❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦
❊s❝♦❧❛ ❙✉♣❡r✐♦r ❞❡ ❆❣r✐❝✉❧t✉r❛ ✏▲✉✐③ ❞❡ ◗✉❡✐r♦③✑
▼♦❞❡❧♦s ❝♦♠ s♦❜r❡✈✐✈❡♥t❡s ❞❡ ❧♦♥❣❛ ❞✉r❛çã♦ ♣❛r❛♠étr✐❝♦s ❡
s❡♠✐✲♣❛r❛♠étr✐❝♦s ❛♣❧✐❝❛❞♦s ❛ ✉♠ ❡♥s❛✐♦ ❝❧í♥✐❝♦ ❛❧❡❛t♦r✐③❛❞♦
■t❛❧♦ ▼❛r❝✉s ❞❛ ▼♦t❛ ❋r❛③ã♦
❉✐ss❡rt❛çã♦ ❛♣r❡s❡♥t❛❞❛ ♣❛r❛ ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ▼❡s✲ tr❡ ❡♠ ❈✐ê♥❝✐❛s✳ ➪r❡❛ ❞❡ ❝♦♥❝❡♥tr❛çã♦✿ ❊st❛tíst✐❝❛ ❡ ❊①♣❡r✐♠❡♥t❛çã♦ ❆❣r♦♥ô♠✐❝❛
■t❛❧♦ ▼❛r❝✉s ❞❛ ▼♦t❛ ❋r❛③ã♦ ▲✐❝❡♥❝✐❛❞♦ ❡♠ ▼❛t❡♠át✐❝❛
▼♦❞❡❧♦s ❝♦♠ s♦❜r❡✈✐✈❡♥t❡s ❞❡ ❧♦♥❣❛ ❞✉r❛çã♦ ♣❛r❛♠étr✐❝♦s ❡ s❡♠✐✲♣❛r❛♠étr✐❝♦s ❛♣❧✐❝❛❞♦s ❛ ✉♠ ❡♥s❛✐♦ ❝❧í♥✐❝♦ ❛❧❡❛t♦r✐③❛❞♦
❖r✐❡♥t❛❞♦r❛✿ Pr♦❢a
✳ ❉ra
✳ ❙❯❊▲❨ ❘❯■❩ ●■❖▲❖
❉✐ss❡rt❛çã♦ ❛♣r❡s❡♥t❛❞❛ ♣❛r❛ ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ▼❡s✲ tr❡ ❡♠ ❈✐ê♥❝✐❛s✳ ➪r❡❛ ❞❡ ❝♦♥❝❡♥tr❛çã♦✿ ❊st❛tíst✐❝❛ ❡ ❊①♣❡r✐♠❡♥t❛çã♦ ❆❣r♦♥ô♠✐❝❛
Dados Internacionais de Catalogação na Publicação DIVISÃO DE BIBLIOTECA - ESALQ/USP
Frazão, Italo Marcus da Mota
Modelos com sobreviventes de longa duração paramétricos e semi-paramétricos aplicados a um ensaio clínico aleatorizado / Italo Marcus da Mota Frazão.- - Piracicaba, 2012.
114 p: il.
Dissertação (Mestrado) - - Escola Superior de Agricultura “Luiz de Queiroz”, 2012.
1. Análise de sobrevivência 2. Ensaio clínico 3. Regressão logística 4. Modelos não-lineares 5. Modelos de riscos proporcionais 6. Dados censurados I. Título
CDD 519.546 F848m
✸ ❉❡❞✐❝❛tór✐❛
❆♦ ♠❡✉ ♣❛✐✱
■r✐♥❡✉ ❋r❛③ã♦ ✭✐♥ ♠❡♠♦r✐❛♥✮✱ ♣❡ss♦❛ ❢✉♥❞❛♠❡♥t❛❧ ♣❛r❛ q✉❡ ❡ss❛ ❝♦♥q✉✐st❛ s❡ r❡❛❧✐③❛ss❡✳ ❊①❡♠♣❧♦ ❞❡ ✈✐❞❛ ❡ ❤♦♥❡st✐❞❛❞❡✳ ❙✉❛ ❛❧❡❣r✐❛ ❡r❛ ❝♦♥t❛❣✐❛♥t❡ ❡ ♥♦s ❞❡✐①♦✉ ♠✉✐t❛s s❛✉❞❛❞❡s✳ ❊ss❛ ✈✐tór✐❛ t❛♠❜é♠ é s✉❛✦
➚ ♠✐♥❤❛ ♠ã❡✱
▼❛r❧❡♥❡ ❞❡ ❋át✐♠❛ ❋❡rr❡✐r❛ ❞❛ ▼♦t❛ ❋r❛③ã♦✱ ❜❛s❡ ❞❡ t♦❞❛ ♥♦ss❛ ❢❛♠í❧✐❛ ❡ q✉❡ ❛❜❞✐❝♦✉ ❞❡ ♠✉✐t❛s ❝♦✐s❛s ♣❛r❛ q✉❡ ❡ss❡ s♦♥❤♦ s❡ ❝♦♥❝r❡t✐③❛ss❡✳ P♦r t♦❞♦ ❛♣♦✐♦✱ ✐♥❝❡♥t✐✈♦ ❡ ❝♦♥✜❛♥ç❛ ❡♠ ♠✐♠ ❞❡♣♦s✐t❛❞❛✳ ❊ss❛ ✈✐tór✐❛ t❛♠❜é♠ é s✉❛✦
➚s ♠✐♥❤❛s ✐r♠ãs✱
❏✉❧✐❛♥❛ ❞❛ ▼♦t❛ ❋r❛③ã♦ ◆❡s♣♦❧♦ ❡ ❉é❜♦r❛ ❞❛ ▼♦t❛ ❋r❛③ã♦✱ s❡♠♣r❡ ♣r❡s❡♥t❡s ❡♠ t♦❞♦s ♦s ♠♦♠❡♥t♦s✳ ❊①❡♠♣❧♦s ❞❡ ❢❛♠í❧✐❛✱ ✉♥✐ã♦✱ ❛♠♦r ❡ ❝❛r✐♥❤♦✳ ❊ss❛ ✈✐tór✐❛ t❛♠❜é♠ é ❞❡ ✈♦❝ês✦
✺ ❆●❘❆❉❊❈■▼❊◆❚❖❙
Pr✐♠❡✐r❛♠❡♥t❡ ❛ ❉❡✉s✱ ♣♦r ♠❡ ♠❛♥t❡r s❡♠♣r❡ ❢♦rt❡✱ ❝♦♥✜❛♥t❡ ❡ ❞❡❞✐❝❛❞♦ ❡♠ ♠❡✉s ♦❜❥❡t✐✈♦s✱ ♠❡s♠♦ ♥♦s ♠♦♠❡♥t♦s ♠❛✐s ❞✐❢í❝❡✐s✳
➚ t♦❞❛ ♠✐♥❤❛ ❢❛♠í❧✐❛ q✉❡ s❡♠♣r❡ ❡st❡✈❡ ❛♦ ♠❡✉ ❧❛❞♦✱ ❝♦♠♣r❡❡♥❞❡♥❞♦ ♠✐♥❤❛s ❛✉sê♥❝✐❛s ❡ ♠❡ ❞❛♥❞♦ ❢♦rç❛s ♣❛r❛ s❡❣✉✐r ❡♠ ❢r❡♥t❡✳
➚ ♠✐♥❤❛ ♦r✐❡♥t❛❞♦r❛✱ Pr♦❢❛✳ ❉r❛✳ ❙✉❡❧② ❘✉✐③ ●✐♦❧♦✱ ♣♦r t♦❞♦s ♦s ❡♥s✐✲
♥❛♠❡♥t♦s✱ ❝♦♥✈❡rs❛s✱ ❝♦♥s❡❧❤♦s✱ ❝♦♠♣r❡❡♥sã♦✱ ♣❛❝✐ê♥❝✐❛ ❡ ❝♦♥✜❛♥ç❛ ❞❡♣♦s✐t❛❞❛✳ ❋❛t♦r❡s ❡ss❡♥❝✐❛✐s ♣❛r❛ q✉❡ ♦ tr❛❜❛❧❤♦ ❢♦ss❡ r❡❛❧✐③❛❞♦ ❝♦♠ q✉❛❧✐❞❛❞❡✳
➚ t♦❞♦s ♣r♦❢❡ss♦r❡s ❞♦ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❈✐ê♥❝✐❛s ❊①❛t❛s ❞❛ ❊❙❆▲◗✴❯❙P✱ ♣❡❧❛ ❞❡❞✐❝❛çã♦ ❡ ❝♦♠♣❡tê♥❝✐❛ ❡♠ ❧❡❝✐♦♥❛r✱ ♣❡❧❛ ❛♠✐③❛❞❡ ❡ ♣❡❧❛ ❢♦r♠❛çã♦ q✉❡ ♠❡ ♣r♦♣♦r✲ ❝✐♦♥❛r❛♠✳
➚ t♦❞♦s ♦s ❢✉♥❝✐♦♥ár✐♦s ❞♦ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❈✐ê♥❝✐❛s ❊①❛t❛s ❞❛ ❊❙❆▲◗✴❯❙P✱ ♣♦r t♦❞♦ ❛✉①í❧✐♦ ❢♦r♥❡❝✐❞♦ ❞✉r❛♥t❡ ❡st❡ ♣❡rí♦❞♦✳
➚ t♦❞♦s ♦s ❛❧✉♥♦s ❞❡ ♠❡str❛❞♦ ❡ ❞♦✉t♦r❛❞♦✱ q✉❡ ❞✐r❡t❛ ♦✉ ✐♥❞✐r❡t❛♠❡♥t❡✱ ❝♦♥tr✐❜✉ír❛♠ ♣♦s✐t✐✈❛♠❡♥t❡ ♣❛r❛ q✉❡ ❡st❡ tr❛❜❛❧❤♦ ❢♦ss❡ r❡❛❧✐③❛❞♦✳
❆♦s ❛♠✐❣♦s ❞❡ r❡♣ú❜❧✐❝❛✱ ❈áss✐♦✱ ●✉✐❧❤❡r♠❡ ❡ P❡❞r♦✱ ♣♦r t♦❞♦ ❛♣♦✐♦ ❞❛❞♦ ♥♦s ♠♦♠❡♥t♦s ❞❡ ❞ú✈✐❞❛s ❡ ❞✐✜❝✉❧❞❛❞❡s✳
➚ ♠✐♥❤❛ ♥❛♠♦r❛❞❛ ●❛❜r✐❡❧❛✱ ♣♦r ❡st❛r s❡♠♣r❡ ❞♦ ♠❡✉ ❧❛❞♦ ❡ ❡♥t❡♥❞❡r ♠✐✲ ♥❤❛s ❛✉sê♥❝✐❛s✳ P♦r t♦❞♦ ❛♣♦✐♦✱ ❝❛r✐♥❤♦ ❡ ❝♦♠♣r❡❡♥sã♦ ❢♦r♥❡❝✐❞❛ ♥❡st❛ ❝♦♥q✉✐st❛✳
❆♦ ❆❧❡①❛♥❞r❡ ❈♦st❛ P❡r❡✐r❛ ❞♦ ■♥❈♦r✴❯❙P q✉❡ ❝❡❞❡✉ ♦ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s ✉t✐❧✐③❛❞♦ ♣❛r❛ ❛♥á❧✐s❡✳
➚ ❈❆P❊❙ ✲ ❈♦♦r❞❡♥❛çã♦ ❞❡ ❆♣❡r❢❡✐ç♦❛♠❡♥t♦ ❞❡ P❡ss♦❛❧ ❞❡ ◆í✈❡❧ ❙✉♣❡r✐♦r✱ ♣❡❧❛ ❜♦❧s❛ ❞❡ ♠❡str❛❞♦ ❝♦♥❝❡❞✐❞❛✳
❊♥✜♠✱ ✉♠ ❛❣r❛❞❡❝✐♠❡♥t♦ ❛ t♦❞♦s q✉❡✱ ❞❡ ✉♠ ❢♦r♠❛ ♦✉ ♦✉tr❛✱ ❝♦♥tr✐❜✉ír❛♠ ♥❛ r❡❛❧✐③❛çã♦ ❞❡st❡ tr❛❜❛❧❤♦✳
✻
✼ ❙❯▼➪❘■❖
❘❊❙❯▼❖ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾ ❆❇❙❚❘❆❈❚ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ▲■❙❚❆ ❉❊ ❋■●❯❘❆❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸ ▲■❙❚❆ ❉❊ ❚❆❇❊▲❆❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✶ ■◆❚❘❖❉❯➬➹❖ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✷ ❘❊❱■❙➹❖ ❇■❇▲■❖●❘➪❋■❈❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✷✳✶ ❈♦♥❝❡✐t♦s ❜ás✐❝♦s ❞❡ ❛♥á❧✐s❡ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✷✳✷ ▼♦❞❡❧♦s ❝♦♠ s♦❜r❡✈✐✈❡♥t❡s ❞❡ ❧♦♥❣❛ ❞✉r❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✸ ▼❆❚❊❘■❆▲ ❊ ▼➱❚❖❉❖❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✸✳✶ ▼❛t❡r✐❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✸✳✷ ▼ét♦❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✸✳✷✳✶ ▼♦❞❡❧♦s ❞❡ ♠✐st✉r❛ ♣❛❞rã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✸✳✷✳✷ ▼♦❞❡❧♦ ❞❡ t❡♠♣♦ ❞❡ ♣r♦♠♦çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✸✳✷✳✸ ▼♦❞❡❧♦ ❞❡ ♠✐st✉r❛ s❡♠✐✲♣❛r❛♠étr✐❝♦ ❞❡ ❈♦① ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼ ✸✳✸ ❆♥á❧✐s❡ ❞❡ r❡sí❞✉♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ✸✳✸✳✶ ❘❡sí❞✉♦s q✉❛♥t✐s ✲ ●rá✜❝♦s ❲♦r♠ P❧♦t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✸✳✸✳✷ ❘❡sí❞✉♦s ▼❛rt✐♥❣❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✸✳✸✳✸ ❘❡sí❞✉♦s ❉❡✈✐❛♥❝❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ✸✳✹ ■♥t❡r✈❛❧♦s ❞❡ ❝♦♥✜❛♥ç❛ ♣❛r❛ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ s❡r s♦❜r❡✈✐✈❡♥t❡ ❞❡ ❧♦♥❣❛ ❞✉r❛çã♦ ✻✷ ✸✳✺ ❆s♣❡❝t♦s ❝♦♠♣✉t❛❝✐♦♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ✹ ❘❊❙❯▲❚❆❉❖❙ ❊ ❉■❙❈❯❙❙➹❖ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ✹✳✶ ▼♦❞❡❧♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❞❡ ❧♦♥❣❛ ❞✉r❛çã♦ ♣❛r❛♠étr✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ✹✳✶✳✶ ■♥❢❡rê♥❝✐❛s ✲ ▼♦❞❡❧♦ ❞❡ t❡♠♣♦ ❞❡ ♣r♦♠♦çã♦ P♦✐ss♦♥✲▲♦❣✐t♦✲❲❡✐❜✉❧❧ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺ ✹✳✷ ▼♦❞❡❧♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❞❡ ❧♦♥❣❛ ❞✉r❛çã♦ s❡♠✐✲♣❛r❛♠étr✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶ ✹✳✷✳✶ ■♥❢❡rê♥❝✐❛s✲ ▼♦❞❡❧♦ ❞❡ ♠✐st✉r❛ ▲♦❣✐t♦✲❈♦① ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺ ✹✳✸ ▼♦❞❡❧♦ ❞❡ t❡♠♣♦ ❞❡ ♣r♦♠♦çã♦ P♦✐ss♦♥✲▲♦❣✐t♦✲❲❡✐❜✉❧❧ ✈❡rs✉s ♠♦❞❡❧♦ ❞❡ ♠✐st✉r❛
✾ ❘❊❙❯▼❖
▼♦❞❡❧♦s ❝♦♠ s♦❜r❡✈✐✈❡♥t❡s ❞❡ ❧♦♥❣❛ ❞✉r❛çã♦ ♣❛r❛♠étr✐❝♦s ❡ s❡♠✐✲♣❛r❛♠étr✐❝♦s ❛♣❧✐❝❛❞♦s ❛ ✉♠ ❡♥s❛✐♦ ❝❧í♥✐❝♦ ❛❧❡❛t♦r✐③❛❞♦
❉✐✈❡rs♦s ♠♦❞❡❧♦s tê♠ s✐❞♦ ♣r♦♣♦st♦s ♥❛ ❧✐t❡r❛t✉r❛ ❝♦♠ ♦ ♦❜❥❡t✐✈♦ ❞❡ ❛♥❛❧✐s❛r ❞❛❞♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❡♠ q✉❡ ❛ ♣♦♣✉❧❛çã♦ s♦❜ ❡st✉❞♦ é ❛ss✉♠✐❞❛ s❡r ✉♠❛ ♠✐st✉r❛ ❞❡ ✐♥❞✐✈í❞✉♦s s✉s❝❡tí✈❡✐s ✭❡♠ r✐s❝♦✮ ❡ ♥ã♦ s✉s❝❡tí✈❡✐s ❛ ✉♠ ❡s♣❡❝í✜❝♦ ❡✈❡♥t♦ ❞❡ ✐♥t❡r❡ss❡✳ ❚❛✐s ♠♦❞❡❧♦s sã♦ ✉s✉❛❧♠❡♥t❡ ❞❡♥♦♠✐♥❛❞♦s ♠♦❞❡❧♦s ❝♦♠ s♦❜r❡✈✐✈❡♥t❡s ❞❡ ❧♦♥❣❛ ❞✉r❛çã♦ ♦✉ ♠♦❞❡❧♦s ❝♦♠ ❢r❛çã♦ ❞❡ ❝✉r❛✳ ◆❡st❡ tr❛❜❛❧❤♦✱ ❞✐✈❡rs♦s ❞❡ss❡s ♠♦❞❡❧♦s ✭♥♦s ❝♦♥t❡①t♦s ♣❛r❛♠étr✐❝♦ ❡ s❡♠✐✲♣❛r❛♠étr✐❝♦✮ ❢♦r❛♠ ❝♦♥s✐❞❡r❛❞♦s ♣❛r❛ ❛♥❛❧✐s❛r ♦s ❞❛❞♦s ❞❡ ✉♠ ❡♥s❛✐♦ ❝❧í♥✐❝♦ ❛❧❡❛t♦r✐③❛❞♦ ❝♦♥❞✉③✐❞♦ ❝♦♠ ♦ ♦❜❥❡t✐✈♦ ❞❡ ❝♦♠♣❛r❛r três ❡str❛té❣✐❛s t❡r❛♣ê✉t✐❝❛s ✭❝✐r✉r❣✐❛✱ ❛♥❣✐♦♣❧❛st✐❛ ❡ ♠❡❞✐❝❛♠❡♥t♦s♦✮ ✉t✐❧✐③❛❞❛s ♥♦ tr❛t❛♠❡♥t♦ ❞❡ ♣❛❝✐❡♥t❡s ❝♦♠ ❞♦❡♥ç❛ ❝♦r♦♥❛r✐❛♥❛ ♠✉❧t✐❛rt❡r✐❛❧✳ ❊♠ t♦❞♦s ♦s ♠♦❞❡❧♦s✱ ❛s ❢✉♥çõ❡s ❞❡ ❧✐❣❛çã♦ ❧♦❣✐t♦ ❡ ❝♦♠♣❧❡♠❡♥t♦ ❧♦❣✲❧♦❣ ❢♦r❛♠ ✉t✐❧✐③❛❞❛s ♣❛r❛ ♠♦❞❡❧❛r ❛ ♣r♦♣♦rçã♦ ❞❡ s♦❜r❡✈✐✈❡♥t❡s ❞❡ ❧♦♥❣❛ ❞✉r❛çã♦ ✭✐♥❞✐✈í❞✉♦s ♥ã♦ s✉s❝❡tí✈❡✐s✮✳ ◗✉❛♥t♦ à ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❞♦s ✐♥❞✐✈í❞✉♦s s✉s❝❡tí✈❡✐s✱ ❢♦r❛♠ ✉t✐❧✐③❛❞♦s ♦s ♠♦❞❡❧♦s ❞❡ ❲❡✐❜✉❧❧ ❡ ❞❡ ❈♦①✳ ❈♦✈❛r✐á✈❡✐s ❢♦r❛♠ ❝♦♥s✐❞❡r❛❞❛s t❛♥t♦ ♥❛ ♣r♦♣♦rçã♦ ❞❡ s♦❜r❡✈✐✈❡♥t❡s ❞❡ ❧♦♥❣❛ ❞✉r❛çã♦ q✉❛♥t♦ ♥❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❞♦s ✐♥❞✐✈í❞✉♦s s✉s❝❡tí✈❡✐s✳ ❉❡ ♠♦❞♦ ❣❡r❛❧✱ ♦s ♠♦❞❡❧♦s ❝♦♥s✐✲ ❞❡r❛❞♦s s❡ ♠♦str❛r❛♠ ❛❞❡q✉❛❞♦s ♣❛r❛ ❛♥❛❧✐s❛r ♦s ❞❛❞♦s ❞♦ ❡♥s❛✐♦ ❝❧í♥✐❝♦ ❛❧❡❛t♦r✐③❛❞♦✱ ✐♥❞✐❝❛♥❞♦ ❛ ❝✐r✉r❣✐❛ ❝♦♠♦ ❛ ❡str❛té❣✐❛ t❡r❛♣ê✉t✐❝❛ ♠❛✐s ❡✜❝✐❡♥t❡✳ ■♥❞✐❝❛r❛♠ t❛♠❜é♠✱ q✉❡ ❛s ❝♦✈❛r✐á✈❡✐s ✐❞❛❞❡✱ ❤✐♣❡rt❡♥sã♦ ❡ ❞✐❛❜❡t❡s ♠❡❧❧✐t✉s ❡①❡r❝❡♠ ✐♥✢✉ê♥❝✐❛ ♥❛ ♦❝♦rrê♥❝✐❛ ❞♦ ó❜✐t♦ ❝❛r❞í❛❝♦✱ ♠❛s ♥ã♦ ♥♦ t❡♠♣♦ ❛té ❛ ♦❝♦rrê♥❝✐❛ ❞❡st❡ ó❜✐t♦ ♥♦s ♣❛❝✐❡♥t❡s s✉s❝❡tí✈❡✐s✳ P❛❧❛✈r❛s✲❝❤❛✈❡✿ ❆♥á❧✐s❡ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛❀ ▼♦❞❡❧♦ ❧♦❣íst✐❝♦❀ ❋r❛çã♦ ❞❡ ❝✉r❛❀ ▼♦❞❡❧♦s ❞❡
✶✶ ❆❇❙❚❘❆❈❚
P❛r❛♠❡tr✐❝ ❛♥❞ s❡♠✐♣❛r❛♠❡tr✐❝ ❧♦♥❣✲t❡r♠ s✉r✈✐✈❛❧ ♠♦❞❡❧s ❛♣♣❧✐❡❞ t♦ ❛ r❛♥❞♦♠✐③❡❞ ❝❧✐♥✐❝❛❧ tr✐❛❧
❙❡✈❡r❛❧ ♠♦❞❡❧s ❤❛✈❡ ❜❡❡♥ ♣r♦♣♦s❡❞ ✐♥ t❤❡ ❧✐t❡r❛t✉r❡ ✇✐t❤ t❤❡ ❛✐♠ ♦❢ ❛♥❛❧②③✐♥❣ s✉r✈✐✈❛❧ ❞❛t❛ ✇❤❡♥ t❤❡ ♣♦♣✉❧❛t✐♦♥ ✉♥❞❡r st✉❞② ✐s ❛ss✉♠❡❞ t♦ ❜❡ ❛ ♠✐①t✉r❡ ♦❢ s✉s❝❡♣t✐❜❧❡ ✭❛t r✐s❦✮ ❛♥❞ ♥♦t s✉s❝❡♣t✐❜❧❡ ✐♥❞✐✈✐❞✉❛❧s t♦ ❛ s♣❡❝✐✜❝ ❡✈❡♥t ♦❢ ✐♥t❡r❡st✳ ❙✉❝❤ ♠♦❞❡❧s ❛r❡ ✉s✉❛❧❧② ❝❛❧❧❡❞ ❧♦♥❣✲t❡r♠ s✉r✈✐✈♦rs ♠♦❞❡❧s ♦r ❝✉r❡ r❛t❡ ♠♦❞❡❧s✳ ■♥ t❤✐s ✇♦r❦✱ s❡✈❡r❛❧ ♦❢ t❤❡s❡ ♠♦❞❡❧s ✭✉♥❞❡r ❜♦t❤ ♣❛r❛♠❡tr✐❝ ❛♥❞ s❡♠✐✲♣❛r❛♠❡tr✐❝ ❛♣♣r♦❛❝❤❡s✮ ✇❡r❡ ❝♦♥s✐❞❡r❡❞ t♦ ❛♥❛❧②③❡ t❤❡ ❞❛t❛ ❢r♦♠ ❛ r❛♥❞♦♠✐③❡❞ ❝❧✐♥✐❝❛❧ tr✐❛❧ ❝♦♥❞✉❝t❡❞ ✐♥ ♦r❞❡r t♦ ❝♦♠♣❛r❡ t❤r❡❡ t❤❡r❛♣❡✉t✐❝ str❛t❡❣✐❡s ✭s✉r❣❡r②✱ ❛♥❣✐♦♣❧❛st② ❛♥❞ ♠❡❞✐❝✐♥❡✮ ✉s❡❞ ✐♥ t❤❡ tr❡❛t♠❡♥t ♦❢ ♣❛t✐❡♥ts ✇✐t❤ ♠✉❧t✐✈❡ss❡❧ ❝♦r♦♥❛r② ❛rt❡r② ❞✐s❡❛s❡✳ ❋♦r ❛❧❧ ♠♦❞❡❧s t❤❡ ❧♦❣✐t ❛♥❞ ❝♦♠♣❧❡♠❡♥t❛r② ❧♦❣✲ ❧♦❣ ❧✐♥❦ ❢✉♥❝t✐♦♥s ✇❡r❡ ✉s❡❞ t♦ ♠♦❞❡❧ t❤❡ ♣r♦♣♦rt✐♦♥ ♦❢ ❧♦♥❣✲t❡r♠ s✉r✈✐✈♦rs ✭♥♦t s✉s❝❡♣t✐❜❧❡ ✐♥❞✐✈✐❞✉❛❧s✮✳ ■♥ r❡❣❛r❞s t♦ t❤❡ s✉r✈✐✈❛❧ ❢✉♥❝t✐♦♥ ♦❢ t❤❡ s✉s❝❡♣t✐❜❧❡ ✐♥❞✐✈✐❞✉❛❧s✱ t❤❡ ❲❡✐❜✉❧❧ ❛♥❞ ❈♦① ♠♦❞❡❧s ✇❡r❡ ✉s❡❞✳ ❈♦✈❛r✐❛t❡s ✇❡r❡ ❝♦♥s✐❞❡r❡❞ ❜♦t❤ ✐♥ t❤❡ ♣r♦♣♦rt✐♦♥ ♦❢ ❧♦♥❣✲ t❡r♠ s✉r✈✐✈♦rs ❛♥❞ ✐♥ t❤❡ s✉r✈✐✈❛❧ ❢✉♥❝t✐♦♥ ♦❢ t❤❡ s✉s❝❡♣t✐❜❧❡ ✐♥❞✐✈✐❞✉❛❧s✳ ❖✈❡r❛❧❧✱ t❤❡ ♠♦❞❡❧s ❝♦♥s✐❞❡r❡❞ ✇❡r❡ s✉✐t❛❜❧❡ ❢♦r ❛♥❛❧②③✐♥❣ t❤❡ ❞❛t❛ ❢r♦♠ t❤❡ r❛♥❞♦♠✐③❡❞ ❝❧✐♥✐❝❛❧ tr✐❛❧ ✐♥❞✐❝❛t✐♥❣ s✉r❣❡r② ❛s t❤❡ ♠♦st ❡✛❡❝t✐✈❡ t❤❡r❛♣❡✉t✐❝ str❛t❡❣②✳ ❚❤❡② ❛❧s♦ ✐♥❞✐❝❛t❡❞ t❤❛t t❤❡ ❝♦✈❛r✐❛t❡s ❛❣❡✱ ❤②♣❡rt❡♥s✐♦♥ ❛♥❞ ❞✐❛❜❡t❡s ♠❡❧❧✐t✉s ❡①❤✐❜✐t ✐♥✢✉❡♥❝❡ ♦♥ t❤❡ ♦❝❝✉rr❡♥❝❡ ♦❢ ❝❛r❞✐❛❝ ❞❡❛t❤✱ ❜✉t ♥♦t ♦♥ t❤❡ t✐♠❡ t♦ t❤❡ ♦❝❝✉rr❡♥❝❡ ♦❢ t❤✐s ❞❡❛t❤ ✐♥ s✉s❝❡♣t✐❜❧❡ ♣❛t✐❡♥ts✳
