ♥♦r♠❛❧ ✐♥✢❛❝✐♦♥❛❞♦ ✭❞✐r❡✐t❛ s✉♣❡r✐♦r✮ ❡ ❚♦❜✐t ♥♦r✲ ♠❛❧ ♣♦tê♥❝✐❛ ✐♥✢❛❝✐♦♥❛❞♦ ✭✐♥❢❡r✐♦r✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻
✸✳✽ ●rá✜❝♦ ❞♦s r❡sí❞✉♦s ❇❛②❡s✐❛♥♦s ❝♦♥❞✐❝✐♦♥❛✐s ♣❛❞r♦♥✐③❛❞♦s ♣❡❧❛s ♦❜s❡r✈❛çõ❡s ♣❛r❛ ♦s ♠♦❞❡❧♦s ❇■❩❯ ✭❡sq✉❡r❞❛ s✉♣❡r✐♦r✮✱ ❚♦❜✐t ♥♦r♠❛❧ ✐♥✢❛❝✐♦♥❛❞♦ ✭❞✐r❡✐t❛ s✉♣❡r✐♦r✮ ❡ ❚♦❜✐t ♥♦r♠❛❧ ♣♦tê♥❝✐❛ ✐♥✢❛❝✐♦♥❛❞♦ ✭✐♥❢❡r✐♦r✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼
✸✳✾ ●rá✜❝♦ ❞❛ ❞✐✈❡r❣ê♥❝✐❛ ❞❡ ❑✲▲ ♣❛r❛ ♦s ♠♦❞❡❧♦s ❇■❩❯ ✭❡sq✉❡r❞❛ s✉♣❡r✐♦r✮✱ ❚♦❜✐t ♥♦r♠❛❧ ✐♥✢❛❝✐♦♥❛❞♦ ✭❞✐r❡✐t❛ s✉♣❡r✐♦r✮ ❡ ❚♦❜✐t ♥♦r♠❛❧ ♣♦tê♥❝✐❛ ✐♥✢❛❝✐♦♥❛❞♦ ✭✐♥❢❡r✐♦r✮✳ ✹✽
✸✳✶✵ ●rá✜❝♦ ❞❛ ❞✐stâ♥❝✐❛✲χ2 ♣❛r❛ ♦s ♠♦❞❡❧♦s ❇■❩❯ ✭❡sq✉❡r❞❛ s✉♣❡r✐♦r✮✱ ❚♦❜✐t ♥♦r♠❛❧
✐♥✢❛❝✐♦♥❛❞♦ ✭❞✐r❡✐t❛ s✉♣❡r✐♦r✮ ❡ ❚♦❜✐t ♥♦r♠❛❧ ♣♦tê♥❝✐❛ ✐♥✢❛❝✐♦♥❛❞♦ ✭✐♥❢❡r✐♦r✮✳ ✳ ✳ ✳ ✳ ✹✾
✸✳✶✶ ●rá✜❝♦ ❞♦s r❡sí❞✉♦s ❇❛②❡s✐❛♥♦s ♣❛❞r♦♥✐③❛❞♦s ♣❡❧❛s ♦❜s❡r✈❛çõ❡s ♣❛r❛ ♦s ♠♦❞❡❧♦s ❇■❩ ✭❡sq✉❡r❞❛✮ ❡ ❚♦❜✐t ✐♥✢❛❝✐♦♥❛❞♦ ✭❞✐r❡✐t❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷
✸✳✶✷ ●rá✜❝♦ ❞♦s r❡sí❞✉♦s ❇❛②❡s✐❛♥♦s ♣❛❞r♦♥✐③❛❞♦s ♣❡❧❛s ♦❜s❡r✈❛çõ❡s ♣❛r❛ ♦ ♠♦❞❡❧♦ t♦❜✐t ♥♦r♠❛❧✲♣♦tê♥❝✐❛ ✐♥✢❛❝✐♦♥❛❞♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷
✸✳✶✸ ●rá✜❝♦ ❞❛ ❞✐stâ♥❝✐❛✲χ2 ♣❛r❛ ♦ ♠♦❞❡❧♦ ❇■❩ ✭❡sq✉❡r❞❛✮ ❡ t♦❜✐t ✐♥✢❛❝✐♦♥❛❞♦ ✭❞✐r❡✐t❛✮✳ ✳ ✺✸
✸✳✶✹ ●rá✜❝♦ ❞❛ ❞✐stâ♥❝✐❛✲χ2 ♣❛r❛ ♦ ♠♦❞❡❧♦ t♦❜✐t ♥♦r♠❛❧✲♣♦tê♥❝✐❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸
✹✳✶ ❊str✉t✉r❛ ❞♦ ♠♦❞❡❧♦ ❧✐♥❡❛r ❞✐♥â♠✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻
✹✳✷ ●rá✜❝♦ ❞❡ ❛❥✉st❡ ❞♦s ❡❢❡✐t♦s ❞❡ ♥í✈❡❧✱ t❡♥❞ê♥❝✐❛ ❡ s❛③♦♥❛❧✐❞❛❞❡ ♣❛r❛ ❛ ♠é❞✐❛ ❝♦♠ ❜❛♥❞❛s ❞❡ ❝♦♥✜❛♥ç❛ ❞❡95%✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵
✹✳✸ ●rá✜❝♦ ❞❡ ❛❥✉st❡ ❞♦s ❡❢❡✐t♦s ❞❡ ♥í✈❡❧ ❡ t❡♥❞ê♥❝✐❛ ♣❛r❛ ❛ ♣r❡❝✐sã♦ ❝♦♠ ❜❛♥❞❛s ❞❡ ❝♦♥✜❛♥ç❛ ❞❡95%✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶
✹✳✹ ●rá✜❝♦ ❞❡ ❛❥✉st❡ ❞♦s ♣r❡❞✐t♦r❡s ❧✐♥❡❛r❡s ❞♦ ♠♦❞❡❧♦ ❝♦♠ ❜❛♥❞❛s ❞❡ ❝♦♥✜❛♥ç❛ ❞❡95%✳ ✻✶
✹✳✺ ●rá✜❝♦ ❞❛s ❞✐str✐❜✉✐çõ❡s ❛ ♣♦st❡r✐♦r✐ ❞♦s ♣❛râ♠❡tr♦s ❡stát✐❝♦sα ❡ γ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷
✻✳✶ ●rá✜❝♦s ❞♦s ❞❛❞♦s s✐♠✉❧❛❞♦s ❞♦ ♠♦❞❡❧♦BIZU ❝♦♠ ♣❛ss❡✐♦ ❛❧❡❛tór✐♦ ✭❧✐♥❤❛ ❝♦♥tí♥✉❛✮ ❡ s❡✉ ♣❛râ♠❡tr♦µt ✭❧✐♥❤❛ ♣♦♥t✐❧❤❛❞❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸
