Análise de sobrevivência na presença de censura informativa

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❆♥á❧✐s❡ ❞❡ ❙♦❜r❡✈✐✈ê♥❝✐❛ ♥❛

♣r❡s❡♥ç❛ ❞❡ ❈❡♥s✉r❛ ■♥❢♦r♠❛t✐✈❛

P❛✉❧♦ ❈❡rq✉❡✐r❛ ❞♦s ❙❛♥t♦s ❏✉♥✐♦r

❉✐ss❡rt❛çã♦ ❛♣r❡s❡♥t❛❞❛

❛♦

❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❊st❛tíst✐❝❛

❞❛

❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ▼✐♥❛s ●❡r❛✐s

♣❛r❛

♦❜t❡♥çã♦ ❞♦ tít✉❧♦

❞❡

▼❡str❡ ❡♠ ❈✐ê♥❝✐❛s

Pr♦❣r❛♠❛✿ Pós✲●r❛❞✉❛çã♦ ❡♠ ❊st❛tíst✐❝❛

❖r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❉r✳ ❊♥r✐❝♦ ❆♥tô♥✐♦ ❈♦❧♦s✐♠♦

❈♦♦r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❉r✳ ❋á❜✐♦ ◆♦❣✉❡✐r❛ ❉❡♠❛rq✉✐

❉✉r❛♥t❡ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡st❡ tr❛❜❛❧❤♦ ♦ ❛✉t♦r r❡❝❡❜❡✉ ❛✉①í❧✐♦ ✜♥❛♥❝❡✐r♦ ❞❛ ❋❆P❊▼■●

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❆♥á❧✐s❡ ❞❡ ❙♦❜r❡✈✐✈ê♥❝✐❛ ♥❛

♣r❡s❡♥ç❛ ❞❡ ❈❡♥s✉r❛ ■♥❢♦r♠❛t✐✈❛

❊st❛ ❞✐ss❡rt❛çã♦ ❝♦♥té♠ ❛s ❝♦rr❡çõ❡s ❡ ❛❧t❡r❛çõ❡s s✉❣❡r✐❞❛s ♣❡❧❛ ❈♦♠✐ssã♦ ❏✉❧❣❛❞♦r❛ ❞✉r❛♥t❡ ❛ ❞❡❢❡s❛ r❡❛❧✐③❛❞❛ ♣♦r ✭P❛✉❧♦ ❈❡rq✉❡✐r❛ ❞♦s ❙❛♥t♦s ❏✉♥✐♦r✮ ❡♠ ✵✶✴✵✸✴✷✵✶✷✳ ❖ ♦r✐❣✐♥❛❧ ❡♥❝♦♥tr❛✲s❡ ❞✐s♣♦♥í✈❡❧ ♥♦ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❞❡ ❊st❛tíst✐❝❛ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ▼✐♥❛s ●❡r❛✐s✳

❈♦♠✐ssã♦ ❏✉❧❣❛❞♦r❛✿

• Pr♦❢✳ ❉r✳ ❊♥r✐❝♦ ❆♥tô♥✐♦ ❈♦❧♦s✐♠♦ ✭♦r✐❡♥t❛❞♦r✮ ✲ ❯❋▼●

• Pr♦❢✳ ❉r✳ ❋á❜✐♦ ◆♦❣✉❡✐r❛ ❉❡♠❛rq✉✐ ✲ ❯❋▼● ✭❈♦♦r✐❡♥t❛❞♦r✮

• Pr♦❢❛✳ ❉r❛✳ ▼❛❣❞❛ ❈❛r✈❛❧❤♦ P✐r❡s ✲ ❯❋▼●

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➚ ❉❡✉s ❡ ♠❡✉s ♣❛✐s✳

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❆❣r❛❞❡❝✐♠❡♥t♦s

⋆ ❆❣r❛❞❡ç♦ ❛♦ ♠❡✉ ❉❡✉s ❡ ◆♦ss❛ ❙❡♥❤♦r❛ ♣❡❧❛s ♦♣♦rt✉♥✐❞❛❞❡s q✉❡ sã♦ ❝♦❧♦❝❛❞❛s ❡♠ ♠✐♥❤❛ ✈✐❞❛✱ ♣♦r s❡✉ ✐♠❡♥s♦ ❛♠♦r ❡ ♣♦r s❡♠♣r❡ ❛❜❡♥ç♦❛r✲♠❡ ❡♠ ♠❡✉s ♣❛ss♦s❀

⋆ ❆♦s ♠❡✉s ♣❛✐s✱ P❛✉❧♦ ❡ ▼❛r✐③❡t❡✱ ♣♦r t♦❞♦ ❝❛r✐♥❤♦✱ ❛♠♦r✱ ✐♥❝❡♥t✐✈♦s ❡ s✉♣♦rt❡ ♣❛r❛ ♠❛✐s ✉♠❛ ❡t❛♣❛ ❡♠ ♠✐♥❤❛ ✈✐❞❛❀

⋆➚ ♠✐♥❤❛ ♥❛♠♦r❛❞❛ ❋❛❜rí❝✐❛ ♣♦r s❡♠♣r❡ ❛♦ ♠❡✉ ❧❛❞♦ ♠❡ ❞❛♥❞♦ ❢♦rç❛s ♥♦s ♠♦♠❡♥t♦s ❝♦♠♣❧✐❝❛❞♦s✱ ❡ ♣♦r s❡ s✉❥❡✐t❛r ❛ ✉♠❛ ❞✐stâ♥❝✐❛ ♥ã♦ ♠❡♥s✉rá✈❡❧ ❛♦ ❧♦♥❞♦ ❞❡st❛ ❡t❛♣❛✳ ❚❡ ❛♠♦❀

⋆ ❆♦s ♠❡✉s ✐r♠ã♦s✿ ▲❛r✐ss❛ ✭❱❡❧❤❛✮✱ ❘❛❢❛❡❧ ❡ P❛✉❧✐♥❤❛✱ q✉❡ ♠❡s♠♦ ❞✐st❛♥t❡ t♦r❝❡r❛♠ ♠✉✐t♦ ♣❡❧♦ ♠❡✉ s✉❝❡ss♦ ♥❡st❡ tr❛❜❛❧❤♦❀

⋆ ❆♦ ♠❡✉ ❖r✐❡♥t❛❞♦r ❊♥r✐❝♦ ❆✳ ❈♦❧♦s✐♠♦ ♣❡❧❛ ♦♣♦rt✉♥✐❞❛❞❡ ❞❡ ♦r✐❡♥t❛çã♦ ♥❡ss❡ tr❛❜❛❧❤♦ ❞❡ ❞✐s✲ s❡rt❛çã♦✱ ♣❡❧❛ ♣❛❝✐ê♥❝✐❛✳