✶✸
▲■❙❚❆ ❉❊ ❋■●❯❘❆❙
❋✐❣✉r❛ ✶ ✲ ❘❡♣r❡s❡♥t❛çã♦ ❣rá✜❝❛ ❞❡ ❞✉❛s ♣♦ssí✈❡✐s ❢♦r♠❛s ❞❛ ❝✉r✈❛ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ♦❜t✐❞❛ ♣❡❧♦ ❡st✐♠❛❞♦r ❞❡ ❑❛♣❧❛♥✲▼❡✐❡r✳ ❆ ❝✉r✈❛ à ❡sq✉❡r❞❛ ♥ã♦ ❛t✐♥❣❡ ♦ ✈❛❧♦r ③❡r♦✱ ♦ q✉❡ ♦❝♦rr❡ q✉❛♥❞♦ ♦ ♠❛✐♦r t❡♠♣♦ ♦❜s❡r✈❛❞♦ ♥❛ ❛♠♦str❛ ❢♦r ✉♠❛ ❝❡♥s✉r❛✳ ❏á ❛ ❝✉r✈❛ à ❞✐r❡✐t❛ ❛t✐♥❣❡ ♦ ✈❛❧♦r ③❡r♦✱ ✉♠❛ ✈❡③ q✉❡ ♦ ♠❛✐♦r t❡♠♣♦ ♦❜s❡r✈❛❞♦ r❡❢❡r❡✲s❡ ❛ ✉♠❛ ❢❛❧❤❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ❋✐❣✉r❛ ✷ ✲ ❈✉r✈❛ ❞❡ ❑❛♣❧❛♥✲▼❡✐❡r ❡st✐♠❛❞❛ ♣❛r❛ ♦s ❞❛❞♦s ❞❡ t❡♠♣♦ ❛té ♦ ó❜✐t♦
❝❛r❞í❛❝♦ r❡❣✐str❛❞♦s ♣❛r❛ ♦s ✻✶✶ ♣❛❝✐❡♥t❡s ♣❛rt✐❝✐♣❛♥t❡s ❞♦ ❡st✉❞♦ ▼❆❙❙ ■■ ✭❍❯❊❇ ❡t ❛❧✳✱ ✷✵✶✵✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ❋✐❣✉r❛ ✸ ✲ ■❧✉str❛çã♦ ❞♦ ❣rá✜❝♦ ❞❡ ❲♦r♠ P❧♦t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ❋✐❣✉r❛ ✹ ✲ ❈✉r✈❛s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ♦❜t✐❞❛s ♣❛r❛ ❝❛❞❛ ❝♦✈❛r✐á✈❡❧ ♣❡❧♦ ♠ét♦❞♦ ❞❡
❑❛♣❧❛♥✲▼❡✐❡r ❡ r❡s♣❡❝t✐✈♦s r❡s✉❧t❛❞♦s ❞♦ t❡st❡ ❧♦❣r❛♥❦✱ ❝♦♥s✐❞❡r❛♥❞♦ ❛ ❛♠♦str❛ ❝♦♠♣❧❡t❛ ✭n = 611✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾
❋✐❣✉r❛ ✺ ✲ ❈✉r✈❛s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ♦❜t✐❞❛s ♣❛r❛ ❝❛❞❛ ❝♦✈❛r✐á✈❡❧ ♣❡❧♦ ♠ét♦❞♦ ❞❡ ❑❛♣❧❛♥✲▼❡✐❡r ❡ r❡s♣❡❝t✐✈♦s r❡s✉❧t❛❞♦s ❞♦ t❡st❡ ❧♦❣r❛♥❦✱ ❝♦♥s✐❞❡r❛♥❞♦ ❛ s✉❜✲❛♠♦str❛ ❞♦s ✐♥❞✐✈í❞✉♦s q✉❡ ❢❛❧❤❛r❛♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ❋✐❣✉r❛ ✻ ✲ ●rá✜❝♦s ❲♦r♠ ❞♦s q✉❛♥t✐s r❡s✐❞✉❛✐s✿ ✭❛✮ ▼♦❞❡❧♦ ❞❡ t❡♠♣♦ ❞❡ ♣r♦♠♦✲
çã♦ P♦✐ss♦♥✲▲♦❣✐t♦✲❲❡✐❜✉❧❧❀ ✭❜✮ ▼♦❞❡❧♦ ❞❡ t❡♠♣♦ ❞❡ ♣r♦♠♦çã♦ ❇✐♥♦♠✐❛❧ ◆❡❣❛t✐✈♦✲▲♦❣✐t♦✲❲❡✐❜✉❧❧❀ ❡ ✭❝✮ ▼♦❞❡❧♦ ❞❡ ♠✐st✉r❛ ▲♦❣✐t♦✲❲❡✐❜✉❧❧ ✳ ✳ ✳ ✳ ✼✸ ❋✐❣✉r❛ ✼ ✲ ❊st✐♠❛t✐✈❛s ❞❡ ❑❛♣❧❛♥✲▼❡✐❡r ❞❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❣❧♦❜❛❧ ❡ ❡st✐✲
♠❛t✐✈❛s ♦❜t✐❞❛s ♣❡❧♦s ♠♦❞❡❧♦s ✭❧✐♥❤❛ ✈❡r♠❡❧❤❛✮✿✭❛✮ ▼♦❞❡❧♦ ❞❡ Pr♦♠♦✲ çã♦ P♦✐ss♦♥✲▲♦❣✐t♦✲❲❡✐❜✉❧❧❀ ✭❜✮ ▼♦❞❡❧♦ ❞❡ t❡♠♣♦ ❞❡ ♣r♦♠♦çã♦ ❇✐♥♦♠✐❛❧ ◆❡❣❛t✐✈♦✲▲♦❣✐t♦✲❲❡✐❜✉❧❧❀ ❡ ✭❝✮ ▼♦❞❡❧♦ ❞❡ ♠✐st✉r❛ ▲♦❣✐t♦✲❲❡✐❜✉❧❧✱ s❡♠ ❝♦♥s✐❞❡r❛r ❝♦✈❛r✐á✈❡✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸ ❋✐❣✉r❛ ✽ ✲ ❊st✐♠❛t✐✈❛s ❞❡ ❑❛♣❧❛♥✲▼❡✐❡r ❞❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❡ ❡st✐♠❛t✐✈❛s
✶✹
❋✐❣✉r❛ ✾ ✲ ❊st✐♠❛t✐✈❛s ❞❡ ❑❛♣❧❛♥✲▼❡✐❡r ❞❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❡ ❡st✐♠❛t✐✈❛s ♦❜t✐❞❛s ♣❡❧♦s ♠♦❞❡❧♦s ✭❧✐♥❤❛ ✈❡r♠❡❧❤❛✮✿✭❛✮ ▼♦❞❡❧♦ ❞❡ t❡♠♣♦ ❞❡ ♣r♦♠♦✲ çã♦ P♦✐ss♦♥✲▲♦❣✐t♦✲❲❡✐❜✉❧❧❀ ✭❜✮ ▼♦❞❡❧♦ ❞❡ t❡♠♣♦ ❞❡ ♣r♦♠♦çã♦ ❇✐♥♦♠✐❛❧ ◆❡❣❛t✐✈♦✲▲♦❣✐t♦✲❲❡✐❜✉❧❧❀ ❡ ✭❝✮ ▼♦❞❡❧♦ ❞❡ ♠✐st✉r❛ ▲♦❣✐t♦✲❲❡✐❜✉❧❧✱ ❝♦♥✲ s✐❞❡r❛♥❞♦ ❛ ❝♦♠❜✐♥❛çã♦ ✭✷✱✶✱✵✱✵✮ ❞❛ ❚❛❜❡❧❛ ✷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹ ❋✐❣✉r❛ ✶✵ ✲❊st✐♠❛t✐✈❛s ❞❡ ❑❛♣❧❛♥✲▼❡✐❡r ❞❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❡ ❡st✐♠❛t✐✈❛s
♦❜t✐❞❛s ♣❡❧♦s ♠♦❞❡❧♦s ✭❧✐♥❤❛ ✈❡r♠❡❧❤❛✮✿✭❛✮ ▼♦❞❡❧♦ ❞❡ t❡♠♣♦ ❞❡ ♣r♦♠♦✲ çã♦ P♦✐ss♦♥✲▲♦❣✐t♦✲❲❡✐❜✉❧❧❀ ✭❜✮ ▼♦❞❡❧♦ ❞❡ t❡♠♣♦ ❞❡ ♣r♦♠♦çã♦ ❇✐♥♦♠✐❛❧ ◆❡❣❛t✐✈♦✲▲♦❣✐t♦✲❲❡✐❜✉❧❧❀ ❡ ✭❝✮ ▼♦❞❡❧♦ ❞❡ ♠✐st✉r❛ ▲♦❣✐t♦✲❲❡✐❜✉❧❧✱ ❝♦♥✲ s✐❞❡r❛♥❞♦ ❛ ❝♦♠❜✐♥❛çã♦ ✭✸✱✶✱✵✱✵✮ ❞❛ ❚❛❜❡❧❛ ✷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺ ❋✐❣✉r❛ ✶✶ ✲❘❡sí❞✉♦s ❉❡✈✐❛♥❝❡ ♣❛r❛ ♦s ♠♦❞❡❧♦s✿ ✭❛✮ ▼✐st✉r❛ ▲♦❣✐t♦✲❈♦① ❡ ✭❜✮ ▼✐s✲
t✉r❛ ▲♦❣✐t♦✲❈♦①✲■❆▼ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷ ❋✐❣✉r❛ ✶✷ ✲❘❡sí❞✉♦s ▼❛rt✐♥❣❛❧ ♣❛r❛ ♦s ♠♦❞❡❧♦s✿ ✭❛✮ ▼✐st✉r❛ ▲♦❣✐t♦✲❈♦① ❡ ✭❜✮ ▼✐s✲
t✉r❛ ▲♦❣✐t♦✲❈♦①✲■❆▼ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷ ❋✐❣✉r❛ ✶✸ ✲❊st✐♠❛t✐✈❛s ❞❡ ❑❛♣❧❛♥✲▼❡✐❡r ❞❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❣❧♦❜❛❧ ✈❡rs✉s às
♦❜t✐❞❛s ♣❡❧♦s ♠♦❞❡❧♦s ✭❧✐♥❤❛s ✈❡r♠❡❧❤❛✮✿ ✭❛✮ ▼♦❞❡❧♦ ❞❡ ▼✐st✉r❛ ▲♦❣✐t♦✲ ❈♦① ❡ ✭❜✮ ▼♦❞❡❧♦ ❞❡ ▼✐st✉r❛ ▲♦❣✐t♦✲❈♦①✲■❆▼✱ s❡♠ ❝♦♥s✐❞❡r❛r ❝♦✈❛r✐á✈❡✐s ✽✸ ❋✐❣✉r❛ ✶✹ ✲❊st✐♠❛t✐✈❛s ❞❡ ❑❛♣❧❛♥✲▼❡✐❡r ❞❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❡ ❛s ❡st✐♠❛t✐✈❛s
♦❜t✐❞❛s ♣❡❧♦ ▼♦❞❡❧♦ ❞❡ ▼✐st✉r❛ ▲♦❣✐t♦✲❈♦① ✭❧✐♥❤❛ ✈❡r♠❡❧❤❛✮✱ ♣❛r❛ ❝❛❞❛ ❣r✉♣♦ ❞❡ tr❛t❛♠❡♥t♦✱ ❝♦♥s✐❞❡r❛♥❞♦ ❛ ❝♦♠❜✐♥❛çã♦ ❍❆❙❂✶✱■❞❛❞❡✻✺❂✵ ❡ ❉▼❂✵ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹ ❋✐❣✉r❛ ✶✺ ✲❊st✐♠❛t✐✈❛s ❞❡ ❑❛♣❧❛♥✲▼❡✐❡r ❞❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❡ ❛s ❡st✐✲
♠❛t✐✈❛s ♦❜t✐❞❛s ♣❡❧♦ ▼♦❞❡❧♦ ❞❡ ▼✐st✉r❛ ▲♦❣✐t♦✲❈♦①✲■❆▼ ✭❧✐♥❤❛ ✈❡r✲ ♠❡❧❤❛✮✱ ♣❛r❛ ❝❛❞❛ ❣r✉♣♦ ❞❡ tr❛t❛♠❡♥t♦✱ ❝♦♥s✐❞❡r❛♥❞♦ ❛ ❝♦♠❜✐♥❛çã♦ ❍❆❙❂✶✱■❞❛❞❡✻✺❂✵✱ ❉▼❂✵ ❡ ■❆▼❂✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹ ❋✐❣✉r❛ ✶✻ ✲❊st✐♠❛t✐✈❛s ❞❡ ❑❛♣❧❛♥✲▼❡✐❡r ❞❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❣❧♦❜❛❧ ❡ ❛s ❡s✲
t✐♠❛t✐✈❛s ♦❜t✐❞❛s ♣❡❧♦s ▼♦❞❡❧♦s✭❧✐♥❤❛ ✈❡r♠❡❧❤❛✮✿✭❛✮▼♦❞❡❧♦ ❞❡ t❡♠♣♦ ❞❡ ♣r♦♠♦çã♦ P♦✐ss♦♥✲▲♦❣✐t♦✲❲❡✐❜✉❧❧ ❡ ✭❜✮ ▼♦❞❡❧♦ ❞❡ ▼✐st✉r❛ ▲♦❣✐t♦✲❈♦① ✳ ✾✺ ❋✐❣✉r❛ ✶✼ ✲❊st✐♠❛t✐✈❛s ❞❡ ❑❛♣❧❛♥✲▼❡✐❡r ❞❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❡ ❛s ❡st✐♠❛t✐✈❛s
✶✺ ❋✐❣✉r❛ ✶✽ ✲❊st✐♠❛t✐✈❛s ❞❡ ❑❛♣❧❛♥✲▼❡✐❡r ❞❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❡ ❛s ❡st✐♠❛t✐✈❛s