✻✳✷ ●rá✜❝♦s ❞♦s ♣r❡❞✐t♦r❡s ❧✐♥❡❛r❡s ❞❡ µt ❡φt ❞♦ ♠♦❞❡❧♦BIZU ❡st✐♠❛❞♦s ✈✐❛ ✜❧tr♦ ▲❲✳ ✽✸
✻✳✸ ●rá✜❝♦ ❞❛ ❡st✐♠❛t✐✈❛ ❞❛s ❝♦♠♣♦♥❡♥t❡s ❞❛ ✈❛r✐â♥❝✐❛ W ❞♦ ♠♦❞❡❧♦ BIZU ✈✐❛ ✜❧tr♦ ▲❲✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹
✻✳✹ ●rá✜❝♦ ❞❛ ❡st✐♠❛t✐✈❛ ❞❛s ♣r♦❜❛❜✐❧✐❞❛❞❡sα ❡ γ ❞♦ ♠♦❞❡❧♦BIZU ✈✐❛ ✜❧tr♦ ▲❲✳ ✳ ✳ ✳ ✽✺ ✻✳✺ ●rá✜❝♦s ❞♦s ♣r❡❞✐t♦r❡s ❧✐♥❡❛r❡s ❞❡ µt ❡φt ❞♦ ♠♦❞❡❧♦BIZU ❡st✐♠❛❞♦s ✈✐❛ ✜❧tr♦ P▲✳ ✽✻
✻✳✻ ●rá✜❝♦ ❞❛ ❡st✐♠❛t✐✈❛ ❞❛s ❝♦♠♣♦♥❡♥t❡s ❞❛ ✈❛r✐â♥❝✐❛ W ❞♦ ♠♦❞❡❧♦ BIZU ✈✐❛ ✜❧tr♦ P▲✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✼
✻✳✼ ●rá✜❝♦ ❞❛ ❡st✐♠❛t✐✈❛ ❞❛s ♣r♦❜❛❜✐❧✐❞❛❞❡sα ❡ γ ❞♦ ♠♦❞❡❧♦BIZU ✈✐❛ ✜❧tr♦ P▲✳ ✳ ✳ ✳ ✽✽ ✻✳✽ ●rá✜❝♦s ❞♦s ❞❛❞♦s s✐♠✉❧❛❞♦s ❞♦ ♠♦❞❡❧♦ ❇■❩❯ ❝♦♠ ♣❛ss❡✐♦ ❛❧❡❛tór✐♦ ✭❧✐♥❤❛ ❝♦♥tí♥✉❛✮
❡µt ✭❧✐♥❤❛ ♣♦♥t✐❧❤❛❞❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾
▲■❙❚❆ ❉❊ ❋■●❯❘❆❙ ①✐✐✐
✻✳✶✵ ●rá✜❝♦ ❞❛ ❡st✐♠❛t✐✈❛ ❞❛s ❝♦♠♣♦♥❡♥t❡s ❞❛ ✈❛r✐â♥❝✐❛ W ❞♦ ♠♦❞❡❧♦ BIZU ✈✐❛ ✜❧tr♦ ▲❲✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✶
✻✳✶✶ ●rá✜❝♦ ❞❛ ❡st✐♠❛t✐✈❛ ❞❛s ♣r♦❜❛❜✐❧✐❞❛❞❡sα ❡ γ ❞♦ ♠♦❞❡❧♦ ❇■❩❯ ✈✐❛ ✜❧tr♦ ▲❲✳ ✳ ✳ ✳ ✳ ✾✷ ✻✳✶✷ ●rá✜❝♦s ❞♦s ♣r❡❞✐t♦r❡s ❧✐♥❡❛r❡s ❞❡ µt ❡φt ❞♦ ♠♦❞❡❧♦BIZU ❡st✐♠❛❞♦s ✈✐❛ ✜❧tr♦ P▲✳ ✾✸
✻✳✶✸ ●rá✜❝♦ ❞❛ ❡st✐♠❛t✐✈❛ ❞❛s ❝♦♠♣♦♥❡♥t❡s ❞❛ ✈❛r✐â♥❝✐❛ W ❞♦ ♠♦❞❡❧♦ BIZU ✈✐❛ ✜❧tr♦ P▲✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✹
✻✳✶✹ ●rá✜❝♦ ❞❛ ❡st✐♠❛t✐✈❛ ❞❛s ♣r♦❜❛❜✐❧✐❞❛❞❡sα ❡ γ ❞♦ ♠♦❞❡❧♦BIZU ✈✐❛ ✜❧tr♦ P▲✳ ✳ ✳ ✳ ✾✺ ✻✳✶✺ ●rá✜❝♦ ❞❛ sér✐❡ s✐♠✉❧❛❞❛ ❞♦ ♠♦❞❡❧♦ ❞✐♥â♠✐❝♦ ❇■❩❯ ❝♦♠ ♥í✈❡❧✱ t❡♥❞ê♥❝✐❛ ❡ s❛③♦♥❛✲
❧✐❞❛❞❡✱ ❝♦♠ yt✭❧✐♥❤❛ ❝♦♥t✐♥✉❛✮ ❡µt ✭❧✐♥❤❛ ♣♦♥t✐❧❤❛❞❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✼
✻✳✶✻ ●rá✜❝♦ ❞♦s ♣r❡❞✐t♦r❡s ❧✐♥❡❛r❡s ❞❡ µt ❡ φt❞♦ ♠♦❞❡❧♦ ❞✐♥â♠✐❝♦ ❇■❩❯✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✼
✻✳✶✼ ●rá✜❝♦ ❞♦s ❡st❛❞♦s µt ❡φt ❞♦ ♠♦❞❡❧♦ ❞✐♥â♠✐❝♦ ❇■❩❯✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✽
✻✳✶✽ ●rá✜❝♦ ❞♦ ❞❡s✈✐♦ ♣❛❞rã♦ ❡st✐♠❛❞♦ ❞❛ ❝♦♠♣♦♥❡♥t❡ ❝♦♥tí♥✉❛ ❞♦ ♠♦❞❡❧♦ ❞✐♥â♠✐❝♦ ❇■❩❯✳ ✾✾
✻✳✶✾ ●rá✜❝♦ ❞❛s ♣r✐♥❝✐♣❛✐s ❝♦♠♣♦♥❡♥t❡s ❞❛ ♠❛tr✐③ ❞❡ ✈❛r✐â♥❝✐❛ W ❡st✐♠❛❞♦s ♥♦ ♠♦❞❡❧♦ ❇■❩❯✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✵
✻✳✷✵ ●rá✜❝♦ ❞❛ ❡st✐♠❛t✐✈❛ ❞❛s ♣r♦❜❛❜✐❧✐❞❛❞❡sα ❡ γ ❞♦ ♠♦❞❡❧♦ ❇■❩❯✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✶ ✻✳✷✶ ●rá✜❝♦ ❞♦s ♣r❡❞✐t♦r❡s ❧✐♥❡❛r❡s ηt s✉❛✈✐③❛❞♦s ❡♠ ❝♦♠♣❛r❛çã♦ ❛♦s ❡st✐♠❛❞♦s ✈✐❛ ♦