⋆ ❆♦ ♠❡✉ ❈♦♦r✐❡♥t❛❞♦r ❋á❜✐♦ ◆✳ ❉❡♠❛rq✉✐ ♣♦r ♠❡ ❞❛r ❛ ♦♣♦rt✉♥✐❞❛❞❡ ❞❡ ❝♦♠♣❛rt✐❧❤❛r s✉❛ ❡①♣❡✲ r✐ê♥❝✐❛ ❞❡ tr❛❜❛❧❤♦✱ ♣❡❧❛ ♣❛❝✐ê♥❝✐❛ ❛♦ ❧♦♥❣♦ ❞❡st❛ ❞✐ss❡rt❛çã♦❀

⋆ ❆♦s ♣r♦❢❡ss♦r❡s ▼❛♥♦❡❧ ❖tá✈✐♦✱ ❈❛r♠✐♥❤❛✱ ❱❛♥❞❛❝❦ ❡ ❚♦♠✱ ♣❡❧❛ ♦♣♦rt✉♥✐❞❛❞❡ ❞❡ ❜♦❧s❛ ❡ ♣❡❧❛ ♥♦✈❛ ❡①♣❡r✐ê♥❝✐❛ ❞❡ tr❛❜❛❧❤♦ ♥❛ ♠❡❞✐❝✐♥❛ tr♦♣✐❝❛❧✳

❆♦s ♠❡♠❜r♦s ❞❛ ❜❛♥❝❛✱ Pr♦❢❛✳ ▼❛❣❞❛ P✐r❡s ❡ Pr♦❢✳ ❊❞✇✐♥ ❖rt❡❣❛✱ ♣❡❧❛s s✉❣❡stõ❡s ❡♠ ♥❡st❛ ❞✐ss❡r✲ t❛çã♦✳

⋆❆♦s ❛♠✐❣♦s ❞♦ Pr♦❣r❛♠❛ ❡♠ ❊st❛tíst✐❝❛✱ ❡♠ ❡s♣❡❝✐❛❧ ❛♦ ♠❡✉ ❣r✉♣♦ ❞❡ ❡st✉❞♦s✿ ❘♦❞r✐❣♦✱ ●❛❜r✐❡❧✱ ❲❡❝s❧❡②✱ ❘♦❞♦❧❢♦✱ ❱❛♥❡ss❛✱ ♣❡❧♦s ♠♦♠❡♥t♦s ❞❡ ❡st✉❞♦✱ ❞✐✈❡rsã♦ ❡ ❛♠✐③❛❞❡✳ ❆s ♠✐♥❤❛s ♥♦✈❛s ❛♠✐❣❛s ❞❡ ♠❡str❛❞♦ ◆í✈❡❛✱ ❚❛❧✐t❛✱ ■③❛❜❡❧❧❛ ❡ ❙✐❧✈❛♥❛✱ ♣❡❧♦s ♠♦♠❡♥t♦s ❣❛str♦♥ô♠✐❝♦s❀

⋆ ➚ ♣r♦❢❡ss♦r❛ ❉❡♥✐s❡ ❉✉❛rt❡✱ ♣❡❧♦s ❡♥s✐♥❛♠❡♥t♦s ❝♦♥s❡❣✉✐❞♦s✱ ❝♦♥s❡❧❤♦s✱ ❡ ❝❧❛r♦✱ ♣❡❧❛ ♠♦r❛❞✐❛❀

❆♦s ♣r♦❢❡ss♦r❡s ❞♦ ❞❡♣❛rt❛♠❡♥t♦✱ ▼❛r❝❡❧♦ ❆③❡✈❡❞♦✱ ❘♦s❛♥❣❡❧❛ ▲♦s❝❤✐❀

⋆ ➚ ❋❆P❊▼■● ♣❡❧♦ ❛♣♦✐♦ ✜♥❛♥❝❡✐r♦❀

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✏◆ã♦ ✐♠♣♦rt❛ ♦ q✉ã♦ ❢♦rt❡ s❡ ♣♦❞❡ ❜❛t❡r✱ ♠❛s s✐♠ ♦ q✉ã♦ ❢♦rt❡ ♣♦❞❡ s❡r ❛t✐♥❣✐❞♦ ❡ ❝♦♥t✐♥✉❛r s❡❣✉✐♥❞♦ ❡♠ ❢r❡♥t❡✧✳

❘♦❝❦② ❇❛❧❜♦❛ ✭❙②❧✈❡st❡r ❙t❛❧❧♦♥❡✮✳

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❘❡s✉♠♦

◆❛ ♠♦❞❡❧❛❣❡♠ ❞❡ ❞❛❞♦s ❡♠ ❛♥á❧✐s❡ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛✱ ❛ ♠❛✐♦r✐❛ ❞♦s ♣r♦❝❡❞✐♠❡♥t♦s ❡①✐s✲ t❡♥t❡s ♥❛ ❧✐t❡r❛t✉r❛ ❛ss✉♠❡♠ ♦ ♠❡❝❛♥✐s♠♦ ❞❡ ❝❡♥s✉r❛ ❝♦♠♦ ♥ã♦✲✐♥❢♦r♠❛t✐✈♦✱ ♦✉ s❡❥❛✱ ♦s t❡♠♣♦s ❛té ♦ ❡✈❡♥t♦ ❞❡ ✐♥t❡r❡ss❡ ❡ ♦ ❞❡ ❝❡♥s✉r❛ sã♦ ✐♥❞❡♣❡♥❞❡♥t❡s ✭❛ ❞✐str✐❜✉✐çã♦ ❞♦s t❡♠♣♦s ❞❡ ❝❡♥s✉r❛ ♥ã♦ ❝❛rr❡❣❛♠ ✐♥❢♦r♠❛çã♦ ❞♦s ♣❛râ♠❡tr♦s ❞❛ ❞✐str✐❜✉✐çã♦ ❞♦s t❡♠♣♦s ❞❡ ❢❛❧❤❛✮✳ ❊♥tr❡t❛♥t♦✱ ❡♠ ❛❧❣✉♥s ❝❛s♦s ❡ss❛ s✉♣♦s✐çã♦ é ✈✐♦❧❛❞❛✱ ❡ ❛ss✐♠ ♠ét♦❞♦s q✉❡ ✐♥❝♦r♣♦r❡♠ ❡s✲ tr✉t✉r❛s ♣❛r❛ ❛s s✐t✉❛çõ❡s ❡♠ q✉❡ ♦ ♠❡❝❛♥✐s♠♦ ❞❡ ❝❡♥s✉r❛ é ✐♥❢♦r♠❛t✐✈♦ sã♦ ♥❡❝❡ssár✐♦s✳ ◆❡st❡ tr❛❜❛❧❤♦ ❞❡ ❞✐ss❡rt❛çã♦ ❝♦♥s✐❞❡r❛♠♦s ♥❛ ♠♦❞❡❧❛❣❡♠ ❛ s✉♣♦s✐çã♦ ❞❡ q✉❡ ♦s t❡♠♣♦s ❞❡ ❢❛❧❤❛ ❚ ❡ ❞❡ ❝❡♥s✉r❛ ❈ sã♦ ❝♦♥❞✐❝✐♦♥❛❧♠❡♥t❡ ✐♥❞❡♣❡♥❞❡♥t❡s ❞❛❞♦ ✉♠❛ ❢r❛❣✐❧✐❞❛❞❡ ❩✱ ❛ q✉❛❧ ♣♦ss✉✐ ❞✐str✐❜✉✐çã♦ ●❛♠❛ ❡ ♣❛râ♠❡tr♦s ❞❡ ❡s❝❛❧❛ ❡ ❧♦❝❛çã♦ ✐❣✉❛✐s ❛φ✳ ❆ss✉♠✐♠♦s ♦s ♠♦❞❡❧♦s