✶✻
✶✼
▲■❙❚❆ ❉❊ ❚❆❇❊▲❆❙
❚❛❜❡❧❛ ✶ ✲ ❈❛r❛❝t❡ríst✐❝❛s ❞♦s ✻✶✶ ♣❛❝✐❡♥t❡s ❞❡s✐❣♥❛❞♦s ❛ ▼❚✱ P❈■ ❡ ❈❆❇● ♥♦ ❡st✉❞♦ ▼❆❙❙ ■■ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ❚❛❜❡❧❛ ✷ ✲ ❊st❛tíst✐❝❛s ♣❛r❛ ❝❛❞❛ ✉♠❛ ❞❛s ✷✹ ❝♦♠❜✐♥❛çõ❡s ❡♥tr❡ ❛s ❝❛t❡❣♦r✐❛s ❞❛s
❝♦✈❛r✐á✈❡✐s ●♣s✱ ❍❆❙✱ ■❞❛❞❡✻✺ ❡ ❉▼ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶ ❚❛❜❡❧❛ ✸ ✲ ❊st❛tíst✐❝❛s ❛ss♦❝✐❛❞❛s ❛♦s ♠♦❞❡❧♦s ❛❥✉st❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸ ❚❛❜❡❧❛ ✹ ✲ ❊st✐♠❛t✐✈❛s ❞❡ ♠á①✐♠❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ♦❜t✐❞❛s ❛ ♣❛rt✐r ❞♦ ♠♦❞❡❧♦ ❞❡
t❡♠♣♦ ❞❡ ♣r♦♠♦çã♦ P♦✐ss♦♥✲▲♦❣✐t♦✲❲❡✐❜✉❧❧ ❛❥✉st❛❞♦ ❛♦s ❞❛❞♦s ❞♦ ❡st✉❞♦ ▼❆❙❙ ■■ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻ ❚❛❜❡❧❛ ✺ ✲ Pr♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ✉♠ ✐♥❞✐✈í❞✉♦ s❡r s♦❜r❡✈✐✈❡♥t❡ ❞❡ ❧♦♥❣❛ ❞✉r❛çã♦ ❡st✐✲
♠❛❞❛ ❛ ♣❛rt✐r ❞♦ ▼♦❞❡❧♦ ❞❡ t❡♠♣♦ ❞❡ ♣r♦♠♦çã♦ P♦✐ss♦♥✲▲♦❣✐t♦✲❲❡✐❜✉❧❧✱ ♣❛r❛ ❝❛❞❛ ✉♠ ❞❛s ✷✹ ❝♦♠❜✐♥❛çõ❡s ✭●♣s✱❍❆❙✱■❞❛❞❡✻✺✱❉▼✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✼ ❚❛❜❡❧❛ ✻ ✲ ■♥t❡r✈❛❧♦s ❞❡ ❈♦♥✜❛♥ç❛ ✭✾✺✪✮ ♣❛r❛ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ✉♠ ✐♥❞✐✈í❞✉♦
s❡r s♦❜r❡✈✐✈❡♥t❡ ❞❡ ❧♦♥❣❛ ❞✉r❛çã♦✱ ❝♦♥s✐❞❡r❛♥❞♦ ♦ ♠♦❞❡❧♦ ❞❡ t❡♠♣♦ ❞❡ ♣r♦♠♦çã♦ P♦✐ss♦♥✲▲♦❣✐t♦✲❲❡✐❜✉❧❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✼ ❚❛❜❡❧❛ ✼ ✲ ❘❛③õ❡s ❞❡ ❝❤❛♥❝❡s ♣❛r❛ ❛❧❣✉♥s ❝❡♥ár✐♦s✱ ❝♦♥s✐❞❡r❛♥❞♦ ❛s ❡st✐♠❛t✐✈❛s ♦❜✲
t✐❞❛s ♣❡❧♦ ♠♦❞❡❧♦ ❞❡ t❡♠♣♦ ❞❡ ♣r♦♠♦çã♦ P♦✐ss♦♥✲▲♦❣✐t♦✲❲❡✐❜✉❧❧ ✳ ✳ ✳ ✳ ✼✾ ❚❛❜❡❧❛ ✽ ✲ Pr♦❜❛❜✐❧✐❞❛❞❡ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❡st✐♠❛❞❛✱ Sˆp(t)✱ ♣❛r❛ t♦❞❛s ❛s ❝♦♠❜✐♥❛✲
çõ❡s ❞❛s ❝♦✈❛r✐á✈❡✐s ✭●♣s✱❍❆❙✱■❞❛❞❡✻✺✱❉▼✮ ♥♦s t❡♠♣♦s t = 1✱ ✺ ❡ ✶✵
❛♥♦s ❝♦♥s✐❞❡r❛♥❞♦ ♦ ♠♦❞❡❧♦ ❞❡ t❡♠♣♦ ♣r♦♠♦çã♦ P♦✐ss♦♥✲▲♦❣✐t♦✲❲❡✐❜✉❧❧ ✽✵ ❚❛❜❡❧❛ ✾ ✲ ❊st❛tíst✐❝❛s ♣❛r❛ ♠♦❞❡❧♦s ❛❥✉st❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶ ❚❛❜❡❧❛ ✶✵ ✲❊st✐♠❛t✐✈❛s ❞❡ ♠á①✐♠❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ✈✐❛ ❛❧❣♦r✐t♠♦ ❊▼✱ ♦❜t✐❞❛s ❛
♣❛rt✐r ❞♦ ♠♦❞❡❧♦ ❞❡ ♠✐st✉r❛ ▲♦❣✐t♦✲❈♦① ❛❥✉st❛❞♦ ❛♦s ❞❛❞♦s ❞♦ ❡st✉❞♦ ▼❆❙❙ ■■ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺ ❚❛❜❡❧❛ ✶✶ ✲Pr♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ✉♠ ✐♥❞✐✈í❞✉♦ s❡r s♦❜r❡✈✐✈❡♥t❡ ❞❡ ❧♦♥❣❛ ❞✉r❛çã♦✱ ❡st✐✲
♠❛❞❛ ❛ ♣❛rt✐r ❞♦ ♠♦❞❡❧♦ ❞❡ ▼✐st✉r❛ ▲♦❣✐t♦✲❈♦①✱ ♣❛r❛ ❝❛❞❛ ✉♠❛ ❞❛s ✷✹ ❝♦♠❜✐♥❛çõ❡s ✭●♣s✱❍❆❙✱■❞❛❞❡✻✺✱❉▼✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✻ ❚❛❜❡❧❛ ✶✷ ✲■♥t❡r✈❛❧♦s ❞❡ ❈♦♥✜❛♥ç❛ ✭✾✺✪✮ ♣❛r❛ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ✉♠ ✐♥❞✐✈í❞✉♦
s❡r s♦❜r❡✈✐✈❡♥t❡ ❞❡ ❧♦♥❣❛ ❞✉r❛çã♦✱ ❝♦♥s✐❞❡r❛♥❞♦ ♦ ♠♦❞❡❧♦ ❞❡ ♠✐st✉r❛ ▲♦❣✐t♦✲❈♦① ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✼ ❚❛❜❡❧❛ ✶✸ ✲❘❛③õ❡s ❞❡ ❝❤❛♥❝❡s ♣❛r❛ ❛❧❣✉♥s ❝❡♥ár✐♦s✱ ❝♦♥s✐❞❡r❛♥❞♦ ❛s ❡st✐♠❛t✐✈❛s ♦❜✲
✶✽
❚❛❜❡❧❛ ✶✹ ✲Pr♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ❙♦❜r❡✈✐✈ê♥❝✐❛ ❡st✐♠❛❞❛✱ Sˆp(t)✱ ♣❛r❛ t♦❞❛s ❛s ❝♦♠❜✐♥❛✲ çõ❡s ❞❛s ❝♦✈❛r✐á✈❡✐s ✭●♣s✱❍❆❙✱■❞❛❞❡✻✺✱❉▼✮ ♥♦s t❡♠♣♦s t ❂ ✶✱ ✺ ❡ ✶✵ ❛♥♦s✱ ❝♦♥s✐❞❡r❛♥❞♦ ♦ ♠♦❞❡❧♦ ❞❡ ♠✐st✉r❛ ▲♦❣✐t♦✲❈♦① ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✵ ❚❛❜❡❧❛ ✶✺ ✲❊st✐♠❛t✐✈❛s ❞❡ ♠á①✐♠❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ♦❜t✐❞❛s ❛ ♣❛rt✐r ❞♦s ♠♦❞❡❧♦s
❞❡ t❡♠♣♦ ❞❡ ♣r♦♠♦çã♦ P♦✐ss♦♥✲▲♦❣✐t♦✲❲❡✐❜✉❧❧ ❡ ▼✐st✉r❛ ▲♦❣✐t♦✲❈♦①✱ ❛❥✉st❛❞♦s ❛♦s ❞❛❞♦s ❞♦ ❡st✉❞♦ ▼❆❙❙ ■■ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✶ ❚❛❜❡❧❛ ✶✻ ✲Pr♦❜❛❜✐❧✐❞❛❞❡ ✉♠ ✐♥❞✐✈í❞✉♦ s❡r s♦❜r❡✈✐✈❡♥t❡ ❞❡ ❧♦♥❣❛ ❞✉r❛çã♦✱ ❡st✐♠❛❞❛
❛ ♣❛rt✐r ❞♦s ♠♦❞❡❧♦s ❞❡ ❚❡♠♣♦ ❞❡ Pr♦♠♦çã♦ P♦✐ss♦♥✲▲♦❣✐t♦✲❲❡✐❜✉❧❧ ❡ ▼✐st✉r❛ ▲♦❣✐t♦✲❈♦① ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✷ ❚❛❜❡❧❛ ✶✼ ✲❘❛③ã♦ ❞❡ ❝❤❛♥❝❡s✱ ❝♦♥s✐❞❡r❛♥❞♦ ❛s ❡st✐♠❛t✐✈❛s ♦❜t✐❞❛s ♣❡❧♦s ♠♦❞❡❧♦s
❚❡♠♣♦ ❞❡ Pr♦♠♦çã♦ P♦✐ss♦♥✲▲♦❣✐t♦✲❲❡✐❜✉❧❧ ❡ ▼✐st✉r❛ ▲♦❣✐t♦✲❈♦① ✳ ✳ ✳ ✾✸ ❚❛❜❡❧❛ ✶✽ ✲Pr♦❜❛❜✐❧✐❞❛❞❡ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❡st✐♠❛❞❛✱ Sˆp(t)✱ ♣❛r❛ t♦❞❛s ❛s ❝♦♠❜✐♥❛✲
✶✾
✶ ■◆❚❘❖❉❯➬➹❖
Pr❡s❡♥t❡ ❡♠ ♣r❛t✐❝❛♠❡♥t❡ t♦❞❛s ❛s ár❡❛s ❞♦ ❝♦♥❤❡❝✐♠❡♥t♦✱ ❛ ❊st❛tíst✐❝❛ ❞❡s❡♥✈♦❧✈❡ ✉♠ ♣❛♣❡❧ ❞❡ ❞❡st❛q✉❡ ♥♦ q✉❡ ❞✐③ r❡s♣❡✐t♦ à ❛♥á❧✐s❡ ❞❡ ❞❛❞♦s✳ ❉❡♥tr♦ ❞❡ s✉❛ ❛♠♣❧❛ ár❡❛ ❞❡ ❛♣❧✐❝❛❜✐❧✐❞❛❞❡✱ ❛ ❛♥á❧✐s❡ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❢♦✐ ✉♠❛ ❞❛s q✉❡ ♠❛✐s ❝r❡s❝❡✉ ♥♦s ú❧t✐♠♦s ❛♥♦s✳ ❚❛❧ ❢❛t♦ é ❡✈✐❞❡♥❝✐❛❞♦ ♣❡❧❛ q✉❛♥t✐❞❛❞❡ ❞❡ ❛♣❧✐❝❛çõ❡s ♥❛s ♠❛✐s ❞✐✈❡rs❛s ár❡❛s ❞❡ ♣❡sq✉✐s❛✱ ❝♦♠ ❞❡st❛q✉❡ ❡s♣❡❝✐❛❧ ♥❛ ♠❡❞✐❝✐♥❛✳ ❊st❡ ❝r❡s❝✐♠❡♥t♦ s❡ ❞❡✈❡ ❡♠ ♣❛rt❡ ❛♦ ❛♣r✐♠♦r❛♠❡♥t♦ ❡ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ té❝♥✐❝❛s ❡ ♠ét♦❞♦s ❡st❛tíst✐❝♦s ❝❛❞❛ ✈❡③ ♠❛✐s ❡✜❝✐❡♥t❡s✱ ❛❧✐❛❞♦ ❛♦ ❣r❛♥❞❡ ❛✈❛♥ç♦ t❡❝♥♦❧ó❣✐❝♦ ❡ ❝♦♠♣✉t❛❝✐♦♥❛❧✳