♣r♦❝❡ss♦ ❞❡ ✜❧tr❛❣❡♠✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✷
✻✳✷✷ ●rá✜❝♦ ❞❛ ❞✐str✐❜✉✐çã♦ ♣r❡❞✐t✐✈❛ p(yt|Dt−1) ❞❛ ❝♦♠♣♦♥❡♥t❡ ❝♦♥tí♥✉❛ ❞♦ ♠♦❞❡❧♦ ❞✐✲ ♥â♠✐❝♦ ❇■❩❯✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✷
✻✳✷✸ ●rá✜❝♦ ❞❛ ❞✐str✐❜✉✐çã♦ ♣r❡❞✐t✐✈❛ p(yt|Dt−1) ❞❛ ❝♦♠♣♦♥❡♥t❡ ❝♦♥tí♥✉❛ ❞♦ ♠♦❞❡❧♦ ❞✐✲
♥â♠✐❝♦ ❇■❩❯ ❝♦♠ ♣r❡✈✐sã♦ ❛ ✶✵ ♣❛ss♦s ❛ ❢r❡♥t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✸
✻✳✷✹ ●rá✜❝♦ ❞❛ sér✐❡ s✐♠✉❧❛❞❛ ❞♦ ♠♦❞❡❧♦ ❞✐♥â♠✐❝♦ ❇■❩❯ ❝♦♠ ♥í✈❡❧✱ t❡♥❞ê♥❝✐❛ ❡ s❛③♦♥❛✲ ❧✐❞❛❞❡ ❡ ❝♦✈❛r✐á✈❡✐s✱ ❝♦♠yt ✭❧✐♥❤❛ ❝♦♥tí♥✉❛✮ ❡µt ✭❧✐♥❤❛ ♣♦♥t✐❧❤❛❞❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✺
✻✳✷✺ ●rá✜❝♦ ❞♦s ♣r❡❞✐t♦r❡s ❧✐♥❡❛r❡s ❞❡ µt ❡ φt❞♦ ♠♦❞❡❧♦ ❞✐♥â♠✐❝♦ ❇■❩❯✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✻
✻✳✷✻ ●rá✜❝♦ ❞♦s ❡st❛❞♦s µt ❡φt ❞♦ ♠♦❞❡❧♦ ❞✐♥â♠✐❝♦ ❇■❩❯✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✼
✻✳✷✼ ●rá✜❝♦ ❞♦ ❞❡s✈✐♦ ♣❛❞rã♦ ❡st✐♠❛❞♦ ❞❛ ❝♦♠♣♦♥❡♥t❡ ❝♦♥tí♥✉❛ ❞♦ ♠♦❞❡❧♦ ❞✐♥â♠✐❝♦ ❇■❩❯✳✶✵✼
✻✳✷✽ ●rá✜❝♦ ❞❛s ♣r✐♥❝✐♣❛✐s ❝♦♠♣♦♥❡♥t❡s ❞❛ ♠❛tr✐③ ❞❡ ✈❛r✐â♥❝✐❛ W ❡st✐♠❛❞♦s ♥♦ ♠♦❞❡❧♦ ❇■❩❯✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✽
✻✳✷✾ ●rá✜❝♦ ❞❛ ❡st✐♠❛t✐✈❛ ❞❛s ♣❛râ♠❡tr♦s ❞❛s ❝♦✈❛r✐á✈❡✐s ❞♦ ♠♦❞❡❧♦ ❇■❩❯✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✾
✻✳✸✵ ●rá✜❝♦ ❞❛ ❡st✐♠❛t✐✈❛ ❞❛s ♣r♦❜❛❜✐❧✐❞❛❞❡sα ❡ γ ❞♦ ♠♦❞❡❧♦ ❇■❩❯✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✵ ✻✳✸✶ ●rá✜❝♦ ❞❛ ❞✐str✐❜✉✐çã♦ ♣r❡❞✐t✐✈❛ p(yt|Dt−1) ❞❛ ❝♦♠♣♦♥❡♥t❡ ❝♦♥tí♥✉❛ ❞♦ ♠♦❞❡❧♦ ❞✐✲
♥â♠✐❝♦ ❇■❩❯✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✵
✻✳✸✷ ●rá✜❝♦ ❞❛ ❞✐str✐❜✉✐çã♦ ♣r❡❞✐t✐✈❛ p(yt|Dt−1) ❞❛ ❝♦♠♣♦♥❡♥t❡ ❝♦♥tí♥✉❛ ❞♦ ♠♦❞❡❧♦ ❞✐✲
♥â♠✐❝♦ ❇■❩❯ ❝♦♠ ♣r❡✈✐sã♦ ❛ ✶✵ ♣❛ss♦s ❛ ❢r❡♥t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✶
✻✳✸✸ ●rá✜❝♦ ❞❛ sér✐❡ s✐♠✉❧❛❞❛ ❞♦ ♠♦❞❡❧♦ ❞✐♥â♠✐❝♦ ❚♦❜✐t ❝♦♠ ♥í✈❡❧✱ t❡♥❞ê♥❝✐❛ ❡ s❛③♦♥❛✲ ❧✐❞❛❞❡✱ ❝♦♠ yt✭❧✐♥❤❛ ❝♦♥tí♥✉❛✮ ❡µt ✭❧✐♥❤❛ ♣♦♥t✐❧❤❛❞❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✸
✻✳✸✹ ●rá✜❝♦ ❞♦s ♣r❡❞✐t♦r❡s ❧✐♥❡❛r❡s ❞❡ µt ❡ σt ❞♦ ♠♦❞❡❧♦ ❞✐♥â♠✐❝♦ ❚♦❜✐t✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✹
✻✳✸✺ ●rá✜❝♦ ❞♦s ❡st❛❞♦s µt ❡σt❞♦ ♠♦❞❡❧♦ ❞✐♥â♠✐❝♦ ❚♦❜✐t✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✺