♣❛r❛♠étr✐❝♦s ❝♦♠♦ ❊①♣♦♥❡♥❝✐❛❧ ❡ ❲❡✐❜✉❧❧ ♣❛r❛ ♦s t❡♠♣♦s ❚ ❡ ❈✳ ❆ss✐♠✱ ❛♦ ✐♥❝♦r♣♦r❛r ❛ ❢r❛❣✐❧✐❞❛❞❡ ♥❛ ♠♦❞❡❧❛❣❡♠✱ ♦s ❡st✐♠❛❞♦r❡s ❞❡ ♠á①✐♠❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ sã♦ ❡♥❝♦♥tr❛❞♦s ✈✐❛ ❢✉♥çã♦ ❞❡ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ♠❛r❣✐♥❛❧✳ ❘❡❛❧✐③❛♠♦s ✉♠ ❡st✉❞♦ ❞❡ s✐♠✉❧❛çã♦ ▼♦♥t❡ ❈❛r❧♦ ♣❛r❛ ❛✈❛❧✐❛r ♦ ♣r♦❝❡❞✐♠❡♥t♦ ✐♥❢♦r♠❛t✐✈♦ ❡ ✉s✉❛❧✱ s♦❜ ❝❡♥ár✐♦s ❡♠ q✉❡ ♦ ♠❡❝❛♥✐s♠♦ ❞❡ ❝❡♥s✉r❛ ❣❡r❛❞♦ s❡❥❛ ♥ã♦✲✐♥❢♦r♠❛t✐✈♦ ❡ ✐♥❢♦r♠❛t✐✈♦✳ ❆ ✐❧✉str❛çã♦ ❞❛ ♠❡t♦❞♦❧♦❣✐❛ ❞❡s❝r✐t❛ é r❡❛❧✐③❛❞❛ ❝♦♠ ♣❛❝✐❡♥t❡s ✐♥t❡r♥❛❞♦s ♥♦ ❍❈✶_{✴❯❋▼●✱ ❛♣ós ✉♠ tr❛♥s♣❧❛♥t❡ ❞❡ ♠❡❞✉❧❛ óss❡❛ ✈✐❛ ❝❛t❡t❡r}

✐♥tr❛ ✈❡♥♦s♦✱ ♥♦ ♣❡rí♦❞♦ ❞❡ ♠❛✐♦ ❞❡ ✷✵✶✵ ❛ ❥✉♥❤♦ ❞❡ ✷✵✶✶✳

P❛❧❛✈r❛s✲❝❤❛✈❡✿ ❈❡♥s✉r❛ ■♥❢♦r♠❛t✐✈❛✱ ❋r❛❣✐❧✐❞❛❞❡ ●❛♠❛✱ ❱❡r♦ss✐♠✐❧❤❛♥ç❛ ▼❛r❣✐♥❛❧✳

✶_{❍♦s♣✐t❛❧ ❞❛s ❈❧í♥✐❝❛s}

(7)

❆❜str❛❝t

■♥ s✉r✈✐✈❛❧ ❛♥❛❧②s✐s ❞❛t❛ ♠♦❞❡❧✐♥❣✱ t❤❡ ♠♦st ♦❢ ♣r♦❝❡❞✉r❡s ❧❡❛❞ t♦ t❤❡ ♥♦♥✲✐♥❢♦r♠❛t✐✈❡ ❝❡♥s♦r✐♥❣✱ ✐✳❡✱ t❤❡ ❡✈❡♥t ❛♥❞ ❝❡♥s♦r✐♥❣ t✐♠❡ ❛r❡ ✐♥❞❡♣❡♥❞❡♥t ✭t❤❡ ❝❡♥s♦r✐♥❣ t✐♠❡ ❞✐str✐❜✉t✐♦♥ ♣❛r❛♠❡t❡rs ❞♦❡s ♥♦t ❝❛rr② ❛♥② ✐♥❢♦r♠❛t✐♦♥ ❛❜♦✉t t❤❡ ❢❛✐❧✉r❡ t✐♠❡ ❞✐str✐❜✉t✐♦♥ ♣❛r❛♠❡t❡rs✮✳ ❍♦✇❡✈❡r✱ ✐♥ s♦♠❡ ❝❛s❡s t❤❡ ♥♦♥✲✐♥❢♦r♠❛t✐✈❡ ❝❡♥s♦r✐♥❣ ❛ss✉♠♣t✐♦♥ ✐s ✈✐♦❧❛t❡❞ ❛♥❞ t❤✉s ✐t ✐s ♥❡❝❡ss❛r② t♦ ✐♥❝❧✉❞❡ ❛ str✉❝t✉r❡ ✇❤✐❝❤ t❛❦❡s ✐♥t♦ ❛❝❝♦✉♥t t❤❡ ❞❡♣❡♥❞❡♥❝❡ ❜❡t✇❡❡♥ ❚ ❛♥❞ ❈✳ ■♥ t❤✐s ✇♦r❦✱ t❤❡ ♠♦❞❡❧✐♥❣ ❝♦♥s✐❞❡r t❤❡ ❛ss✉♠♣t✐♦♥ t❤❡ ❚ ❛♥❞ ❈ ❛r❡ ❝♦♥❞✐t✐♦♥❛❧❧② ✐♥❞❡♣❡♥❞❡♥ts ❣✐✈❡♥ ❛ ❢r❛✐❧t② ❩✱ ✇❤✐❝❤ ❢♦❧❧♦✇s ❛ ❣❛♠♠❛ ❞✐str✐❜✉t✐♦♥ ✇✐t❤ ❧♦❝❛t✐♦♥ ❛♥❞ s❝❛❧❡ ♣❛r❛♠❡t❡rs ❡q✉❛❧ t♦ φ✳ ❚♦ t❤✐s ❝❛s❡ ✭❛♥❞ t❤❡ ❞❡❢❛✉❧t ❝❛s❡✮✱ ✇❡ ❛ss✉♠❡ ♣❛r❛♠❡tr✐❝ ♠♦❞❡❧s