❉❛❞♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ sã♦ ♣r♦✈❡♥✐❡♥t❡s✱ ❡♠ ❣❡r❛❧✱ ❞❡ ❡st✉❞♦s ❡♠ q✉❡ ♦ ✐♥t❡r❡ss❡ ❡stá ❡♠ ❛♥❛❧✐s❛r ♦ t❡♠♣♦ ❛té ❛ ♦❝♦rrê♥❝✐❛ ❞❡ ✉♠ ❞❡t❡r♠✐♥❛❞♦ ❡✈❡♥t♦✳ ◆❛ ❧✐t❡✲ r❛t✉r❛✱ t❛❧ t❡♠♣♦ é ❝♦♥❤❡❝✐❞♦ ❝♦♠♦ t❡♠♣♦ ❞❡ ❢❛❧❤❛✱ ✉♠❛ ✈❡③ q✉❡✱ ♥❛ ♠❛✐♦r✐❛ ❞♦s ❝❛s♦s✱ ❡❧❡ ❡stá r❡❧❛❝✐♦♥❛❞♦ ❛ ❡✈❡♥t♦s ✐♥❞❡s❡❥á✈❡✐s✱ ❝♦♠♦✱ ♣♦r ❡①❡♠♣❧♦✱ ❛ ♠♦rt❡ ❞❡ ✉♠ ♣❛❝✐❡♥t❡ ♦✉ ❛ ❢❛❧❤❛ ❞❡ ✉♠ ❝♦♠♣♦♥❡♥t❡ ❡❧❡trô♥✐❝♦✳ ❊st✉❞♦s ❡♠ q✉❡ s❡ tê♠ ❞❛❞♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ♣♦❞❡♠ s✉r❣✐r ♥❛s ♠❛✐s ❞✐✈❡rs❛s ár❡❛s✱ t❛✐s ❝♦♠♦✿ ❡♠ ♠❡❞✐❝✐♥❛✱ ❡♠ q✉❡ ♦ ✐♥t❡r❡ss❡ ♣♦❞❡ ❡st❛r ♥♦ t❡♠♣♦ ❞❡❝♦rr✐❞♦ ❞❡s❞❡ ♦ ❞✐❛❣♥óst✐❝♦ ❞❡ ✉♠❛ ❞❡t❡r♠✐♥❛❞❛ ❞♦❡♥ç❛ ❛té ❛ ♠♦rt❡ ❞♦ ♣❛❝✐❡♥t❡❀ ♥❛ ❡❞✉❝❛çã♦✱ ❡♠ q✉❡ ♦ ✐♥t❡r❡ss❡ ♣♦❞❡ ❡st❛r ♥♦ t❡♠♣♦ q✉❡ ✉♠ ❛❧✉♥♦ ❧❡✈❛ ♣❛r❛ ❝♦♥❝❧✉✐r ✉♠ ❝✉rs♦❀ ♥❛ ár❡❛ ❝r✐♠✐♥♦❧ó❣✐❝❛✱ ❡♠ q✉❡ ♦ ✐♥t❡r❡ss❡ ♣♦❞❡ ❡st❛r ♥♦ t❡♠♣♦ ❛té ✉♠ ❡①✲❞❡t❡♥t♦ r❡✐♥❝✐❞✐r ♥♦ ❝r✐♠❡❀ ♥❛ ❡♥❣❡♥❤❛r✐❛✱ ❡♠ q✉❡ ♦ ✐♥t❡r❡ss❡ ♣♦❞❡ ❡st❛r ♥♦ t❡♠♣♦ ❞❡ ✈✐❞❛ ❞❡ ✉♠ ❞❡t❡r♠✐♥❛❞♦ ❝♦♠♣♦♥❡♥t❡ ❡❧❡trô♥✐❝♦✱ ❞❡♥tr❡ ♦✉tr♦s✳
✷✵
✈❛r❛♠✱ ❡ ✈ê♠ ♠♦t✐✈❛♥❞♦✱ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ♠❡t♦❞♦❧♦❣✐❛s ♣❡❧♦s ♣❡sq✉✐s❛❞♦r❡s✱ ❝♦♠ ❞✐✈❡rs❛s ❞❡❧❛s ❛♣r❡s❡♥t❛❞❛s ♥❛ ❧✐t❡r❛t✉r❛✳ ❉❡♥tr❡ ❛s ♠❛✐s ❝♦♥❤❡❝✐❞❛s ❡stã♦ ♦ ❡st✐♠❛❞♦r ♥ã♦✲♣❛r❛♠étr✐❝♦ ❞❡ ❑❛♣❧❛♥ ❡ ▼❡✐❡r ✭❑❆P▲❆◆ ❡ ▼❊■❊❘✱ ✶✾✺✽✮ ❡ ♦ ♠♦❞❡❧♦ ❞❡ r❡❣r❡ssã♦ ❞❡ ❈♦① ✭❈❖❳✱ ✶✾✼✷✮✳
❆ ♣r❡s❡♥ç❛ ❞❡ ❝❡♥s✉r❛s ❡♠ ❞❛❞♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ✐♥❞✐❝❛ q✉❡ ♦ t❡♠♣♦ ❞❡ ❢❛❧❤❛ é s✉♣❡r✐♦r ❛♦ t❡♠♣♦ ♦❜s❡r✈❛❞♦✱ ♦✉ s❡❥❛✱ q✉❡ s❡ ♦ ✐♥❞✐✈í❞✉♦ ❢♦r ❛❝♦♠♣❛♥❤❛❞♦ ♣♦r ✉♠ ♣❡rí♦❞♦ ❞❡ t❡♠♣♦ s✉✜❝✐❡♥t❡♠❡♥t❡ ❣r❛♥❞❡✱ ❛ ❢❛❧❤❛ ❝❡rt❛♠❡♥t❡ ✐rá ❛❝♦♥t❡❝❡r✳ ❊♥tr❡t❛♥t♦✱ ❡♠ ♠✉✐t❛s s✐t✉❛çõ❡s ♣rát✐❝❛s✱ ✉♠❛ ❢r❛çã♦ ❞❡ ✐♥❞✐✈í❞✉♦s ♣♦❞❡ ♥ã♦ ❛♣r❡s❡♥t❛r ♦ ❡✈❡♥t♦ ❞❡ ✐♥t❡r❡ss❡✱ ♠❡s♠♦ s❡ ❢♦r❡♠ ❛❝♦♠♣❛♥❤❛❞♦s ❛té ♦ ✜♥❛❧ ❞❡ s✉❛s ✈✐❞❛s✳ ❯♠ ❡①❡♠♣❧♦ s✉r❣❡ q✉❛♥❞♦ s❡ ❞❡s❡❥❛ ❡st✉❞❛r ♦ t❡♠♣♦ ❛té ❛ r❡❝✐❞✐✈❛ ❞❡ ❝â♥❝❡r ✭❛♣ós tr❛t❛♠❡♥t♦✮ ❡♠ q✉❡ ✉♠❛ ♣❛rt❡ ❞❛ ♣♦♣✉❧❛çã♦ ❡♠ ❡st✉❞♦ ♣♦❞❡ ❡st❛r ❝✉r❛❞❛ ❡✱ ❛ss✐♠✱ ♥ã♦ ❛♣r❡s❡♥t❛r ♠❛✐s ❡ss❛ ❞♦❡♥ç❛✳ ❊♠ t❛✐s ❝❛s♦s✱ ❡①✐st❡ ✉♠❛ ❢r❛çã♦ ♥❛ ♣♦♣✉❧❛çã♦ q✉❡ é ❝♦♥s✐❞❡r❛❞❛ ✏✐♠✉♥❡✑ ♦✉ ✏❝✉r❛❞❛✑ ♣❛r❛ ♦ ❡✈❡♥t♦ ❞❡ ✐♥t❡r❡ss❡✳ ◆❡st❡ s❡♥t✐❞♦✱ ♠❡t♦❞♦❧♦❣✐❛s q✉❡ ✐♥❝♦r♣♦r❛♠ ❡♠ s✉❛s ❛♥á❧✐s❡s ❛ ♣r❡s❡♥ç❛ ❞❡ ✐♠✉♥❡s sã♦ ♥❡❝❡ssár✐❛s✱ t❡♥❞♦ ❡♠ ✈✐st❛ q✉❡ té❝♥✐❝❛s ✉s✉❛✐s ❞❡ ❛♥á❧✐s❡ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ q✉❡ ❞❡s❝♦♥s✐❞❡r❛♠ t❛❧ ✐♥❢♦r♠❛çã♦ ♣♦❞❡♠ ❝♦♥❞✉③✐r ❛ ❝♦♥❝❧✉sõ❡s ❞✐st♦r❝✐✲ ❞❛s✳ ▼♦❞❡❧♦s q✉❡ ✐♥❝♦r♣♦r❛♠ ✉♠❛ ❢r❛çã♦ ❞❡ ✐♠✉♥❡s ❡♠ s✉❛ ❡str✉t✉r❛ sã♦ ❝♦♥❤❡❝✐❞♦s ♥❛ ❧✐t❡r❛t✉r❛ ❝♦♠♦ ✏♠♦❞❡❧♦s ❞❡ ❢r❛çã♦ ❞❡ ❝✉r❛✑ ✭❝✉r❡ r❛t❡ ♠♦❞❡❧s✮ ♦✉ ✏♠♦❞❡❧♦s ❞❡ s♦❜r❡✈✐✲ ✈ê♥❝✐❛ ❞❡ ❧♦♥❣❛ ❞✉r❛çã♦✑ ✭❧♦♥❣✲t❡r♠ s✉r✈✐✈❛❧ ♠♦❞❡❧s✮✳ ❉❡♥tr❡ ❡❧❡s✱ ♣♦❞❡♠ s❡r ❝✐t❛❞♦s✱ ♦ ♠♦❞❡❧♦ ❞❡ ♠✐st✉r❛ ♣r♦♣♦st♦ ♣♦r ❇♦❛❣ ✭✶✾✹✾✮ ❡ ❇❡r❦s♦♥ ❡ ●❛❣❡ ✭✶✾✺✷✮✱ ♦ ♠♦❞❡❧♦ ❞❡ t❡♠♣♦ ❞❡ ♣r♦♠♦çã♦ ♣r♦♣♦st♦ ❡ ✐♥✈❡st✐❣❛❞♦ ♣♦r ❨❛❦♦✈❧❡✈ ❡t ❛❧✳ ✭✶✾✾✸✮ ❡ ❈❤❡♥✱ ■❜r❛❤✐♠ ❡ ❙✐♥❤❛ ✭✶✾✾✾✮✱ ♦ q✉❛❧ ❢♦✐ ♣♦st❡r✐♦r♠❡♥t❡ ❡st❡♥❞✐❞♦ ♣♦r ❘♦❞r✐❣✉❡s ❡t ❛❧✳ ✭✷✵✵✾✮✱ ❡ ♦ ♠♦❞❡❧♦ ❞❡ ❈♦① ❝♦♠ ❢r❛çã♦ ❞❡ ❝✉r❛✱ t❛♠❜é♠ ❝♦♥❤❡❝✐❞♦ ❝♦♠♦ ♠♦❞❡❧♦ ❞❡ ❢r❛çã♦ ❞❡ ❝✉r❛ s❡♠✐✲♣❛r❛♠étr✐❝♦✱ ♣r♦♣♦st♦ ♦r✐❣✐♥❛❧♠❡♥t❡ ♣♦r ❑✉❦ ❡ ❈❤❡♥ ✭✶✾✾✷✮✳ ❚❛♠❜é♠ ♥❛ ❧✐t❡r❛t✉r❛✱ sã♦ ❡♥❝♦♥tr❛❞❛s ♣r♦♣♦st❛s ♣❛r❛ ❛ ❛♥á❧✐s❡ ❞❡ ❞❛❞♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❝♦♠ ❢r❛çã♦ ❞❡ ✐♠✉♥❡s ♥❛ ♣r❡s❡♥ç❛ ❞❡ ❞❛❞♦s ❝♦rr❡❧❛❝✐♦♥❛❞♦s✱ ❝♦♠♦ é ♦ ❝❛s♦ ❞❡ P✐t❦❛♥✐❡♠✐ ❡t ❛❧✳ ✭✷✵✵✼✮ ❡ ▲♦❝❛t❡❧❧✐ ❡t ❛❧✳ ✭✷✵✵✼✮✱ q✉❡ ❡st✉❞❛r❛♠ ♠♦❞❡❧♦s ❝♦♠ ❢r❛çã♦ ❞❡ ❝✉r❛ ❡♠ ❞❛❞♦s ❡♥✈♦❧✈❡♥❞♦ ❢❛♠í❧✐❛s✳
✷✶ ❞♦❡♥ç❛ ❝♦r♦♥❛r✐❛♥❛ ♠✉❧t✐❛rt❡r✐❛❧✳ ❘❡s✉❧t❛❞♦s ❞❡ss❡ ❡♥s❛✐♦ ❝❧í♥✐❝♦ ♦❜t✐❞♦s ❛♣ós ✉♠✱ ❝✐♥❝♦ ❡ ❞❡③ ❛♥♦s ❞❡ ❛❝♦♠♣❛♥❤❛♠❡♥t♦ ❞♦s ♣❛❝✐❡♥t❡s ♣♦❞❡♠ s❡r ❡♥❝♦♥tr❛❞♦s ❡♠ ❍✉❡❜ ❡t ❛❧✳ ✭✷✵✵✹✱ ✷✵✵✼✱ ✷✵✶✵✮✳ ❯♠ ❞❡ss❡s r❡s✉❧t❛❞♦s r❡❧❛t❛ q✉❡ ❛♣ós ♦ ❛❝♦♠♣❛♥❤❛♠❡♥t♦ ❞♦s ♣❛❝✐❡♥t❡s ♣❡❧♦ ♣❡rí♦❞♦ ❞❡ ❞❡③ ❛♥♦s✱ ❢♦✐ ♦❜s❡r✈❛❞♦ ✉♠ ♣❡r❝❡♥t✉❛❧ ❞❡ ó❜✐t♦s ❞❡✈✐❞♦ ❛ ♣r♦❜❧❡♠❛s ❝❛r❞í❛❝♦s ❞❡ ❡♠ t♦r♥♦ ❞❡ ✶✺✪✳ ❉❡♥tr❡ ♦s q✉❡ ♥ã♦ ✈✐❡r❛♠ ❛ ó❜✐t♦ ♥❡ss❡ ♣❡rí♦❞♦✱ ♦❜s❡r✈❡ s❡r r❛③♦á✈❡❧ ❝♦♥s✐❞❡r❛r q✉❡ ✉♠❛ ♣❛rt❡ ❞❡❧❡s ✈❡♥❤❛ ❛ ó❜✐t♦ ❞❡✈✐❞♦ ❛ ♣r♦❜❧❡♠❛s ❝❛r❞í❛❝♦s ❡♠ ❛❧❣✉♠ ♠♦✲ ♠❡♥t♦ ❞❡ s✉❛s ✈✐❞❛s✱ ❡♥q✉❛♥t♦ ♦✉tr❛ ♣❛rt❡ ♥ã♦✳ ❚❛❧ ❢❛t♦ ❥✉st✐✜❝❛✱ ❛ss✐♠✱ ❛ ♠♦t✐✈❛çã♦ ❡♠ s❡ ✉t✐❧✐③❛r ♠♦❞❡❧♦s q✉❡ ❝♦♥s✐❞❡r❛♠ ❛ ♣r❡s❡♥ç❛ ❞❡ s♦❜r❡✈✐✈❡♥t❡s ❞❡ ❧♦♥❣❛ ❞✉r❛çã♦ ✭♦✉ ❞❡ ✉♠❛ ❢r❛çã♦ ❞❡ ✐♠✉♥❡s✮ ♣❛r❛ ❛ ❛♥á❧✐s❡ ❞❡ss❡s ❞❛❞♦s✳ ❆ ✈❛r✐á✈❡❧ r❡s♣♦st❛ ❞❡ ✐♥t❡r❡ss❡✱ ♥❡st❡ ❝❛s♦✱ é ♦ t❡♠♣♦ ❛té ♦ ó❜✐t♦ ❞♦ ♣❛❝✐❡♥t❡ ❞❡✈✐❞♦ ❛ ♣r♦❜❧❡♠❛s ❝❛r❞í❛❝♦s✳ ❆✐♥❞❛✱ ❛❧❣✉♠❛s ❝♦✈❛r✐á✈❡✐s ❛s q✉❛✐s s❡ t❡♠ ✐♥t❡r❡ss❡ ❡♠ ✈❡r✐✜❝❛r s✉❛s ❝♦rr❡s♣♦♥❞❡♥t❡s ❛ss♦❝✐❛çõ❡s ❝♦♠ ❡ss❡ t❡♠♣♦ sã♦✿ ❚r❛t❛♠❡♥t♦ ❆❧♦❝❛❞♦ ✭❊str❛té❣✐❛ ❚❡r❛♣ê✉t✐❝❛✮✱ ■❞❛❞❡✱ ❙❡①♦✱ ❍✐stór✐❝♦ ❞❡ ■♥❢❛rt♦ ❆❣✉❞♦ ❞♦ ▼✐♦❝ár❞✐♦✱ ❍✐♣❡rt❡♥sã♦✱ ❉✐❛❜❡t❡s ▼❡❧❧✐t✉s✱ ❈♦❧❡st❡r♦❧ ❚♦t❛❧✱ ❚❛❜❛❣✐s♠♦ ❡ ◆ú♠❡r♦ ❞❡ ❱❛s♦s ❙❛♥❣✉í♥❡♦s ❉♦❡♥t❡s✳
✷✷
✷✸ ✷ ❘❊❱■❙➹❖ ❇■❇▲■❖●❘➪❋■❈❆
✷✳✶ ❈♦♥❝❡✐t♦s ❜ás✐❝♦s ❞❡ ❛♥á❧✐s❡ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛
❆ ❛♥á❧✐s❡ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ s❡ ❝❛r❛❝t❡r✐③❛ ♣♦r ✉♠ ❝♦♥❥✉♥t♦ ❞❡ té❝♥✐❝❛s ❡st❛✲ tíst✐❝❛s ✉t✐❧✐③❛❞❛s q✉❛♥❞♦ s❡ ❞❡s❡❥❛ ❛♥❛❧✐s❛r ❞❛❞♦s ❝♦rr❡s♣♦♥❞❡♥t❡s ❛♦ t❡♠♣♦ ❞❡ ♦❝♦rrê♥❝✐❛ ❞❡ ✉♠ ❞❡t❡r♠✐♥❛❞♦ ❡✈❡♥t♦✱ ♦✉ s❡❥❛✱ q✉❛♥❞♦ ❛ ✈❛r✐á✈❡❧ r❡s♣♦st❛ é ♦ t❡♠♣♦ ❛té ❛ ♦❝♦rrê♥❝✐❛ ❞❡ss❡ ❡✈❡♥t♦✳ ❚❛❧ t❡♠♣♦ é ❝♦♥❤❡❝✐❞♦ ♥❛ ❧✐t❡r❛t✉r❛ ❝♦♠♦ t❡♠♣♦ ❞❡ ❢❛❧❤❛✱ s❡♥❞♦ ❛ss✐♠ ❞❡✲ ♥♦♠✐♥❛❞♦ ❞❡✈✐❞♦ ❛ ❡st❡s ❡✈❡♥t♦s s❡r❡♠✱ ❡♠ s✉❛ ♠❛✐♦r✐❛✱ ✐♥❞❡s❡❥á✈❡✐s✱ t❛✐s ❝♦♠♦✱ t❡♠♣♦ ❞♦ ❞✐❛❣♥óst✐❝♦ ❞❡ ✉♠❛ ❞♦❡♥ç❛ ❛té ❛ ♠♦rt❡ ❞♦ ♣❛❝✐❡♥t❡❀ t❡♠♣♦ ❛té ❛ ❢❛❧❤❛ ❞❡ ✉♠ ❡q✉✐♣❛♠❡♥t♦ ❡❧❡trô♥✐❝♦✱ ❞❡♥tr❡ ♦✉tr♦s✳