✻✳✸✻ ●rá✜❝♦ ❞❛s ♣r✐♥❝✐♣❛✐s ❝♦♠♣♦♥❡♥t❡s ❞❛ ♠❛tr✐③ ❞❡ ✈❛r✐â♥❝✐❛ W ❡st✐♠❛❞♦s ♥♦ ♠♦❞❡❧♦ ❚♦❜✐t✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✻
✻✳✸✼ ●rá✜❝♦ ❞♦s ♣r❡❞✐t♦r❡s ❧✐♥❡❛r❡s s✉❛✈✐③❛❞♦s ❡♠ ❝♦♠♣❛r❛çã♦ ❛♦ ❡st✐♠❛❞♦s ♥♦ ♣r♦❝❡ss♦ ❞❡ ✜❧tr❛❣❡♠✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✼
①✐✈ ▲■❙❚❆ ❉❊ ❋■●❯❘❆❙
✻✳✸✾ ●rá✜❝♦ ❞❛ ❞✐str✐❜✉✐çã♦ ♣r❡❞✐t✐✈❛ p(yt|Dt−1)❞♦ ♠♦❞❡❧♦ ❞✐♥â♠✐❝♦ ❚♦❜✐t ❝♦♠ ♣r❡✈✐sã♦ ❛ ✶✵ ♣❛ss♦s ❛ ❢r❡♥t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✽
✻✳✹✵ ●rá✜❝♦ ❞❛ sér✐❡ s✐♠✉❧❛❞❛ ❞♦ ♠♦❞❡❧♦ ❞✐♥â♠✐❝♦ ❚♦❜✐t ❝♦♠ ♥í✈❡❧✱ t❡♥❞ê♥❝✐❛ ❡ s❛③♦♥❛✲ ❧✐❞❛❞❡ ❡ ❝♦✈❛r✐á✈❡✐s✱ ❝♦♠yt ✭❧✐♥❤❛ ❝♦♥tí♥✉❛✮ ❡µt ✭❧✐♥❤❛ ♣♦♥t✐❧❤❛❞❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✵
✻✳✹✶ ●rá✜❝♦ ❞♦s ♣r❡❞✐t♦r❡s ❧✐♥❡❛r❡s ❞❡µt ❡ σt ❞♦ ♠♦❞❡❧♦ ❞✐♥â♠✐❝♦ ❚♦❜✐t✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✵
✻✳✹✷ ●rá✜❝♦ ❞♦s ❡st❛❞♦s µt ❡σt❞♦ ♠♦❞❡❧♦ ❞✐♥â♠✐❝♦ ❚♦❜✐t✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✶
✻✳✹✸ ●rá✜❝♦ ❞❛s ♣r✐♥❝✐♣❛✐s ❝♦♠♣♦♥❡♥t❡s ❞❛ ♠❛tr✐③ ❞❡ ✈❛r✐â♥❝✐❛ W ❡st✐♠❛❞♦s ♥♦ ♠♦❞❡❧♦ ❚♦❜✐t✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✷
✻✳✹✹ ●rá✜❝♦ ❞❛ ❡st✐♠❛t✐✈❛ ❞❛s ♣❛râ♠❡tr♦s ❞❛s ❝♦✈❛r✐á✈❡✐s ❞♦ ♠♦❞❡❧♦ ❚♦❜✐t✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✸
✻✳✹✺ ●rá✜❝♦ ❞♦s ♣r❡❞✐t♦r❡s ❧✐♥❡❛r❡s s✉❛✈✐③❛❞♦s ❡♠ ❝♦♠♣❛r❛çã♦ ❛♦ ❡st✐♠❛❞♦s ♥♦ ♣r♦❝❡ss♦ ❞❡ ✜❧tr❛❣❡♠✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✹
✻✳✹✻ ●rá✜❝♦ ❞❛ ❞✐str✐❜✉✐çã♦ ♣r❡❞✐t✐✈❛p(yt|Dt−1) ❞♦ ♠♦❞❡❧♦ ❞✐♥â♠✐❝♦ ❚♦❜✐t✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✹ ✻✳✹✼ ●rá✜❝♦ ❞❛ ❞✐str✐❜✉✐çã♦ ♣r❡❞✐t✐✈❛ p(yt|Dt−1)❞♦ ♠♦❞❡❧♦ ❞✐♥â♠✐❝♦ ❚♦❜✐t ❝♦♠ ♣r❡✈✐sã♦
❛ ✶✵ ♣❛ss♦s ❛ ❢r❡♥t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✺
✻✳✹✽ ■❧✉str❛çã♦ ❞❡ ❝♦♠♦ ❢✉♥❝✐♦♥❛ ♦ s✐st❡♠❛ ❞❡ ❛❜❛st❡❝✐♠❡♥t♦ ❞♦ s✐st❡♠❛ ❞❛ ❈❛♥t❛r❡✐r❛✳ ✳ ✶✷✼
✻✳✹✾ ❙ér✐❡ ❞❡ ❞❛❞♦s ❞✐ár✐❛ ❞♦ ♥í✈❡❧ ❞♦ s✐st❡♠❛ ❞❛ ❈❛♥t❛r❡✐r❛ ❞♦ ✐♥í❝✐♦ ❞❡ ✷✵✶✸ ❛ ♠❛rç♦ ❞❡ ✷✵✶✺✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✼
✻✳✺✵ ●rá✜❝♦ ❞❛ r❡❧❛çã♦ q✉❛❞rát✐❝❛ ❡♥tr❡ ♦ s✐st❡♠❛ ❞❛ ❝❛♥t❛r❡✐r❛ ❝♦♠ ♦s ❞❡♠❛✐s s✐st❡♠❛s ❛ ♣❛rt✐r ❞♦ ❛♥♦ ❞❡ ✷✵✶✸✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✽
✻✳✺✶ ●rá✜❝♦ ❞❛ r❡❧❛çã♦ q✉❛❞rát✐❝❛ ❡♥tr❡ ♦ s✐st❡♠❛ ❞❛ ❝❛♥t❛r❡✐r❛ ❝♦♠ ♦s ❞❡♠❛✐s s✐st❡♠❛s ❛ ♣❛rt✐r ❞♦ ❛♥♦ ❞❡ ✷✵✶✸✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✾
✻✳✺✷ ●rá✜❝♦ ❞❛ r❡❧❛çã♦ q✉❛❞rát✐❝❛ ❡♥tr❡ ♦ s✐st❡♠❛ ❞❛ ❝❛♥t❛r❡✐r❛ ❝♦♠ ♦s ❞❡♠❛✐s s✐st❡♠❛s ❛ ♣❛rt✐r ❞♦ ❛♥♦ ❞❡ ✷✵✶✸✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✾
✻✳✺✸ ●rá✜❝♦ ❞❛ ❡st✐♠❛t✐✈❛ ❞❛s ❝♦♠♣♦♥❡♥t❡s ❞❛ ✈❛r✐â♥❝✐❛W ❞♦ ♠♦❞❡❧♦ ❞✐♥â♠✐❝♦ t♦❜✐t✳ ✳ ✶✸✸ ✻✳✺✹ ●rá✜❝♦ ❞❛ ❡st✐♠❛t✐✈❛ ❞♦s ♣❛râ♠❡tr♦s β ❞♦ ♠♦❞❡❧♦ ❞✐♥â♠✐❝♦ t♦❜✐t✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✹ ✻✳✺✺ ●rá✜❝♦ ❞♦s ♣r❡❞✐t♦r❡s ❧✐♥❡❛r❡s η ❡st✐♠❛❞♦s ♣❡❧♦ ♠♦❞❡❧♦ ❞✐♥â♠✐❝♦ t♦❜✐t✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✺ ✻✳✺✻ ●rá✜❝♦ ❞♦s ❡st❛❞♦s µt ❡σt❞♦ ♠♦❞❡❧♦ ❞✐♥â♠✐❝♦ t♦❜✐t✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✻
✻✳✺✼ ●r❛✜❝♦ ❞❛ ❞✐str✐❜✉✐çã♦ ♣r❡❞✐t✐✈❛p(yt|Dt−1) ❞♦ ♠♦❞❡❧♦ ❞✐♥â♠✐❝♦ t♦❜✐t✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✻
✻✳✺✽ ●r❛✜❝♦ ❞❛ ❞✐str✐❜✉✐çã♦ ♣r❡❞✐t✐✈❛ p(yt|Dt−1) ❝♦♠ ♣r❡❞✐çã♦ ❞❡ ✸✵ ♣❛ss♦s ❛ ❢r❡♥t❡ ❞♦
♠♦❞❡❧♦ ❞✐♥â♠✐❝♦ t♦❜✐t✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✼
✻✳✺✾ ●rá✜❝♦ ❞❛ ❡st✐♠❛t✐✈❛ ❞❛s ❝♦♠♣♦♥❡♥t❡s ❞❛ ✈❛r✐â♥❝✐❛W ❞♦ ♠♦❞❡❧♦ ❞✐♥â♠✐❝♦ ❇■❩❯✳ ✳ ✶✸✽ ✻✳✻✵ ●rá✜❝♦ ❞❛ ❡st✐♠❛t✐✈❛ ❞❛ ❝♦♠♣♦♥❡♥t❡ ❞✐s❝r❡t❛α ❞♦ ♠♦❞❡❧♦ ❞✐♥â♠✐❝♦ ❇■❩❯✳ ✳ ✳ ✳ ✳ ✳ ✶✸✾ ✻✳✻✶ ●rá✜❝♦ ❞♦s ♣r❡❞✐t♦r❡s ❧✐♥❡❛r❡s η ❡st✐♠❛❞♦s ♣❡❧♦ ♠♦❞❡❧♦ ❞✐♥â♠✐❝♦ ❇■❩❯✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✾ ✻✳✻✷ ●rá✜❝♦ ❞♦s ❡st❛❞♦s µt ❡φt ❞♦ ♠♦❞❡❧♦ ❞✐♥â♠✐❝♦ ❇■❩❯✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✵
✻✳✻✸ ●rá✜❝♦ ❞♦ ❞❡s✈✐♦ ♣❛❞rã♦ ❞❛ ❝♦♠♣♦♥❡♥t❡ ❝♦♥tí♥✉❛ ❞♦ ♠♦❞❡❧♦ ❞✐♥â♠✐❝♦ ❇■❩❯✳ ✳ ✳ ✳ ✳ ✶✹✵
✻✳✻✹ ●rá✜❝♦ ❞❛ ❞✐str✐❜✉✐çã♦ ♣r❡❞✐t✐✈❛ p(yt|Dt−1) ❞❛ ❝♦♠♣♦♥❡♥t❡ ❝♦♥tí♥✉❛ ❞♦ ♠♦❞❡❧♦ ❞✐✲
♥â♠✐❝♦ ❇■❩❯✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✶
✻✳✻✺ ●rá✜❝♦ ❞❛ ❞✐str✐❜✉✐çã♦ ♣r❡❞✐t✐✈❛ p(yt|Dt−1) ❝♦♠ ♣r❡❞✐çã♦ ❞❡ ✸✵ ♣❛ss♦s ❛ ❢r❡♥t❡ ❞❛ ❝♦♠♣♦♥❡♥t❡ ❝♦♥tí♥✉❛ ❞♦ ♠♦❞❡❧♦ ❞✐♥â♠✐❝♦ ❇■❩❯✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✶
✻✳✻✻ ●rá✜❝♦ ❞❛ ❞✐str✐❜✉✐çã♦ ♣r❡❞✐t✐✈❛p(yt|Dt−1) ❞♦ ♠♦❞❡❧♦ ❞✐♥â♠✐❝♦ ❜❡t❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✶
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✸✳✶ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ♦s ♠♦❞❡❧♦s ✈✐❛ ❉■❈✱ EAICd ✱EBICd ❡ ▲▼P▲✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✸✳✷ ❊st❛tíst✐❝❛s ❞❛s ❞✐str✐❜✉✐çõ❡s ♠❛r❣✐♥❛✐s ❛ ♣♦st❡r✐♦r✐ ❞♦s ♣❛râ♠❡tr♦s ♣❛r❛ ♦ ♠♦❞❡❧♦