❆ ❞❡♥♦♠✐♥❛çã♦ ✏s♦❜r❡✈✐✈ê♥❝✐❛✑ r❡❢❡r❡✲s❡ ❜❛s✐❝❛♠❡♥t❡ ❛ s✐t✉❛çõ❡s ♠é❞✐❝❛s✳ P♦ré♠✱ ❛s té❝♥✐❝❛s ❞❡ ❛♥á❧✐s❡ ❞❡ss❡s ❞❛❞♦s sã♦ ❛♣❧✐❝á✈❡✐s ❛ ❞✐✈❡rs❛s ár❡❛s ❞♦ ❝♦♥❤❡❝✐♠❡♥t♦✳ P♦r ❡①❡♠♣❧♦✱ ♥❛ ❡♥❣❡♥❤❛r✐❛ ✭❡♠ q✉❡ é ❞❡♥♦♠✐♥❛❞❛ ❝♦♥✜❛❜✐❧✐❞❛❞❡ ❡ ♥ã♦ s♦❜r❡✈✐✈ê♥❝✐❛✮ ♦ ✐♥t❡r❡ss❡ ♣♦❞❡ ❡st❛r ♥♦s t❡♠♣♦s ❞❡ ✈✐❞❛ ❞❡ ♣r♦❞✉t♦s ♦✉ ❝♦♠♣♦♥❡♥t❡s❀ ♥❛ ❡❞✉❝❛çã♦✱ ♦ ✐♥t❡r❡ss❡ ♣♦❞❡ ❡st❛r ❡♠ s❛❜❡r ♦ t❡♠♣♦ ♠é❞✐♦ ❛té ❛ ❝♦♥❝❧✉sã♦ ❞❡ ✉♠ ❝✉rs♦ ♣♦r ✉♠ ❛❧✉♥♦❀ ♦✉✱ ❛✐♥❞❛✱ ♥❛ ❝r✐♠✐♥♦❧♦❣✐❛✱ ❡♠ q✉❡ ♦ ✐♥t❡r❡ss❡ ♣♦❞❡ ❡st❛r ♥♦ t❡♠♣♦ ❛té ✉♠ ❡①✲❞❡t❡♥t♦ r❡✐♥❝✐❞✐r ♥♦ ❝r✐♠❡✳
❯♠❛ ❝❛r❛❝t❡ríst✐❝❛ ✐♠♣♦rt❛♥t❡ ❞❡ ❞❛❞♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ é ❛ ♣r❡s❡♥ç❛ ❞❡ ❝❡♥s✉r❛s✳ ❆ ❝❡♥s✉r❛ é ❛ ✐♥❢♦r♠❛çã♦ ♣❛r❝✐❛❧ ❞❛ r❡s♣♦st❛ ❡ ♦❝♦rr❡ ❞❡✈✐❞♦ à ♣❡r❞❛ ❞❡ ❛❝♦♠✲ ♣❛♥❤❛♠❡♥t♦ ❞♦ ✐♥❞✐✈í❞✉♦✱ ♣♦r ✉♠❛ ❝❛✉s❛ ❞✐❢❡r❡♥t❡ ❞❛ ❡st✉❞❛❞❛✳ ◆❛ ár❡❛ ❝❧í♥✐❝❛✱ ❛ ❝❡♥s✉r❛ ♣♦❞❡ s✉r❣✐r✱ ♣♦r ❡①❡♠♣❧♦✱ ❞❡✈✐❞♦ ❛♦ ❢❛t♦ ❞♦ ♣❛❝✐❡♥t❡ t❡r ♠✉❞❛❞♦ ❞❡ ❝✐❞❛❞❡✱ t❡r ♠♦rr✐❞♦ ❞❡ ❝❛✉s❛ ❞✐❢❡r❡♥t❡ ❞❛ ❡st✉❞❛❞❛ ♦✉✱ ❞❡✈✐❞♦ ❛♦ tér♠✐♥♦ ❞♦ ❡st✉❞♦ s❡♠ q✉❡ ♦ ❡✈❡♥t♦ ❢♦ss❡ ♦❜s❡r✈❛❞♦✳ ❆ss✐♠✱ té❝♥✐❝❛s ❡st❛tíst✐❝❛s ❞❡ ❛♥á❧✐s❡ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ sã♦ ♥❡❝❡ssár✐❛s ♣❛r❛ ❛♥❛❧✐s❛r ❞❛❞♦s ❝♦♠ ❡st❛ ❝❛r❛❝t❡ríst✐❝❛✱ ♣♦✐s ❡❧❛s ♣❡r♠✐t❡♠ ✐♥❝♦r♣♦r❛r ❛ ✐♥❢♦r♠❛çã♦ ❞❛ ❝❡♥s✉r❛ ♥❛ ❛♥á❧✐s❡✳ ❯♠ ❞❛❞♦ ❝❡♥s✉r❛❞♦ à ❞✐r❡✐t❛ ✐♥❞✐❝❛ q✉❡ ♦ t❡♠♣♦ ❞❡ ❢❛❧❤❛ é s✉♣❡r✐♦r ❛♦ t❡♠♣♦ ♦❜s❡r✈❛❞♦✱ ♦✉ s❡❥❛✱ ✐♥❢♦r♠❛ q✉❡ ❛té ♦ ú❧t✐♠♦ r❡❣✐str♦ ♦ ❡✈❡♥t♦ ❛✐♥❞❛ ♥ã♦ ♦❝♦r✲ r❡✉✳ P♦rt❛♥t♦✱ ❛ ❡①❝❧✉sã♦ ❞❡st❛ ✐♥❢♦r♠❛çã♦ ♥❛ ❛♥á❧✐s❡ ❡st❛tíst✐❝❛ ♣♦❞❡ ❢♦r♥❡❝❡r ❝♦♥❝❧✉sõ❡s ✈✐❡s❛❞❛s✳ ❉❡♥tr❡ ♦s ♠❡❝❛♥✐s♠♦s ❞❡ ❝❡♥s✉r❛ à ❞✐r❡✐t❛ ❡①✐st❡♥t❡s✱ t❡♠✲s❡✿
• ❈❡♥s✉r❛ ❞♦ t✐♣♦ ■✿ ❖❝♦rr❡ q✉❛♥❞♦ ♦ ❡st✉❞♦ t❡♠ ✉♠ t❡♠♣♦ ♣ré✲❡st❛❜❡❧❡❝✐❞♦ ♣❛r❛
t❡r♠✐♥❛r✳ ❆ss✐♠✱ ♦ t❡♠♣♦ ❞❡ ✈✐❞❛ ❞♦ ✐♥❞✐✈✐❞✉♦ é ❝♦♥❤❡❝✐❞♦ ❛♣❡♥❛s s❡ ❡❧❡ ❛♣r❡s❡♥✲ t❛r ❢❛❧❤❛ ❛♥t❡s ❞♦ ✜♥❛❧ ❞♦ ❡st✉❞♦✳ ◆❡st❡ ❝❛s♦✱ ♦ ♥ú♠❡r♦ ❞❡ ❢❛❧❤❛s é ✉♠❛ ✈❛r✐á✈❡❧ ❛❧❡❛tór✐❛✳
✷✹
♣ré✲❡st❛❜❡❧❡❝✐❞♦ ❞❡ ✐♥❞✐✈í❞✉♦s ❛♣r❡s❡♥t❛r❡♠ ♦ ❡✈❡♥t♦ ❞❡ ✐♥t❡r❡ss❡ ✭❢❛❧❤❛✮✳ ❖ t❡♠♣♦ ❞❡ ❞✉r❛çã♦ ❞♦ ❡①♣❡r✐♠❡♥t♦ s❡rá ✉♠❛ ✈❛r✐á✈❡❧ ❛❧❡❛tór✐❛✳
• ❈❡♥s✉r❛ ❞♦ t✐♣♦ ❛❧❡❛tór✐♦✿ ❈❛r❛❝t❡r✐③❛❞❛ ♣❡❧❛ ♣❡r❞❛ ❞❡ ❛❝♦♠♣❛♥❤❛♠❡♥t♦ ❞♦ ✐♥❞✐✲
✈í❞✉♦ ♥♦ ❞❡❝♦rr❡r ❞♦ ❡st✉❞♦ s❡♠ ❡st❡ t❡r ❛♣r❡s❡♥t❛❞♦ ❢❛❧❤❛✳ ❊st❡ t✐♣♦ ❞❡ ❝❡♥s✉r❛ é ❛ q✉❡ ♠❛✐s ❛♣❛r❡❝❡ ♥❛ ♣rát✐❝❛✱ ♣♦❞❡♥❞♦ s❡r r❡♣r❡s❡♥t❛❞❛ ♣♦r ♠❡✐♦ ❞❡ ❞✉❛s ✈❛✲ r✐á✈❡✐s ❛❧❡❛tór✐❛s ✐♥❞❡♣❡♥❞❡♥t❡s T ❡ C ✱ ❡♠ q✉❡ ❛ ✈❛r✐á✈❡❧ ❛❧❡❛tór✐❛ T r❡♣r❡s❡♥t❛
♦ t❡♠♣♦ ❞❡ ❢❛❧❤❛ ❞❡ ✉♠ ✐♥❞✐✈í❞✉♦✱ ❛ ✈❛r✐á✈❡❧ ❛❧❡❛tór✐❛ C r❡♣r❡s❡♥t❛ ♦ t❡♠♣♦ ❞❡
❝❡♥s✉r❛ ❛ss♦❝✐❛❞♦ ❛ ❡st❡ ✐♥❞✐✈í❞✉♦ ❡✱ ❛ ♦❜s❡r✈❛çã♦ ♣❛r❛ ❡st❡ ✐♥❞✐✈í❞✉♦✱ é ❞❛❞❛ ♣♦r
t =♠✐♥(T, C)
❊♠ ❣❡r❛❧✱ ♦s ❞❛❞♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ♣❛r❛ ✉♠ ✐♥❞✐✈í❞✉♦ i s♦❜ ❡st✉❞♦ sã♦
r❡♣r❡s❡♥t❛❞♦s ♣❡❧♦ ♣❛r (ti, δi)✱ i = 1, ..., n ❡♠ q✉❡ ti r❡♣r❡s❡♥t❛ ♦ t❡♠♣♦ ❞❡ ❢❛❧❤❛ ♦✉ ❞❡ ❝❡♥s✉r❛ ❡ δi é ❛ ✈❛r✐á✈❡❧ ✐♥❞✐❝❛❞♦r❛ r❡♣r❡s❡♥t❛♥❞♦ ❢❛❧❤❛ (δi = 1) ♦✉ ❝❡♥s✉r❛ (δi = 0)✳ ◆❛ ♣r❡s❡♥ç❛ ❞❡ ❝♦✈❛r✐á✈❡✐s✱ t❛✐s ❞❛❞♦s sã♦ r❡♣r❡s❡♥t❛❞♦s ♣♦r(ti, δi,xi)✱ ♦✉ s❡❥❛✱ ❝♦♠ ❛ ✐♥❝❧✉sã♦
❞♦ ✈❡t♦r ❞❡ ✈❛❧♦r❡s ❞❛s ❝♦✈❛r✐á✈❡✐s ♣❛r❛ ♦ ✐✲és✐♠♦ ✐♥❞✐✈í❞✉♦✳
❯♠ ✐♥t❡r❡ss❡ ❡s♣❡❝✐❛❧ ❡♠ ❛♥á❧✐s❡ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ é ❡♥❝♦♥tr❛r ❛ ♣r♦❜❛❜✐❧✐✲ ❞❛❞❡ ❞❡ ✉♠ ✐♥❞✐✈í❞✉♦ s♦❜r❡✈✐✈❡r ❛♦ t❡♠♣♦ t✱ ✐st♦ é✱ ❞❡ ♥ã♦ ❢❛❧❤❛r ❛té ❡st❡ t❡♠♣♦✳ ■st♦
♣♦❞❡ s❡r ❡st❛❜❡❧❡❝✐❞♦ ♣♦r ♠❡✐♦ ❞❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛✱ ❞❡✜♥✐❞❛ ♣r♦❜❛❜✐❧✐st✐❝❛♠❡♥t❡ ♣♦r✿
S(t) = P(T > t) = 1−P(T ≤t) = 1−F(t),
❡♠ q✉❡ T é ✉♠❛ ✈❛r✐á✈❡❧ ❛❧❡❛tór✐❛ ♥ã♦ ♥❡❣❛t✐✈❛✱ ✉s✉❛❧♠❡♥t❡ ❝♦♥tí♥✉❛✱ r❡♣r❡s❡♥t❛♥❞♦
♦ t❡♠♣♦ ❞❡ ❢❛❧❤❛ ❡ F(t) é ❛ ❢✉♥çã♦ ❞❡ ❞✐str✐❜✉✐çã♦ ❛❝✉♠✉❧❛❞❛✱ ❞❡✜♥✐❞❛ ♣♦r F(t) =
Rt
−∞f(µ)dµ✱ ❝♦♠ f(t) s❡♥❞♦ ❛ ❢✉♥çã♦ ❞❡♥s✐❞❛❞❡ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ♣❛r❛ ❛ ✈❛r✐á✈❡❧ ❛❧❡❛✲
tór✐❛ T✳
❆ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ é ♠♦♥ót♦♥❛ ❞❡❝r❡s❝❡♥t❡ ❝♦♠ ❛s s❡❣✉✐♥t❡s ♣r♦✲ ♣r✐❡❞❛❞❡s✿ S(0) = 1 ❡ limt→∞S(t) = 0✳ ❋✉♥çõ❡s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ q✉❡ ♥ã♦ s❛t✐s❢❛ç❛♠
❡st❛ s❡❣✉♥❞❛ ♣r♦♣r✐❡❞❛❞❡ sã♦ ❞❡♥♦♠✐♥❛❞❛s ❢✉♥çõ❡s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ✐♠♣ró♣r✐❛s ♦✉ ❝♦♠ ❢r❛çã♦ ❞❡ ❝✉r❛ ♦✉✱ ❛✐♥❞❛✱ ❝♦♠ s♦❜r❡✈✐✈❡♥t❡s ❞❡ ❧♦♥❣❛ ❞✉r❛çã♦ ✭❘❖❉❘■●❯❊❙✱ ❈❆◆❈❍❖ ❡ ❈❆❙❚❘❖✱ ✷✵✵✽✮✳
❖✉tr❛s ❞✉❛s ❢✉♥çõ❡s ❞❡ ✐♥t❡r❡ss❡ ❡♠ ❛♥á❧✐s❡ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ sã♦✿ ❛ ❢✉♥çã♦ ❞❡ t❛①❛ ❞❡ ❢❛❧❤❛ ✭♦✉ r✐s❝♦✮✱ q✉❡ ❡s♣❡❝✐✜❝❛ ❛ t❛①❛ ❞❡ ❢❛❧❤❛ ✐♥st❛♥tâ♥❡❛ ♥♦ t❡♠♣♦ t ❝♦♥❞✐✲
❝✐♦♥❛❧ à s♦❜r❡✈✐✈ê♥❝✐❛ ❛té ❡st❡ t❡♠♣♦ t ✱ ❡ ❛ ❢✉♥çã♦ t❛①❛ ❞❡ ❢❛❧❤❛ ❛❝✉♠✉❧❛❞❛✱ ❞❡✜♥✐❞❛s✱
✷✺
λ(t) = lim
∆t→∞
P(t≤T ≤t+ ∆t|T ≥t)
∆t ❡ Λ(t) =
Z t
0
λ(µ)dµ.