❇■❩❯✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺
✸✳✸ ❊st❛tíst✐❝❛s ❞❛s ❞✐str✐❜✉✐çõ❡s ♠❛r❣✐♥❛✐s ❛ ♣♦st❡r✐♦r✐ ❞♦s ♣❛râ♠❡tr♦s ♣❛r❛ ♦ ♠♦❞❡❧♦ ❚♦❜✐t ✐♥✢❛❝✐♦♥❛❞♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺
✸✳✹ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ♦s ♠♦❞❡❧♦s ✈✐❛ ❉■❈✱ EAICd ✱EBICd ❡ ▲▼P▲✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾ ✸✳✺ ❊st❛tíst✐❝❛s ❞❛s ❞✐str✐❜✉✐çõ❡s ♠❛r❣✐♥❛✐s ❛ ♣♦st❡r✐♦r✐ ❞♦s ♣❛râ♠❡tr♦s ♣❛r❛ ♦ ♠♦❞❡❧♦
❇■❩❯✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾
✸✳✻ ❊st❛tíst✐❝❛s ❞❛s ❞✐str✐❜✉✐çõ❡s ♠❛r❣✐♥❛✐s ❛ ♣♦st❡r✐♦r✐ ❞♦s ♣❛râ♠❡tr♦s ♣❛r❛ ♦ ♠♦❞❡❧♦ ❚♦❜✐t ✐♥✢❛❝✐♦♥❛❞♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾
✸✳✼ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ♦s ♠♦❞❡❧♦s ✈✐❛ ❉■❈✱ EAIC✱d EBICd ❡ ▲▼P▲✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✸✳✽ ❊st❛tíst✐❝❛s ❞❛s ❞✐str✐❜✉✐çõ❡s ♠❛r❣✐♥❛✐s ❛ ♣♦st❡r✐♦r✐ ❞♦s ♣❛râ♠❡tr♦s ♣❛r❛ ♦ ♠♦❞❡❧♦
❇■❩❯✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺
✸✳✾ ❊st❛tíst✐❝❛s ❞❛s ❞✐str✐❜✉✐çõ❡s ♠❛r❣✐♥❛✐s ❛ ♣♦st❡r✐♦r✐ ❞♦s ♣❛râ♠❡tr♦s ♣❛r❛ ♦ ♠♦❞❡❧♦ ❚♦❜✐t ♥♦r♠❛❧ ✐♥✢❛❝✐♦♥❛❞♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺
✸✳✶✵ ❊st❛tíst✐❝❛s ❞❛s ❞✐str✐❜✉✐çõ❡s ♠❛r❣✐♥❛✐s ❛ ♣♦st❡r✐♦r✐ ❞♦s ♣❛râ♠❡tr♦s ♣❛r❛ ♦ ♠♦❞❡❧♦ ❚♦❜✐t ♥♦r♠❛❧ ♣♦tê♥❝✐❛ ✐♥✢❛❝✐♦♥❛❞♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺
✸✳✶✶ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ♦s ♠♦❞❡❧♦s ✈✐❛ ❉■❈✱ EAICd ✱EBICd ❡ ▲▼P▲✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ✸✳✶✷ ❊st❛tíst✐❝❛s ❞❛s ❞✐str✐❜✉✐çõ❡s ♠❛r❣✐♥❛✐s ❛ ♣♦st❡r✐♦r✐ ❞♦s ♣❛râ♠❡tr♦s ♣❛r❛ ♦ ♠♦❞❡❧♦
❇■❩✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶
✸✳✶✸ ❊st❛tíst✐❝❛s ❞❛s ❞✐str✐❜✉✐çõ❡s ♠❛r❣✐♥❛✐s ❛ ♣♦st❡r✐♦r✐ ❞♦s ♣❛râ♠❡tr♦s ♣❛r❛ ♦ ♠♦❞❡❧♦ ❚♦❜✐t ♥♦r♠❛❧ ✐♥✢❛❝✐♦♥❛❞♦ ❞❡ ③❡r♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶
✸✳✶✹ ❊st❛tíst✐❝❛s ❞❛s ❞✐str✐❜✉✐çõ❡s ♠❛r❣✐♥❛✐s ❛ ♣♦st❡r✐♦r✐ ❞♦s ♣❛râ♠❡tr♦s ♣❛r❛ ♦ ♠♦❞❡❧♦ t♦❜✐t ♥♦r♠❛❧✲♣♦tê♥❝✐❛ ✐♥✢❛❝✐♦♥❛❞♦ ❞❡ ③❡r♦✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶
✻✳✶ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ❛s ❡s♣❡❝✐✜❝❛çõ❡s ❞♦ ♠♦❞❡❧♦ ❚♦❜✐t s❡❣✉♥❞♦ ♦s ❝r✐tér✐♦s DIC ❡ LM P L✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✷ ✻✳✷ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ❛s ❡s♣❡❝✐✜❝❛çõ❡s ❞♦ ♠♦❞❡❧♦ ❇■❩❯ s❡❣✉♥❞♦ ♦s ❝r✐tér✐♦s DIC ❡
LM P L✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✷
✻✳✸ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ♦s ♠♦❞❡❧♦s ❚♦❜✐t✱ ❇■❩❯ ❡ ❇❡t❛ ♣❡❧♦s ❝r✐té❞✐♦s DIC✱ LM P L ❡ ♠étr✐❝❛s ❞❡ ♣r❡❞✐çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✷
✻✳✹ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ♦s ♠♦❞❡❧♦s ❚♦❜✐t✱ ❇■❩❯ ❡ ❇❡t❛ ♣❡❧♦ ❝r✐té❞✐♦DIC ❡M SEs♦♠❡♥t❡ ♥❛ ♣r❡✈✐sã♦ ❞❡ ✸✵ ♣❛ss♦s ❛ ❢r❡♥t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✷
❈❛♣ít✉❧♦ ✶
■♥tr♦❞✉çã♦
❆ ♠♦❞❡❧❛❣❡♠ ❡st❛tíst✐❝❛ ♣❛r❛ ❞❛❞♦s ❝♦♥tí♥✉♦s r❡str✐t♦s ❛ ✉♠ ✐♥t❡r✈❛❧♦ ❧✐♠✐t❛❞♦ t❡♠ s✐❞♦ ♦ ❢♦❝♦ ❞❡ ♠✉✐t♦s ❡st✉❞♦s✳ ❊st❡ ✐♥t❡r❡ss❡ é ❛✐♥❞❛ ♠❛✐s ❢r❡q✉❡♥t❡ ♥❛ ❧✐t❡r❛t✉r❛ ♣❛r❛ ❞❛❞♦s r❡str✐t♦s ❛♦ ✐♥t❡r✈❛❧♦ [0,1]✱ ♥♦ q✉❡ s❡ r❡❢❡r❡ ❛ ❝♦♥❥✉♥t♦s ❞❡ ❞❛❞♦s q✉❡ r❡♣r❡s❡♥t❛♠ ✈❛❧♦r❡s ❞❡ t❛①❛s ♦✉ ♣r♦♣♦r✲
çõ❡s✳ ❆❧❣✉♥s ❡①❡♠♣❧♦s ❞❡ ❞❛❞♦s ❝♦♥tí♥✉♦s ❞❡ ♣r♦♣♦rçõ❡s ✐♥❝❧✉❡♠ t❛①❛ ❞❡ ❞❡s❡♠♣r❡❣♦✱ ♠♦rt❛❧✐❞❛❞❡ ♣♦r ❛❝✐❞❡♥t❡s ❞❡ trâ♥s✐t♦✱ ❢r❛çã♦ ❞❡ r❡♥❞❛ ❞❡st✐♥❛❞❛ ❛♦ ❢✉♥❞♦ ❞❡ ❛♣♦s❡♥t❛❞♦r✐❛✱ ❢r❛çã♦ ❞♦ ✈❛❧♦r ❞❡ ❡①♣♦rt❛çã♦ ❞❛ ❡♠♣r❡s❛ ♥♦ s❡t♦r ❞❡ ✐♥❞ústr✐❛✱ ❡t❝✳ ▼♦❞❡❧♦s ❞❡ r❡❣r❡ssã♦ ❧✐♥❡❛r❡s ❡ ♥ã♦ ❧✐♥❡❛r❡s ✉s✉❛✐s ♥ã♦ sã♦ ❛❞❡q✉❛❞♦s ♣❛r❛ ❡st❡ t✐♣♦ ❞❡ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s✳ ❆❧❣✉♠❛s ❞✐❢❡r❡♥t❡s ❛❧t❡r♥❛t✐✈❛s tê♠ s✐❞♦ ♣r♦♣♦st❛s ♣❛r❛ ♠♦❞❡❧❛r ♣r♦♣♦rçõ❡s ❝♦♥tí♥✉❛s ❝♦♠ ❛ ♣♦ss✐❜✐❧✐❞❛❞❡ ❞❡ r❡❧❛❝✐♦♥á✲❧❛s ❛ ✈❛r✐á✈❡✐s ❡①ó❣❡♥❛s✱ ❝♦♠♦ ♦ ✉s♦ ❞❡ tr❛♥s❢♦r♠❛çõ❡s ♥❛ ✈❛r✐á✈❡❧ r❡s♣♦st❛ ✭✈✐❞❡ ❆✐t❝❤✐s♦♥✱ ✶✾✽✷✮✱ ❝❡♥s✉r❛ ♥❛ ✈❛r✐á✈❡❧ r❡s♣♦st❛ ♦✉ ❛ss✉♠✐♥❞♦ ✉♠❛ ❞✐str✐❜✉✐çã♦ ♣❛r❛ ❛ ✈❛r✐á✈❡❧ r❡s♣♦st❛ q✉❡ ❡stá r❡str✐t❛ ❛ ✐♥t❡r✲ ✈❛❧♦s ❧✐♠✐t❛❞♦s✳ ❖s ♠♦❞❡❧♦s ❞❡ r❡❣r❡ssã♦ ❚♦❜✐t ❡ r❡❣r❡ssã♦ ❜❡t❛ sã♦ ❞❡ ✐♥t❡r❡ss❡ ♣❛rt✐❝✉❧❛r ❞❡st❡ tr❛❜❛❧❤♦✳
❆ ❞✐str✐❜✉✐çã♦ ❜❡t❛ t❡♠ ❞❡s♣❡rt❛❞♦ ❜❛st❛♥t❡ ✐♥t❡r❡ss❡ ♣❛r❛ ♠♦❞❡❧❛❣❡♠ ❡♠ ✐♥t❡r✈❛❧♦s ❧✐♠✐t❛❞♦s ❞❡✈✐❞♦ ❛ s✉❛ ✢❡①✐❜✐❧✐❞❛❞❡✱ ✉♠❛ ✈❡③ q✉❡ s✉❛ ❞❡♥s✐❞❛❞❡ ♣♦❞❡ ❛ss✉♠✐r ❞✐❢❡r❡♥t❡s ❢♦r♠❛s ❞❡♣❡♥❞❡♥❞♦ ❛♣❡♥❛s ❞♦s ❞♦✐s ♣❛râ♠❡tr♦s q✉❡ ❝❛r❛❝t❡r✐③❛♠ ❛ ❞✐str✐❜✉✐çã♦ ✭✈✐❞❡❏♦❤♥s♦♥ ❡t ❛❧✳✱✶✾✾✺✮✳ ❆❧❣✉♥s ♠♦✲ ❞❡❧♦s ❢r❡q✉❡♥t✐st❛s ❞❡ r❡❣r❡ssã♦ ❜❡t❛ ❢♦r❛♠ ♣r♦♣♦st♦s ♣♦rP❛♦❧✐♥♦✭✷✵✵✶✮✱❑✐❡s❝❤♥✐❝❦ ❡ ▼❝❈✉❧❧♦✉❣❤
✭✷✵✵✸✮✱❋❡rr❛r✐ ❡ ❈r✐❜❛r✐✲◆❡t♦✭✷✵✵✹✮ ❡❖s♣✐♥❛ ❡ ❋❡rr❛r✐✭✷✵✶✷✮✱ ❡♥tr❡ ♦✉tr♦s✳ ◆❛ ❝❧❛ss❡ ❞❡ ♠♦❞❡❧♦s ❞❡ r❡❣r❡ssã♦ ✐♥tr♦❞✉③✐❞♦s ♣♦r❋❡rr❛r✐ ❡ ❈r✐❜❛r✐✲◆❡t♦✭✷✵✵✹✮✱ ❛ ❝♦♥❞✐çã♦ ❜ás✐❝❛ ❛ss✉♠✐❞❛ é q✉❡ ❛ ✈❛✲ r✐á✈❡❧ r❡s♣♦st❛ s❡❣✉❡ ❛ ❞✐str✐❜✉✐çã♦ ♦♥❞❡ ♦ s❡✉ ✈❛❧♦r ❡s♣❡r❛❞♦ ❡stá r❡❧❛❝✐♦♥❛❞♦ ❛ ✉♠ ♣r❡❞✐t♦r ❧✐♥❡❛r ♣♦r ♠❡✐♦ ❞❡ ✉♠❛ ❢✉♥çã♦ ❞❡ ❧✐❣❛çã♦✳ ❆❧❣✉♥s ♠♦❞❡❧♦s ❞❡ r❡❣r❡ssã♦ ❜❡t❛ ❇❛②❡s✐❛♥♦s ❢♦r❛♠ ❡st✉❞❛❞♦s ♣♦r ❇r❛♥s❝✉♠ ❡t ❛❧✳ ✭✷✵✵✼✮✱ ❆❧❜✐ ❡t ❛❧✳ ✭✷✵✵✾✮✱ ❇❛②❡s ❡t ❛❧✳✭✷✵✶✷✮✱ ❡♥tr❡ ♦✉tr♦s✳ ❯♠❛ ❛❜♦r❞❛❣❡♠ ❛❧t❡r♥❛t✐✈❛ ♣❛r❛ ♠♦❞❡❧❛❣❡♠ ❞❡ ❞❛❞♦s ❝♦♠ ❡st❛s ❝❛r❛❝t❡ríst✐❝❛s ❞❡s❝r✐t❛s ❛❝✐♠❛ é ❜❛s❡❛❞❛ ❡♠ ❡①t❡♥✲ sõ❡s ❞♦s ♠♦❞❡❧♦s ❝❡♥s✉r❛❞♦s ❚♦❜✐t ♣r♦♣♦st♦ ♣♦r❚♦❜✐♥✭✶✾✺✽✮✱ t❛♠❜é♠ ❡①♣❧♦r❛❞♦ ♣♦r▼r♦③✭✶✾✽✼✮✱ ✉t✐❧✐③❛♥❞♦ ❝❡♥s✉r❛ ❞✉♣❧❛ ♥❛s ❡①tr❡♠✐❞❛❞❡s ❞♦ ✐♥t❡r✈❛❧♦ [0,1]✳ ❆ ✈❡rsã♦ ❇❛②❡s✐❛♥❛ ❞♦ ♠♦❞❡❧♦ ❚♦❜✐t
❢♦✐ ❡st✉❞❛❞❛ ♣♦r❈❤✐❜ ✭✶✾✾✷✮✳
❈♦♥t✉❞♦✱ ❞❛❞♦s ❞❡ ♣r♦♣♦rçõ❡s ♣♦❞❡ ✐♥❝❧✉✐r ✉♠❛ q✉❛♥t✐❞❛❞❡ ♥ã♦ ❞❡s♣r❡③í✈❡❧ ❞❡ ✈❛❧♦r❡s ❡①tr❡♠♦s✱ ③❡r♦s ❡✴♦✉ ✉♥s✳ ◆❡st❛ s✐t✉❛çã♦✱ ❛ ❞✐str✐❜✉✐çã♦ ❜❡t❛ ❡♠ s✐ ♥ã♦ ♣r♦✈✐❞❡♥❝✐❛ ✉♠❛ ❞❡s❝r✐çã♦ s❛t✐s❢❛tór✐❛ ❞♦s ❞❛❞♦s✱ ✉♠❛ ✈❡③ q✉❡ ❡❧❛ ♥ã♦ ♣❡r♠✐t❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ♣♦s✐t✐✈❛ ♣❛r❛ ♥❡♥❤✉♠ ♣♦♥t♦ ❞♦ ✐♥t❡r✈❛❧♦[0,1]✳
P❛r❛ ❝♦♥t♦r♥❛r ❡st❡ ♣r♦❜❧❡♠❛✱❖s♣✐♥❛✭✷✵✵✽✮ ♣r♦♣ôs ✉♠❛ ✈❡rsã♦ ❝♦♠ ♠✐st✉r❛ ❝♦♥tí♥✉❛✲❞✐s❝r❡t❛ ❞♦ ♠♦❞❡❧♦ ❛♣r❡s❡♥t❛❞♦ ♣♦r ❋❡rr❛r✐ ❡ ❈r✐❜❛r✐✲◆❡t♦ ✭✷✵✵✹✮ ✱ ✉t✐❧✐③❛♥❞♦ ❛ ❞✐str✐❜✉✐çã♦ ❜❡t❛ ♣❛r❛ ❞❡✜♥✐r ❛ ❝♦♠♣♦♥❡♥t❡ ❝♦♥tí♥✉❛ ❞❛ ❞✐str✐❜✉✐çã♦ ❡ ❛ ❝♦♠♣♦♥❡♥t❡ ❞✐s❝r❡t❛ é ❞❡✜♥✐❞❛ ♣♦r ✉♠❛ ❇❡r♥♦✉❧❧✐ ♦✉ ✉♠❛ ❞✐str✐❜✉✐çã♦ ❞❡❣❡♥❡r❛❞❛ ❡♠ ③❡r♦ ♦✉ ✉♠✳
P❛r❛ ♦ ♠♦❞❡❧♦ ❚♦❜✐t ❞✉♣❧❛♠❡♥t❡ ❝❡♥s✉r❛❞♦ ♠✉✐t❛s ✈❡③❡s ❛ ❝❡♥s✉r❛ ♥ã♦ é ♦ s✉✜❝✐❡♥t❡ ♣❛r❛ ❝♦♥✲ t❡♠♣❧❛r ❛ q✉❛♥t✐❞❛❞❡s ❞❡ ✈❛❧♦r❡s ❡①tr❡♠♦s ♥♦ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s✳ ❈♦♠ ✐ss♦✱ ✐♥✢❛çõ❡s ❞❡ ③❡r♦s ❡ ✉♥s t❛♠❜é♠ ♣♦❞❡♠ s❡r ❝♦♥s✐❞❡r❛❞❛s ✉t✐❧✐③❛♥❞♦ ❛ ❡①t❡♥sã♦ ❞♦ ♠♦❞❡❧♦ ❞❡ ♠✐st✉r❛s ❛♣r❡s❡♥t❛❞♦ ♣♦r
❈r❛❣❣ ✭✶✾✼✶✮✱ ♦♥❞❡ ♦s ✈❛❧♦r❡s ❡①tr❡♠♦s ❞♦ ✐♥t❡r✈❛❧♦ sã♦ t❛♠❜é♠ ❞❡✜♥✐❞♦s ♣♦r ✉♠❛ ❇❡r♥♦✉❧❧✐ ♦✉ ✉♠❛ ❞✐str✐❜✉✐çã♦ ❞❡❣❡♥❡r❛❞❛✳ ❖s ♠♦❞❡❧♦s ❞❡ ❤✉r❞❧❡ ✭▼❝❉♦✇❡❧❧✱ ✷✵✵✸✮ t❛♠❜é♠ ♣♦❞❡♠ s❡r ✐♥s❡r✐✲ ❞♦s ♥❡st❡ ❝♦♥t❡①t♦✳ ❖✉tr❛ ❢♦r♠❛ ❞❡ ✉t✐❧✐③❛r ❛ ❡①t❡♥sã♦ ❞♦ ♠♦❞❡❧♦ ♣r♦♣♦st♦ ♣♦r ▼♦✉❧t♦♥ ❡ ❍❛❧s❡②
✭✶✾✾✺✮✱ ♦♥❞❡ ♦s ✈❛❧♦r❡s ❡①tr❡♠♦s ♣♦❞❡♠ ✈✐r ❞❡ ✉♠❛ ❝♦♠♣♦♥❡♥t❡ ❞✐s❝r❡t❛ ♦✉ ❞❡ ✉♠❛ ❝❡♥s✉r❛ ❞❛