❆ ❢✉♥çã♦ t❛①❛ ❞❡ ❢❛❧❤❛ ♣❛r❛ ♦ t❡♠♣♦ ❞❡ ✈✐❞❛ ❞♦s s❡r❡s ❤✉♠❛♥♦s é ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ ❝✉r✈❛ ❞❛ ❜❛♥❤❡✐r❛ ❡ t❡♠ ✉♠❛ t❛①❛ ❞❡ ❢❛❧❤❛ ❞❡❝r❡s❝❡♥t❡ ♥♦ ♣❡rí♦❞♦ ✐♥✐❝✐❛❧ ✭r❡♣r❡s❡♥✲ t❛♥❞♦ ❛ ♠♦rt❛❧✐❞❛❞❡ ✐♥❢❛♥t✐❧✮✱ ❝♦♥st❛♥t❡ ♥❛ ❢❛✐①❛ ✐♥t❡r♠❡❞✐ár✐❛ ❡ ❝r❡s❝❡♥t❡ ♥❛ ♣❛rt❡ ✜♥❛❧ ✭❈❖▲❖❙■▼❖ ❡ ●■❖▲❖✱ ✷✵✵✻✮✳
❆s três ❢✉♥çõ❡s ❞❡✜♥✐❞❛s ❛♥t❡r✐♦r♠❡♥t❡ ✭s♦❜r❡✈✐✈ê♥❝✐❛✱ t❛①❛ ❞❡ ❢❛❧❤❛ ❡ t❛①❛ ❞❡ ❢❛❧❤❛ ❛❝✉♠✉❧❛❞❛✮ ❡stã♦ r❡❧❛❝✐♦♥❛❞❛s ❡♥tr❡ s✐✱ ❡♠ t❡r♠♦s ♠❛t❡♠át✐❝♦s✱ ❞❛ s❡❣✉✐♥t❡ ♠❛♥❡✐r❛✿
λ(t) = f(t)
S(t) =−
d
dt(logS(t)),
Λ(t) =
Z t
0
λ(µ)dµ=−logS(t) ❡
S(t) = exp{−Λ(t)}= exp
− Z t 0 λ(µ)dµ .
❉❡✈✐❞♦ à ♣r❡s❡♥ç❛ ❞❡ ❝❡♥s✉r❛s ❡♠ ❞❛❞♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛✱ ♦ ♣r✐♥❝✐♣❛❧ ❝♦♠✲ ♣♦♥❡♥t❡ ♥❛ ❛♥á❧✐s❡ ❞❡s❝r✐t✐✈❛ é ❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛✳ ❆ss✐♠✱ t♦r♥❛✲s❡ ♥❡❝❡ssár✐♦ ❡♥❝♦♥tr❛r ❡st✐♠❛❞♦r❡s ♣❛r❛ t❛❧ ❢✉♥çã♦ ♣❛r❛ q✉❡ s❡❥❛ ♣♦ssí✈❡❧ ❡♥❝♦♥tr❛r ❛❧❣✉♠❛s q✉❛♥t✐❞❛✲ ❞❡s ❞❡ ✐♥t❡r❡ss❡✱ t❛✐s ❝♦♠♦ ♦ t❡♠♣♦ ♠é❞✐♦ ♦✉ ♠❡❞✐❛♥♦✱ ♣❡r❝❡♥t✐s ❡ ❢r❛çõ❡s ❞❡ ❢❛❧❤❛s ❡♠ t❡♠♣♦s ✜①♦s ❞❡ ❛❝♦♠♣❛♥❤❛♠❡♥t♦✳
❊♠ ✶✾✺✽✱ ❑❛♣❧❛♥ ❡ ▼❡✐❡r ♣r♦♣✉s❡r❛♠ ✉♠ ❡st✐♠❛❞♦r ♥ã♦✲♣❛r❛♠étr✐❝♦ ♣❛r❛ ❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ✭❑❆P▲❆◆ ❡ ▼❊■❊❘✱ ✶✾✺✽✮✳ ❊st❡ ❡st✐♠❛❞♦r✱ ❝♦♥❤❡❝✐❞♦ ♥❛ ❧✐t❡r❛✲ t✉r❛ ♣♦r ❡st✐♠❛❞♦r ❑❛♣❧❛♥✲▼❡✐❡r ♦✉ ❡st✐♠❛❞♦r ♣r♦❞✉t♦✲❧✐♠✐t❡✱ é ❝♦♥str✉í❞♦ ❝♦♥s✐❞❡r❛♥❞♦ ♦ ♥ú♠❡r♦ ❞❡ ✐♥t❡r✈❛❧♦s ❞❡ t❡♠♣♦ ✐❣✉❛❧ ❛♦ ♥ú♠❡r♦ ❞❡ ❢❛❧❤❛s ❞✐st✐♥t❛s✳ ❙✉❛ ❡①♣r❡ssã♦ ❣❡r❛❧ é ❞❛❞❛ ♣♦r✿
ˆ
S(t) = Y
j:tj<t
(nj −dj nj
) = Y
j:tj<t
(1− dj nj
),
✷✻
❞✐st✐♥t❛s ♦❜s❡r✈❛❞❛s✳ ❘❡♣r❡s❡♥t❛çã♦ ❣rá✜❝❛ ❞❡ss❛ ❝✉r✈❛ é ♠♦str❛❞❛ ♥❛ ❋✐❣✉r❛ ✶✳
0 5 10 15
0.0
0.2
0.4
0.6
0.8
1.0
Tempos (em anos)
S(t) estimada
0 5 10 15
0.0
0.2
0.4
0.6
0.8
1.0
Tempos (em anos)
S(t) estimada
❋✐❣✉r❛ ✶ ✲ ❘❡♣r❡s❡♥t❛çã♦ ❣rá✜❝❛ ❞❡ ❞✉❛s ♣♦ssí✈❡✐s ❢♦r♠❛s ❞❛ ❝✉r✈❛ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ♦❜t✐❞❛ ♣❡❧♦ ❡st✐♠❛❞♦r ❞❡ ❑❛♣❧❛♥✲▼❡✐❡r✳ ❆ ❝✉r✈❛ à ❡sq✉❡r❞❛ ♥ã♦ ❛t✐♥❣❡ ♦ ✈❛❧♦r ③❡r♦✱ ♦ q✉❡ ♦❝♦rr❡ q✉❛♥❞♦ ♦ ♠❛✐♦r t❡♠♣♦ ♦❜s❡r✈❛❞♦ ♥❛ ❛♠♦str❛ ❢♦r ✉♠❛ ❝❡♥s✉r❛✳ ❏á ❛ ❝✉r✈❛ à ❞✐r❡✐t❛ ❛t✐♥❣❡ ♦ ✈❛❧♦r ③❡r♦✱ ✉♠❛ ✈❡③ q✉❡ ♦ ♠❛✐♦r t❡♠♣♦ ♦❜s❡r✈❛❞♦ r❡❢❡r❡✲s❡ ❛ ✉♠❛ ❢❛❧❤❛
❖✉tr♦ ❡st✐♠❛❞♦r ♥ã♦✲♣❛r❛♠étr✐❝♦ ❜❛st❛♥t❡ ❝♦♥❤❡❝✐❞♦ ♥❛ ❧✐t❡r❛t✉r❛ é ♦ ❡st✐✲ ♠❛❞♦r ❞❡ ◆❡❧s♦♥✲❆❛❧❡♥ ♦ q✉❛❧ s❡ ❜❛s❡✐❛✱ ✐♥✐❝✐❛❧♠❡♥t❡✱ ❡♠ ❡st✐♠❛r ❛ ❢✉♥çã♦ t❛①❛ ❞❡ ❢❛❧❤❛ ❛❝✉♠✉❧❛❞❛✱ Λ(t)✳ ❖ ♠❡s♠♦ ❢♦✐ ♣r♦♣♦st♦ ♣♦r ◆❡❧s♦♥ ✭✶✾✼✷✮✱ s❡♥❞♦ q✉❡ ❡♠ ✶✾✼✽ ❆❛❧❡♥
♣r♦✈♦✉ s✉❛s ♣r♦♣r✐❡❞❛❞❡s ❛ss✐♥tót✐❝❛s✳ ❚❛❧ ❡st✐♠❛❞♦r é ❞❛❞♦ ♣❡❧❛ ❡①♣r❡ssã♦✿
˜
Λ(t) = X
j:tj<t
(dj nj
),
❝♦♠ dj ❡ nj ❞❡✜♥✐❞♦s ❞❛ ♠❡s♠❛ ❢♦r♠❛ q✉❡ ♣❛r❛ ♦ ❡st✐♠❛❞♦r ❞❡ ❑❛♣❧❛♥✲▼❡✐❡r✳ ▲♦❣♦✱ ❛ ♣❛rt✐r ❞❡st❡ ❡st✐♠❛❞♦r ❡ ✉t✐❧✐③❛♥❞♦ ❛ ❡①♣r❡ssã♦ ♠❛t❡♠át✐❝❛ q✉❡ r❡❧❛❝✐♦♥❛ ❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❝♦♠ ❛ ❢✉♥çã♦ t❛①❛ ❞❡ ❢❛❧❤❛ ❛❝✉♠✉❧❛❞❛✱ t❡♠✲s❡ q✉❡ ✉♠ ❡st✐♠❛❞♦r ♣❛r❛ ❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ é✿
˜
S(t) = expn−Λ(t)˜ o.
✷✼ ❊st❛ ❡st✐♠❛t✐✈❛ ♣♦❞❡ s❡r ♦❜t✐❞❛ ❝❛❧❝✉❧❛♥❞♦✲s❡ ❛ ár❡❛ s♦❜ ❛ ❝✉r✈❛ ❞❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥✲ ❝✐❛✳ ❈♦♥t✉❞♦✱ ❡ ❝♦♠♦ ♠♦str❛❞♦ ♥❛ ❋✐❣✉r❛ ✶✱ ♦ ♠❛✐♦r t❡♠♣♦ ♦❜s❡r✈❛❞♦ é✱ ❡♠ ♠✉✐t♦s ❝❛s♦s✱ ✉♠❛ ❝❡♥s✉r❛✱ ♦ q✉❡ ❢❛③ ❝♦♠ q✉❡ ❛ ❝✉r✈❛ ❞❡ ❑❛♣❧❛♥✲▼❡✐❡r ♥ã♦ ❛t✐♥❥❛ ♦ ✈❛❧♦r ③❡r♦✳ ❊♠ t❛✐s s✐t✉❛çõ❡s ❤❛✈❡rá✱ ♣♦rt❛♥t♦✱ ♣r♦❜❧❡♠❛s ❝♦♠ ♦ ❝á❧❝✉❧♦ ❞❡ t❛❧ ár❡❛ ❡✱ ❝♦♥s❡q✉❡♥t❡♠❡♥t❡✱ ❞♦ t❡♠♣♦ ♠é❞✐♦ ❞❡ ✈✐❞❛✳
❉❡✈✐❞♦ ❛ ♣r♦❜❧❡♠❛s ❝♦♠♦ ♦ ❝✐t❛❞♦✱ ❞✐✈❡rs♦s ♠♦❞❡❧♦s ♣❛r❛♠étr✐❝♦s ❢♦r❛♠ ❡ ✈ê♠ s❡♥❞♦ ♣r♦♣♦st♦s ♥❛ ❧✐t❡r❛t✉r❛ ❛ ✜♠ ❞❡ ♣❡r♠✐t✐r ✉♠❛ ❛♥á❧✐s❡ ❡st❛tíst✐❝❛ ♠❛✐s ♣r❡❝✐s❛✳ ▼♦❞❡❧♦s ♣❛r❛♠étr✐❝♦s sã♦ ❛ss✐♠ ❞❡♥♦♠✐♥❛❞♦s ♣♦r ❛♣r❡s❡♥t❛r❡♠ q✉❛♥t✐❞❛❞❡s ❞❡s❝♦♥❤❡❝✐✲ ❞❛s ❡♠ s✉❛s ❡①♣r❡ssõ❡s✱ ❞❡♥♦♠✐♥❛❞❛s ♣❛râ♠❡tr♦s✳ ❉❡♥tr❡ ♦s ♠♦❞❡❧♦s ♣❛r❛♠étr✐❝♦s q✉❡ ❛♣❛r❡❝❡♠ ♥❛ ❧✐t❡r❛t✉r❛ ♣❛r❛ ❛ ❛♥á❧✐s❡ ❞❡ ❞❛❞♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛✱ ❛❧❣✉♥s ❛♣r❡s❡♥t❛♠ ❞❡st❛✲ q✉❡ ♣♦r ❥á t❡r❡♠ s✐❞♦ ✉t✐❧✐③❛❞♦s ❡♠ ❞✐✈❡rs❛s s✐t✉❛çõ❡s✳ ❙ã♦ ❡❧❡s✱ ♦s ♠♦❞❡❧♦s✿ ❡①♣♦♥❡♥❝✐❛❧✱ ❞❡ ❲❡✐❜✉❧❧✱ ❧♦❣✲♥♦r♠❛❧✱ ❣❛♠❛ ❡ ❣❛♠❛ ❣❡♥❡r❛❧✐③❛❞❛✳
❖ ♠♦❞❡❧♦ ❡①♣♦♥❡♥❝✐❛❧ ❛♣r❡s❡♥t❛ ✉♠ ú♥✐❝♦ ♣❛râ♠❡tr♦ ❡♠ s✉❛ ❡str✉t✉r❛ r❡♣r❡✲ s❡♥t❛♥❞♦ ♦ t❡♠♣♦ ♠é❞✐♦ ❞❡ ✈✐❞❛✳ ❙✉❛ ❢✉♥çã♦ t❛①❛ ❞❡ ❢❛❧❤❛ é ❝♦♥st❛♥t❡✱ ♦ q✉❡ é ❝♦♥❤❡❝✐❞♦ ♥❛ ❧✐t❡r❛t✉r❛ ❝♦♠♦ ❢❛❧t❛ ❞❡ ♠❡♠ór✐❛ ❞❛ ❞✐str✐❜✉✐çã♦ ❡①♣♦♥❡♥❝✐❛❧ ✭♦ r✐s❝♦ ❞❡ ❢❛❧❤❛ ♣❛r❛ ✉♠ ✐♥❞✐✈í❞✉♦ ❡♠ ❡st✉❞♦ é ♦ ♠❡s♠♦ ❡♠ t♦❞♦ ♦ ♣❡rí♦❞♦ ❞❡ ❛❝♦♠♣❛♥❤❛♠❡♥t♦✮✳ ❯♠❛ ❛♣❧✐❝❛çã♦ ❞❡st❡ ♠♦❞❡❧♦ ♣♦❞❡ s❡r ❡♥❝♦♥tr❛❞❛ ❡♠ ❈♦① ❡ ❙♥❡❧❧ ✭✶✾✽✶✮✱ ❡♠ q✉❡ ♦s ❛✉t♦r❡s ❞❡s❝r❡✈❡♠ ♦ t❡♠♣♦ ❞❡ ✈✐❞❛ ❞❡ ♣❛❝✐❡♥t❡s ❛❞✉❧t♦s ❝♦♠ ❧❡✉❝❡♠✐❛✳ ❖ ♠♦❞❡❧♦ ❞❡ ❲❡✐❜✉❧❧✱ ♣r♦♣♦st♦ ♣♦r ❲❡✐❜✉❧❧ ✭✶✾✸✾✮ ❛♣r❡s❡♥t❛ ❞♦✐s ♣❛râ♠❡tr♦s ♥ã♦✲♥❡❣❛t✐✈♦s✱ s❡♥❞♦ ✉♠ ♦ ♣❛râ♠❡tr♦ ❞❡ ❢♦r♠❛ ❡✱ ♦ ♦✉tr♦✱ ♦ ❞❡ ❡s❝❛❧❛✳ P♦ss✉✐ ✉♠❛ ❢✉♥çã♦ t❛①❛ ❞❡ ❢❛❧❤❛ ♠♦♥ót♦♥❛✱ ♣♦❞❡♥❞♦ s❡r ❝r❡s❝❡♥t❡✱ ❞❡❝r❡s❝❡♥t❡ ♦✉ ❝♦♥st❛♥t❡✳ ➱ ✉♠ ♠♦❞❡❧♦ ❜❛st❛♥t❡ ❝♦♠✉♠ ❡♠ ❡st✉❞♦s ❝❧í♥✐❝♦s ❡ ✐♥❞✉str✐❛✐s ❡ t❡♠ ❝♦♠♦ ✉♠ ❝❛s♦ ♣❛rt✐❝✉❧❛r ♦ ♠♦❞❡❧♦ ❡①♣♦♥❡♥❝✐❛❧✳ ❖✉tr♦ ♠♦❞❡❧♦ ❜❛st❛♥t❡ ✉t✐❧✐③❛❞♦ ❡♠ s✐t✉❛çõ❡s ❝❧í♥✐❝❛s é ♦ ♠♦❞❡❧♦ ❧♦❣✲♥♦r♠❛❧✳ ❆ss✐♠ ❝♦♠♦ ♦ ♠♦❞❡❧♦ ❞❡ ❲❡✐❜✉❧❧✱ ♦ ♠♦❞❡❧♦ ❧♦❣✲♥♦r♠❛❧ ♣♦ss✉✐ ❞♦✐s ♣❛râ♠❡tr♦s ❡♠ s✉❛ ❡str✉t✉r❛✱ ♣♦ré♠ s✉❛ ❢✉♥çã♦ t❛①❛ ❞❡ ❢❛❧❤❛ ❞✐❢❡r❡ ❞❛ ❞♦ ♠♦❞❡❧♦ ❞❡ ❲❡✐❜✉❧❧ ♣♦r ♥ã♦ s❡r ♠♦♥ót♦♥❛✳ ❚❛❧ ❢✉♥çã♦ ❝r❡s❝❡✱ ❛t✐♥❣❡ ✉♠ ✈❛❧♦r ♠á①✐♠♦ ❡ ❞❡♣♦✐s ❞❡❝r❡s❝❡✳ ❖s ♣❛râ♠❡tr♦s ♣❛r❛ ❡st❡ ♠♦❞❡❧♦ r❡♣r❡s❡♥t❛♠ ❛ ♠é❞✐❛ ❞♦ ❧♦❣❛r✐t♠♦ ❞♦ t❡♠♣♦ ❡ ♦ ❞❡s✈✐♦✲♣❛❞rã♦✳ ❯♠ ❢❛t♦ ✐♠♣♦rt❛♥t❡ ❛ s❡r ❝♦♥s✐❞❡r❛❞♦ é q✉❡✱ s❡ ♦s ❞❛❞♦s sã♦ ♣r♦✈❡♥✐❡♥t❡s ❞❡ ✉♠❛ ❞✐str✐❜✉✐çã♦ ❧♦❣✲♥♦r♠❛❧✱ ❡♥tã♦ ♦s ♠❡s♠♦s ♣♦❞❡♠ s❡r ❛♥❛❧✐s❛❞♦s s❡❣✉♥❞♦ ✉♠❛ ❞✐str✐❜✉✐çã♦ ♥♦r♠❛❧✳ P❛r❛ ✐st♦✱ t❡♠✲s❡ q✉❡ ❝♦♥s✐❞❡r❛r ♦ ❧♦❣❛r✐t♠♦ ❞♦s ❞❛❞♦s✱ ❡♠ ✈❡③ ❞♦s ✈❛❧♦r❡s ♦r✐❣✐♥❛✐s✳
✷✽
♥❛ ár❡❛ ♠é❞✐❝❛ é ♠❛✐s r❡❝❡♥t❡✳ ❈♦♠♦ ♥♦s ❞♦✐s ♠♦❞❡❧♦s ❛♥t❡r✐♦r❡s✱ ♦ ♠♦❞❡❧♦ ❣❛♠❛ ♣♦ss✉✐ ❞♦✐s ♣❛râ♠❡tr♦s ❡♠ s✉❛ ❡str✉t✉r❛✱ s❡♥❞♦ ✉♠ ❞❡ ❢♦r♠❛ ❡ ♦ ♦✉tr♦ ❞❡ ❡s❝❛❧❛✳ ❆ ❢✉♥çã♦ t❛①❛ ❞❡ ❢❛❧❤❛ é ❝r❡s❝❡♥t❡ ♦✉ ❞❡❝r❡s❝❡♥t❡✱ ❝♦♥✈❡r❣✐♥❞♦ ♣❛r❛ ✉♠ ✈❛❧♦r ❝♦♥st❛♥t❡ q✉❛♥❞♦ t→ ∞❡
♣♦ss✉✐ ♦ ♠♦❞❡❧♦ ❡①♣♦♥❡♥❝✐❛❧ ❝♦♠♦ ✉♠ ❝❛s♦ ♣❛rt✐❝✉❧❛r✳ ❙t❛❝② ✭✶✾✻✷✮ ♣r♦♣ôs ❛ ❞✐str✐❜✉✐çã♦ ❣❛♠❛ ❣❡♥❡r❛❧✐③❛❞❛✱ ❛ q✉❛❧ ♣♦ss✉✐ três ♣❛râ♠❡tr♦s ♣♦s✐t✐✈♦s ❡♠ s✉❛ ❡str✉t✉r❛✱ s❡♥❞♦ ❞♦✐s ♣❛râ♠❡tr♦s ❞❡ ❢♦r♠❛ ❡ ✉♠ ❞❡ ❡s❝❛❧❛✳ ➱ ✉♠ ♠♦❞❡❧♦ ♠❛✐s ✢❡①í✈❡❧ q✉❡ ♦s ❛♥t❡r✐♦r❡s ♣❡❧♦ ❢❛t♦ ❞❡ ♣♦ss✉✐r ✉♠ ♠❛✐♦r ♥ú♠❡r♦ ❞❡ ♣❛râ♠❡tr♦s✳ ❱❡r✐✜❝❛✲s❡✱ ❛✐♥❞❛✱ q✉❡ ♦ ♠♦❞❡❧♦ ❡①♣♦♥❡♥❝✐❛❧✱ ❞❡ ❲❡✐❜✉❧❧✱ ●❛♠❛ ❡ ❧♦❣✲♥♦r♠❛❧ sã♦ ❝❛s♦s ♣❛rt✐❝✉❧❛r❡s ❞❡ t❛❧ ❞✐str✐❜✉✐çã♦✱ s❡♥❞♦ ♦ ♠♦❞❡❧♦ ❧♦❣✲♥♦r♠❛❧ ✉♠ ❝❛s♦ ❧✐♠✐t❡ ❞❡❧❛✱ ❝♦♥❢♦r♠❡ ♠♦str❛❞♦ ♣♦r ▲❛✇❧❡ss ✭✷✵✵✷✮✳
❊①♣r❡ssõ❡s ♣❛r❛ ❛s ❢✉♥çõ❡s ❞❡ ❞❡♥s✐❞❛❞❡✱ f(t)✱ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛✱ S(t)✱ ❡ ❞❡
t❛①❛ ❞❡ ❢❛❧❤❛✱ λ(t)✱ ♣❛r❛ ♦s ♠♦❞❡❧♦s ❝✐t❛❞♦s✱ ❜❡♠ ❝♦♠♦ ♣❛r❛ ♦✉tr♦s ♠♦❞❡❧♦s ♣♦❞❡♠ s❡r
❡♥❝♦♥tr❛❞❛s ❡♠ ❈♦❧♦s✐♠♦ ❡ ●✐♦❧♦ ✭✷✵✵✻✮✳
❊♠ ❛♥á❧✐s❡ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛✱ ✉♠ ♠ét♦❞♦ ❛♣r♦♣r✐❛❞♦ ♣❛r❛ ❡st✐♠❛çã♦ ❞♦s ♣❛râ♠❡tr♦s ❞♦s ♠♦❞❡❧♦s ♣❛r❛♠étr✐❝♦s é ♦ ♠ét♦❞♦ ❞❛ ♠á①✐♠❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ♣♦r ♣❡r♠✐t✐r ✐♥❝♦r♣♦r❛r ❛ ✐♥❢♦r♠❛çã♦ ❞❡ ❞❛❞♦s ❝❡♥s✉r❛❞♦s✳ ◆❡st❡ ❝♦♥t❡①t♦✱ ❛ ❡①♣r❡ssã♦ ❣❡r❛❧ ♣❛r❛ ❛ ❢✉♥çã♦ ❞❡ ✈❡r♦ss✐♠✐❧❤❛♥ç❛✱ ♥❛ ♣r❡s❡♥ç❛ ❞❡ ❞❛❞♦s ❝❡♥s✉r❛❞♦s à ❞✐r❡✐t❛✱ é ❞❛❞❛ ♣♦r✿
L(θ) =
n
Y
i=1
[f(ti;θ)] δi
[S(ti;θ)]1
−δi
=
n
Y
i=1
[λ(ti;θ)] δi
[S(ti;θ)]
❡♠ q✉❡ ❛ ❝♦♥tr✐❜✉✐çã♦ ❞❡ ❝❛❞❛ ♦❜s❡r✈❛çã♦ ♥ã♦ ❝❡♥s✉r❛❞❛ ♣❛r❛ ❡st❛ ❢✉♥çã♦ é ❞❛❞❛ ♣❡❧❛ s✉❛ ❢✉♥çã♦ ❞❡ ❞❡♥s✐❞❛❞❡ f(ti;θ)❡✱ ❛ ❝♦♥tr✐❜✉✐çã♦ ❞❡ ❝❛❞❛ ♦❜s❡r✈❛çã♦ ❝❡♥s✉r❛❞❛✱ ♣❡❧❛ s✉❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛S(ti;θ)❀θ é ♦ ✈❡t♦r ❞❡ ♣❛râ♠❡tr♦s ❛ s❡r ❡st✐♠❛❞♦ ❡δi é ❛ ✈❛r✐á✈❡❧ ✐♥❞✐❝❛❞♦r❛ ❞❡ ❢❛❧❤❛✱ ❛ss✉♠✐♥❞♦ ♦ ✈❛❧♦r ✶ q✉❛♥❞♦ ❢♦r ❢❛❧❤❛ ❡ ♦ ✈❛❧♦r ✵ q✉❛♥❞♦ ❢♦r ❝❡♥s✉r❛✳ ❆ss✐♠✱ ♦s ❡st✐♠❛❞♦r❡s ❞❡ ♠á①✐♠❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ sã♦ ♦s ✈❛❧♦r❡s ❞❡ θ q✉❡ ♠❛①✐♠✐③❛♠ L(θ)✱ ♦✉✱ ❡q✉✐✈❛❧❡♥t❡♠❡♥t❡✱log(L(θ))✳