s✉❝❤ ❛s ❊①♣♦♥❡♥t✐❛❧ ❡ ❲❡✐❜✉❧❧ ❢♦r t❤❡ t✐♠❡s ✈❛r✐❛❜❧❡s✳ ❇② ✐♥❝♦r♣♦r❛t✐♥❣ t❤❡ ❢r❛✐❧t② ❩ ✐♥ t❤❡ ♠♦❞❡❧✐♥❣✱ t❤❡ ♠❛①✐♠✉♠ ❧✐❦❡❧✐❤♦♦❞ ❡st✐♠❛t♦rs ❛r❡ ❢♦✉♥❞ ❜② ♠❛①✐♠✐③✐♥❣ t❤❡ ♠❛r❣✐♥❛❧ ❧✐❦❡❧✐❤♦♦❞ ❢✉♥❝t✐♦♥✳ ❲❡ ♣❡r❢♦r♠ ❛ ▼♦♥t❡ ❈❛r❧♦ s✐♠✉❧❛t✐♦♥ st✉❞② t♦ ❡✈❛❧✉❛t❡ t❤❡ ✐♥❢♦r♠❛t✐✈❡ ❛♥❞ ✉s✉❛❧ ♠♦❞❡❧s ✉♥❞❡r s❝❡♥❛r✐♦s ✐♥ ✇❤✐❝❤ t❤❡ ❝❡♥s♦r✐♥❣ ♠❡❝❤❛♥✐s♠ ✐s ✐♥❢♦r♠❛t✐✈❡ ❛♥❞ ♥♦♥✲ ✐♥❢♦r♠❛t✐✈❡✳ ❚❤❡ ❛♥❛❧②s✐s ♦❢ ❛ ❞❛t❛ s❡t r❡❣❛r❞✐♥❣ t❤❡ ♣❛t✐❡♥ts ❛❞♠✐tt❡❞ t♦ ❍❈✴❯❋▼●✱ ❛❢t❡r ❛ ❜♦♥❡ ♠❛rr♦✇ tr❛♥s♣❧❛♥t❛t✐♦♥✱ ❢r♦♠ ♠❛② ✷✵✶✵ t♦ ❥✉♥❡ ✷✵✶✶✳

❑❡②✇♦r❞s✿ ■♥❢♦r♠❛t✐✈❡ ❝❡♥s♦r✐♥❣✱ ❋r❛✐❧t② ●❛♠♠❛✱ ▼❛r❣✐♥❛❧ ▲✐❦❡❧✐❤♦♦❞✳

(8)

❙✉♠ár✐♦

▲✐st❛ ❞❡ ❋✐❣✉r❛s ✈✐✐✐

▲✐st❛ ❞❡ ❚❛❜❡❧❛s ①

✶ ■♥tr♦❞✉çã♦ ✶

✶✳✶ ❈♦♥s✐❞❡r❛çõ❡s Pr❡❧✐♠✐♥❛r❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸

✶✳✷ ❖❜❥❡t✐✈♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹

✶✳✸ ❖r❣❛♥✐③❛çã♦ ❞♦ ❚r❛❜❛❧❤♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹

✷ ▼❡t♦❞♦❧♦❣✐❛ ✺

✷✳✶ ▼❡❝❛♥✐s♠♦ ❞❡ ❝❡♥s✉r❛ ♥ã♦ ✐♥❢♦r♠❛t✐✈♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺

✷✳✷ Pr♦❝❡❞✐♠❡♥t♦ ♣❛r❛ ♦ ▼❡❝❛♥✐s♠♦ ❞❡ ❈❡♥s✉r❛ ■♥❢♦r♠❛t✐✈♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻

✷✳✷✳✶ ❊st✐♠❛çã♦ ❞♦s P❛râ♠❡tr♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽

✷✳✸ ❈❛s♦s P❛rt✐❝✉❧❛r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾

✷✳✸✳✶ ▼♦❞❡❧♦ ❊①♣♦♥❡♥❝✐❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾

✷✳✸✳✷ ▼♦❞❡❧♦ ❲❡✐❜✉❧❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶

✸ ❙✐♠✉❧❛çã♦ ▼♦♥t❡ ❈❛r❧♦ ✶✸

✸✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸

✸✳✷ ❊st✐♠❛t✐✈❛s ❞♦s P❛râ♠❡tr♦s ✭❊①♣♦♥❡♥❝✐❛❧✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹

✸✳✸ ❊st✐♠❛t✐✈❛s ❞♦s P❛râ♠❡tr♦s ✭❲❡✐❜✉❧❧✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽

✸✳✹ ❈♦♠♣❛r❛çã♦ ❞❛s ❋✉♥çõ❡s ❞❡ ❙♦❜r❡✈✐✈ê♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵

✸✳✹✳✶ ▼♦❞❡❧♦ ❊①♣♦♥❡♥❝✐❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵

✸✳✹✳✷ ▼♦❞❡❧♦ ✇❡✐❜✉❧❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶

✸✳✺ ■♠♣❛❝t♦ ❞❛ ❛♠♦str❛✱ ✪ ❞❡ ❢❛❧❤❛ ❡ ❢♦r♠❛ ♣❛r❛ ❤✭t✮ ♥❛ ❡st✐♠❛çã♦ ❞❡ φ ✳ ✳ ✳ ✳ ✸✼

✹ ❆♣❧✐❝❛çã♦ ✹✷

✹✳✶ ❆♥á❧✐s❡ ❉❡s❝r✐t✐✈❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷

✹✳✷ ❘❡s✉❧t❛❞♦s ❞♦s ❆❥✉st❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸

✺ ❈♦♥❝❧✉sõ❡s ✹✻

❆ ❉❡r✐✈❛❞❛s ❞❡ ❙❡❣✉♥❞❛ ❖r❞❡♠ ✹✼

❆✳✶ ▼♦❞❡❧♦ ❡①♣♦♥❡♥❝✐❛❧ ❝♦♠ ♠❡❝❛♥✐s♠♦ ❞❡ ❝❡♥s✉r❛ ✐♥❢♦r♠❛t✐✈♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼

❆✳✷ ▼♦❞❡❧♦ ❲❡✐❜✉❧❧ ❝♦♠ ♠❡❝❛♥✐s♠♦ ❞❡ ❝❡♥s✉r❛ ✐♥❢♦r♠❛t✐✈♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼

(9)

❙❯▼➪❘■❖ ✈✐✐

❇ ❚❛❜❡❧❛s ❞❛ ❙✐♠✉❧❛çã♦ ▼♦♥t❡ ❈❛r❧♦ ✹✾

❇✳✶ ▼♦❞❡❧♦ ❡①♣♦♥❡♥❝✐❛❧ ❝♦♠ ♠❡❝❛♥✐s♠♦ ❞❡ ❝❡♥s✉r❛ ✐♥❢♦r♠❛t✐✈♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾

❇✳✷ ▼♦❞❡❧♦ ✇❡✐❜✉❧❧ ❝♦♠ ♠❡❝❛♥✐s♠♦ ❞❡ ❝❡♥s✉r❛ ✐♥❢♦r♠❛t✐✈♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵

❇✳✸ ❉✐stâ♥❝✐❛s ♣♦♥t✉❛✐s ❞❛ ❢✉♥çã♦ ❞❡ ❙♦❜r❡✈✐✈ê♥❝✐❛ ✈❡r❞❛❞❡✐r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷

(10)

▲✐st❛ ❞❡ ❋✐❣✉r❛s

✸✳✶ ❊sq✉❡♠❛ ❞❛ s✐♠✉❧❛çã♦ ♣❛r❛ ♦ ❝❡♥ár✐♦ ✐♥❢♦r♠❛t✐✈♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹

✸✳✷ ❈♦rr❡❧❛çã♦ ❞❡ P❡❛rs♦♥ ✭ρ✮ ❡♥tr❡ t❡♠♣♦s ❞❡ ❢❛❧❤❛ ❡ ❝❡♥s✉r❛✱ ❞❡ ❛❝♦r❞♦ ❝♦♠

❞✐❢❡r❡♥t❡s ✈❛❧♦r❡s ❞❡φ✱ ♣❛r❛ t❡♠♣♦s ❡①♣♦♥❡♥❝✐❛✐s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺

✸✳✸ ●rá✜❝♦s ❞❡ ❝♦♠♣❛r❛çã♦ ❞♦ ❡rr♦ ♣❛❞rã♦✱ ♥♦s ❝❡♥ár✐♦s ✐♥❢♦r♠❛t✐✈♦ ❡ ♥ã♦✲ ✐♥❢♦r♠❛t✐✈♦✱ t❡♠♣♦s ❡①♣♦♥❡♥❝✐❛✐s ✭▲✐♥❤❛ só❧✐❞❛✿λt❀ ▲✐♥❤❛ ❚r❛❝❡❥❛❞❛✿θc❀ ▲✐♥❤❛

♣♦♥t✐❧❤❛❞❛✿λ✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽

✸✳✹ ❈♦rr❡❧❛çã♦ ❞❡ P❡❛rs♦♥ ✭ρ✮ ❡♥tr❡ t❡♠♣♦s ❞❡ ❢❛❧❤❛ ❡ ❝❡♥s✉r❛✱ ❞❡ ❛❝♦r❞♦ ❝♦♠

❞✐❢❡r❡♥t❡s ✈❛❧♦r❡s ❞❡ φ✱ ♣❛r❛ ✉♠❛ ♣r♦♣♦rçã♦ ❞❡ ❢❛❧❤❛ ✷✺✪✱ ✺✵✪ ❡ ✼✺✪✱ ❝❛s♦

❲❡✐❜✉❧❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾

✸✳✺ ●rá✜❝♦s ❞❡ ❝♦♠♣❛r❛çã♦ ❞♦s ❊◗▼✬s✱ ♥♦s ❝❡♥ár✐♦s ✐♥❢♦r♠❛t✐✈♦ ❡ ♥ã♦✲✐♥❢♦r♠❛t✐✈♦✱ ♣❛r❛ ♦s ♣❛râ♠❡tr♦s ❞❡ ❢♦r♠❛✱ ❢✉♥çã♦ r✐s❝♦ ❧✐♥❡❛r ✭▲✐♥❤❛ só❧✐❞❛✿ αt❀ ▲✐♥❤❛

❚r❛❝❡❥❛❞❛✿ αc❀ ▲✐♥❤❛ ♣♦♥t✐❧❤❛❞❛✿ α✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶

✸✳✻ ●rá✜❝♦s ❞❡ ❝♦♠♣❛r❛çã♦ ❞♦s ❊◗▼✬s ♣❛r❛ ✷✺✪✱ ✺✵✪ ❡ ✼✺✪✱ ♥♦s ❝❡♥ár✐♦s ✐♥✲ ❢♦r♠❛t✐✈♦ ❡ ♥ã♦✲✐♥❢♦r♠❛t✐✈♦✱ ♣❛r❛ ♦s ♣❛râ♠❡tr♦s ❞❡ ❡s❝❛❧❛✱❢✉♥çã♦ r✐s❝♦ ❧✐♥❡❛r ✭▲✐♥❤❛ só❧✐❞❛✿ γt❀ ▲✐♥❤❛ ❚r❛❝❡❥❛❞❛✿ γc❀ ▲✐♥❤❛ ♣♦♥t✐❧❤❛❞❛✿ γ✮✳✳ ✳ ✳ ✳ ✳ ✳ ✷✷

✸✳✼ ●rá✜❝♦s ❞❡ ❝♦♠♣❛r❛çã♦ ❞♦s ❊◗▼✬s✱ ♥♦s ❝❡♥ár✐♦s ✐♥❢♦r♠❛t✐✈♦ ❡ ♥ã♦✲✐♥❢♦r♠❛t✐✈♦✱ ♣❛r❛ ♦s ♣❛râ♠❡tr♦s ❞❡ ❡s❝❛❧❛✱ ❢✉♥çã♦ r✐s❝♦ ❝♦♥✈❡①❛ ✭▲✐♥❤❛ só❧✐❞❛✿γt❀ ▲✐♥❤❛

❚r❛❝❡❥❛❞❛✿ γc❀ ▲✐♥❤❛ ♣♦♥t✐❧❤❛❞❛✿γ✮✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻

✸✳✽ ●rá✜❝♦s ❞❡ ❝♦♠♣❛r❛çã♦ ❞♦s ❊◗▼✬s✱ ♥♦s ❝❡♥ár✐♦s ✐♥❢♦r♠❛t✐✈♦ ❡ ♥ã♦✲✐♥❢♦r♠❛t✐✈♦✱ ♣❛r❛ ♦s ♣❛râ♠❡tr♦s ❞❡ ❡s❝❛❧❛✱ ❢✉♥çã♦ r✐s❝♦ ❝♦♥✈❡①❛ ✭▲✐♥❤❛ só❧✐❞❛✿γt❀ ▲✐♥❤❛

❚r❛❝❡❥❛❞❛✿ γc❀ ▲✐♥❤❛ ♣♦♥t✐❧❤❛❞❛✿γ✮✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼

✸✳✾ ●rá✜❝♦s ❞❡ ❝♦♠♣❛r❛çã♦ ❞♦s ❊◗▼✬s✱ ♥♦s ❝❡♥ár✐♦s ✐♥❢♦r♠❛t✐✈♦ ❡ ♥ã♦✲✐♥❢♦r♠❛t✐✈♦✱ ♣❛r❛ ♦s ♣❛râ♠❡tr♦s ❞❡ ❢♦r♠❛✱ ❢✉♥çã♦ r✐s❝♦ ❞❡❝r❡s❝❡♥t❡ ✭▲✐♥❤❛ só❧✐❞❛✿αt❀ ▲✐✲

♥❤❛ ❚r❛❝❡❥❛❞❛✿ αc❀ ▲✐♥❤❛ ♣♦♥t✐❧❤❛❞❛✿α✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾

✸✳✶✵ ●rá✜❝♦s ❞❡ ❝♦♠♣❛r❛çã♦ ❞♦s ❊◗▼✬s✱ ♥♦s ❝❡♥ár✐♦s ✐♥❢♦r♠❛t✐✈♦ ❡ ♥ã♦✲✐♥❢♦r♠❛t✐✈♦✱ ♣❛r❛ ♦s ♣❛râ♠❡tr♦s ❞❡ ❢♦r♠❛✱ ❢✉♥çã♦ r✐s❝♦ ❞❡❝r❡s❝❡♥t❡ ✭▲✐♥❤❛ só❧✐❞❛✿αt❀ ▲✐✲

♥❤❛ ❚r❛❝❡❥❛❞❛✿ αc❀ ▲✐♥❤❛ ♣♦♥t✐❧❤❛❞❛✿α✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵

✸✳✶✶ ❈✉r✈❛s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛✱ ♣❛r❛ ❢♦r♠❛ ❞❛ ❢✉♥çã♦ r✐s❝♦ ❝♦♥✈❡①❛ ❝r❡s❝❡♥t❡✱ ❝♦♠ ✷✺✪✱ ✺✵✪ ❡ ✼✺✪ ❞❡ ❢❛❧❤❛✱ ♥✉♠ ❝❡♥ár✐♦ ✐♥❢♦r♠❛t✐✈♦ ❝♦♠φ = 0,5✱ ❡ t❛♠❛♥❤♦

❛♠♦str❛❧ ✐❣✉❛❧ ❛ ✶✵✵✵✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸

✸✳✶✷ ❈✉r✈❛s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛✱ ♣❛r❛ ❢♦r♠❛ ❞❛ ❢✉♥çã♦ r✐s❝♦ ❞❡❝r❡s❝❡♥t❡✱ ❝♦♠ ✷✺✪✱ ✺✵✪ ❡ ✼✺✪ ❞❡ ❢❛❧❤❛✱ ♥✉♠ ❝❡♥ár✐♦ ✐♥❢♦r♠❛t✐✈♦ ❝♦♠φ = 1✱ ❡ t❛♠❛♥❤♦ ❛♠♦str❛❧

✐❣✉❛❧ ❛ ✶✵✵✵✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺

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▲■❙❚❆ ❉❊ ❋■●❯❘❆❙ ✐①

✸✳✶✸ ❈✉r✈❛s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛✱ ♣❛r❛ ❢♦r♠❛ ❞❛ ❢✉♥çã♦ r✐s❝♦ ❝♦♥st❛♥t❡✱ ❝♦♠ t❛♠❛♥❤♦s ❛♠♦str❛✐s ✐❣✉❛✐s ❛ ✺✵✱ ✶✵✵ ❡ ✶✵✵✵✱ ♥✉♠ ❝❡♥ár✐♦ ✐♥❢♦r♠❛t✐✈♦ ❝♦♠φ = 0,5✱ ❝♦♠

♣r♦♣♦rçã♦ ❞❡ ❢❛❧❤❛ ❞❡ ✷✺✪✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻

✸✳✶✹ ❈✉r✈❛s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛✱ ♣❛r❛ ❢♦r♠❛ ❞❛ ❢✉♥çã♦ r✐s❝♦ ❝ô♥❝❛✈❛✱ ❝♦♠ t❛♠❛♥❤♦s ❛♠♦str❛✐s ✐❣✉❛✐s ❛ ✺✵✱ ✶✵✵ ❡ ✶✵✵✵✱ ♥✉♠ ❝❡♥ár✐♦ ✐♥❢♦r♠❛t✐✈♦ ❝♦♠ φ = 1✱ ❝♦♠

♣r♦♣♦rçã♦ ❞❡ ❢❛❧❤❛ ❞❡ ✼✺✪✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼

✸✳✶✺ ❇♦①✲♣❧♦ts ♣❛r❛ ❛s ❡st✐♠❛t✐✈❛s ❞❡ φ q✉❛♥❞♦ ♦ r❡❛❧ é ✵✱✺✱ ♣❛r❛ ❛✈❛❧✐❛çã♦ ❞❡

✐♠♣❛❝t♦s ❞❡ ❞✐❢❡r❡♥t❡s t❛①❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽

✸✳✶✻ ❇♦①✲♣❧♦ts ✭s❡♠ ♦✉t❧✐❡rs✮ ♣❛r❛ ❛s ❡st✐♠❛t✐✈❛s ❞❡ φ q✉❛♥❞♦ ♦ r❡❛❧ é ✵✱✺✱ ♣❛r❛

❛✈❛❧✐❛çã♦ ❞❡ ✐♠♣❛❝t♦s ❞❡ ❞✐❢❡r❡♥t❡s t❛①❛s✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾

✸✳✶✼ ❇♦①✲♣❧♦ts ♣❛r❛ ❛s ❡st✐♠❛t✐✈❛s ❞❡ φ q✉❛♥❞♦ ♦ r❡❛❧ é ✶✱ ♣❛r❛ ❛✈❛❧✐❛çã♦ ❞❡ ✐♠✲

♣❛❝t♦s ❞❡ ❞✐❢❡r❡♥t❡s ❢♦r♠❛s ♣❛r❛ ❛ ❢✉♥çã♦ r✐s❝♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵

✸✳✶✽ ❇♦①✲♣❧♦ts ✭s❡♠ ♦✉t❧✐❡rs✮ ♣❛r❛ ❛s ❡st✐♠❛t✐✈❛s ❞❡ φ q✉❛♥❞♦ ♦ r❡❛❧ é ✶✱ ♣❛r❛

❛✈❛❧✐❛çã♦ ❞❡ ✐♠♣❛❝t♦s ❞❡ ❞✐❢❡r❡♥t❡s t❛①❛s✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶

✹✳✶ ❍✐st♦❣r❛♠❛ ♣❛r❛ ♦s t❡♠♣♦s ♦❜s❡r✈❛❞♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸

✹✳✷ ❍✐st♦❣r❛♠❛ ♣❛r❛ ♦s t❡♠♣♦s ❞❡ ❢❛❧❤❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸

✹✳✸ ❍✐st♦❣r❛♠❛ ♣❛r❛ ♦s t❡♠♣♦s ❞❡ ❝❡♥s✉r❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸

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▲✐st❛ ❞❡ ❚❛❜❡❧❛s

✸✳✶ ❊st✐♠❛t✐✈❛ ❞♦s ♣❛râ♠❡tr♦s ♣❡❧♦s ♠♦❞❡❧♦s ❡①♣♦♥❡♥❝✐❛❧ ♠❛r❣✐♥❛❧ ❡ ✉s✉❛❧✱ ❝♦♠ ✺✵✵ r❡♣❧✐❝❛çõ❡s✱ s♦❜ ✉♠ ❝❡♥ár✐♦ ♥ã♦✲✐♥❢♦r♠❛t✐✈♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼

✸✳✷ ❊st✐♠❛t✐✈❛ ❞♦s ♣❛râ♠❡tr♦s ♣❡❧♦s ♠♦❞❡❧♦s ✇❡✐❜✉❧❧ ♠❛r❣✐♥❛❧ ❡ ✉s✉❛❧✱ ❝♦♠ ✺✵✵ r❡♣❧✐❝❛çõ❡s✱ s♦❜ ✉♠ ❝❡♥ár✐♦ ♥ã♦✲✐♥❢♦r♠❛t✐✈♦✱ ❝♦♠ ❢✉♥çã♦ r✐s❝♦ ❝ô♥❝❛✈❛✳ ✳ ✳ ✳ ✷✸

✸✳✸ ❊st✐♠❛t✐✈❛ ❞♦s ♣❛râ♠❡tr♦s ♣❡❧♦s ♠♦❞❡❧♦s ❲❡✐❜✉❧❧ ♠❛r❣✐♥❛❧ ❡ ✉s✉❛❧✱ ❝♦♠ ✺✵✵ r❡♣❧✐❝❛çõ❡s✱ s♦❜ ✉♠ ❝❡♥ár✐♦ ✐♥❢♦r♠❛t✐✈♦✱ ❝♦♠φ= 0,5✱ ❝♦♠ ❢✉♥çã♦ r✐s❝♦ ❝ô♥❝❛✈❛✳ ✷✹

✸✳✹ ❊st✐♠❛t✐✈❛ ❞♦s ♣❛râ♠❡tr♦s ♣❡❧♦s ♠♦❞❡❧♦s ❲❡✐❜✉❧❧ ♠❛r❣✐♥❛❧ ❡ ✉s✉❛❧✱ ❝♦♠ ✺✵✵ r❡♣❧✐❝❛çõ❡s✱ s♦❜ ✉♠ ❝❡♥ár✐♦ ✐♥❢♦r♠❛t✐✈♦✱ ❝♦♠φ= 1✱ ❝♦♠ ❢✉♥çã♦ r✐s❝♦ ❝ô♥❝❛✈❛✳ ✷✺

✸✳✺ ❊st✐♠❛t✐✈❛ ❞♦s ♣❛râ♠❡tr♦s ♣❡❧♦s ♠♦❞❡❧♦s ✇❡✐❜✉❧❧ ♠❛r❣✐♥❛❧ ❡ ✉s✉❛❧✱ ❝♦♠ ✺✵✵ r❡♣❧✐❝❛çõ❡s✱ s♦❜ ✉♠ ❝❡♥ár✐♦ ♥ã♦✲✐♥❢♦r♠❛t✐✈♦✱ ❝♦♠ ❢✉♥çã♦ ❞❡ r✐s❝♦ ❞❡❝r❡s❝❡♥t❡✳ ✷✽

✸✳✻ ❉✐stâ♥❝✐❛s ♠é❞✐❛s ❞❛s ❢✉♥çõ❡s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❞♦ ♠♦❞❡❧♦ ❡①♣♦♥❡♥❝✐❛❧ ✐♥❢♦r✲ ♠❛t✐✈♦ ❡ ✉s✉❛❧✱ ❝♦♠ ❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ✈❡r❞❛❞❡✐r❛✱ s♦❜ ✉♠ ❝❡♥ár✐♦ ♥ã♦✲✐♥❢♦r♠❛t✐✈♦✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶

✸✳✼ ❉✐stâ♥❝✐❛s ♠é❞✐❛s ❞❛s ❢✉♥çõ❡s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❞♦ ♠♦❞❡❧♦ ❡①♣♦♥❡♥❝✐❛❧ ✐♥❢♦r✲ ♠❛t✐✈♦ ❡ ✉s✉❛❧✱ ❝♦♠ ❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ✈❡r❞❛❞❡✐r❛✱ s♦❜ ✉♠ ❝❡♥ár✐♦ ✐♥❢♦r♠❛t✐✈♦✱ ❝♦♠ φ= 0,5✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶

✸✳✽ ❉✐stâ♥❝✐❛s ♠é❞✐❛s ❞❛s ❢✉♥çõ❡s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❞♦ ♠♦❞❡❧♦ ✇❡✐❜✉❧❧ ✐♥❢♦r♠❛✲ t✐✈♦ ❡ ✉s✉❛❧✱ ❝♦♠ ❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ✈❡r❞❛❞❡✐r❛✱ s♦❜ ✉♠ ❝❡♥ár✐♦ ♥ã♦✲ ✐♥❢♦r♠❛t✐✈♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷

✸✳✾ ❉✐stâ♥❝✐❛s ♠é❞✐❛s ❞❛s ❢✉♥çõ❡s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❞♦ ♠♦❞❡❧♦ ✇❡✐❜✉❧❧ ✐♥❢♦r♠❛t✐✈♦ ❡ ✉s✉❛❧✱ ❝♦♠ ❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ✈❡r❞❛❞❡✐r❛✱ s♦❜ ✉♠ ❝❡♥ár✐♦ ✐♥❢♦r♠❛t✐✈♦✱ ❝♦♠ φ= 0,5✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷

✸✳✶✵ ❉✐stâ♥❝✐❛s ♠é❞✐❛s ❞❛s ❢✉♥çõ❡s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❞♦ ♠♦❞❡❧♦ ✇❡✐❜✉❧❧ ✐♥❢♦r♠❛✲ t✐✈♦ ❡ ✉s✉❛❧✱ ❝♦♠ ❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ✈❡r❞❛❞❡✐r❛✱ s♦❜ ✉♠ ❝❡♥ár✐♦ ♥ã♦✲ ✐♥❢♦r♠❛t✐✈♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹

✸✳✶✶ ❉✐stâ♥❝✐❛s ♠é❞✐❛s ❞❛s ❢✉♥çõ❡s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❞♦ ♠♦❞❡❧♦ ✇❡✐❜✉❧❧ ✐♥❢♦r♠❛t✐✈♦ ❡ ✉s✉❛❧✱ ❝♦♠ ❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ✈❡r❞❛❞❡✐r❛✱ s♦❜ ✉♠ ❝❡♥ár✐♦ ✐♥❢♦r♠❛t✐✈♦✱ ❝♦♠ φ= 0,5✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹

✹✳✶ ❉❛❞♦s ❞❡s❝r✐t✐✈♦s ♣❛r❛ ♣❛❝✐❡♥t❡s ✐♥t❡r♥❛❞♦s ♣ós✲tr❛♥s♣❧❛♥t❡ ❞❡ ♠❡❞✉❧❛ óss❡❛ ♥♦ ❍❈✲❯❋▼●✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷

✹✳✷ ❊st✐♠❛t✐✈❛ ❞♦s ♣❛râ♠❡tr♦s ♣❡❧♦s ♠♦❞❡❧♦s ❊①♣♦♥❡♥❝✐❛❧ ✉s✉❛❧ ❡ ✈✐❛ ✈❡r♦ss✐♠✐✲ ❧❤❛♥ç❛ ♠❛r❣✐♥❛❧✱ ♣❛r❛ ♣❛❝✐❡♥t❡s ✐♥t❡r♥❛❞♦s ♣ós✲tr❛♥s♣❧❛♥t❡ ♥♦ ❍❈✲❯❋▼●✳ ✳ ✹✹

(13)

▲■❙❚❆ ❉❊ ❚❆❇❊▲❆❙ ①✐

✹✳✸ ❊st✐♠❛t✐✈❛ ❞♦s ♣❛râ♠❡tr♦s ♣❡❧♦s ♠♦❞❡❧♦s ❲❡✐❜✉❧❧ ❯s✉❛❧ ❡ ✈✐❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ♠❛r❣✐♥❛❧✱ ♣❛r❛ ♣❛❝✐❡♥t❡s ✐♥t❡r♥❛❞♦s ♣ós✲tr❛♥s♣❧❛♥t❡ ♥♦ ❍❈✲❯❋▼●✳ ✳ ✳ ✳ ✳ ✳ ✹✹

❇✳✶ ❊st✐♠❛t✐✈❛ ❞♦s ♣❛râ♠❡tr♦s ♣❡❧♦s ♠♦❞❡❧♦s ❡①♣♦♥❡♥❝✐❛❧ ♠❛r❣✐♥❛❧ ❡ ✉s✉❛❧✱ ❝♦♠ ✺✵✵ r❡♣❧✐❝❛çõ❡s✱ s♦❜ ✉♠ ❝❡♥ár✐♦ ✐♥❢♦r♠❛t✐✈♦✱ ❝♦♠φ = 0,5✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾

❇✳✷ ❊st✐♠❛t✐✈❛ ❞♦s ♣❛râ♠❡tr♦s ♣❡❧♦s ♠♦❞❡❧♦s ❡①♣♦♥❡♥❝✐❛❧ ♠❛r❣✐♥❛❧ ❡ ✉s✉❛❧✱ ❝♦♠ ✺✵✵ r❡♣❧✐❝❛çõ❡s✱ s♦❜ ✉♠ ❝❡♥ár✐♦ ✐♥❢♦r♠❛t✐✈♦✱ ❝♦♠φ = 1✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵

❇✳✸ ❊st✐♠❛t✐✈❛ ❞♦s ♣❛râ♠❡tr♦s ♣❡❧♦s ♠♦❞❡❧♦s ✇❡✐❜✉❧❧ ♠❛r❣✐♥❛❧ ❡ ✉s✉❛❧✱ ❝♦♠ ✺✵✵ r❡♣❧✐❝❛çõ❡s✱ s♦❜ ✉♠ ❝❡♥ár✐♦ ♥ã♦✲✐♥❢♦r♠❛t✐✈♦✱ ❝♦♠ ❢✉♥çã♦ r✐s❝♦ ❧✐♥❡❛r✳ ✳ ✳ ✳ ✳ ✺✵

❇✳✹ ❊st✐♠❛t✐✈❛ ❞♦s ♣❛râ♠❡tr♦s ♣❡❧♦s ♠♦❞❡❧♦s ❲❡✐❜✉❧❧ ♠❛r❣✐♥❛❧ ❡ ✉s✉❛❧✱ ❝♦♠ ✺✵✵ r❡♣❧✐❝❛çõ❡s✱ s♦❜ ✉♠ ❝❡♥ár✐♦ ✐♥❢♦r♠❛t✐✈♦✱ ❝♦♠ φ = 0,5✱ ♣❛r❛ ❛ ❢✉♥çã♦ r✐s❝♦

❧✐♥❡❛r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶

❇✳✺ ❊st✐♠❛t✐✈❛ ❞♦s ♣❛râ♠❡tr♦s ♣❡❧♦s ♠♦❞❡❧♦s ❲❡✐❜✉❧❧ ♠❛r❣✐♥❛❧ ❡ ✉s✉❛❧✱ ❝♦♠ ✺✵✵ r❡♣❧✐❝❛çõ❡s✱ s♦❜ ✉♠ ❝❡♥ár✐♦ ✐♥❢♦r♠❛t✐✈♦✱ ❝♦♠φ= 1✱ ♣❛r❛ ❛ ❢✉♥çã♦ r✐s❝♦ ❧✐♥❡❛r✳ ✺✷

❇✳✻ ❊st✐♠❛t✐✈❛ ❞♦s ♣❛râ♠❡tr♦s ♣❡❧♦s ♠♦❞❡❧♦s ✇❡✐❜✉❧❧ ♠❛r❣✐♥❛❧ ❡ ✉s✉❛❧✱ ❝♦♠ ✺✵✵ r❡♣❧✐❝❛çõ❡s✱ s♦❜ ✉♠ ❝❡♥ár✐♦ ♥ã♦✲✐♥❢♦r♠❛t✐✈♦✱ ❝♦♠ ❢✉♥çã♦ r✐s❝♦ ❝♦♥✈❡①❛✳ ✳ ✳ ✳ ✺✸

❇✳✼ ❊st✐♠❛t✐✈❛ ❞♦s ♣❛râ♠❡tr♦s ♣❡❧♦s ♠♦❞❡❧♦s ❲❡✐❜✉❧❧ ♠❛r❣✐♥❛❧ ❡ ✉s✉❛❧✱ ❝♦♠ ✺✵✵ r❡♣❧✐❝❛çõ❡s✱ s♦❜ ✉♠ ❝❡♥ár✐♦ ✐♥❢♦r♠❛t✐✈♦✱ ❝♦♠φ = 0,5✱ ♣❛r❛ ❢✉♥çã♦ r✐s❝♦ ❝♦♥✈❡①❛✳ ✺✸

❇✳✽ ❊st✐♠❛t✐✈❛ ❞♦s ♣❛râ♠❡tr♦s ♣❡❧♦s ♠♦❞❡❧♦s ❲❡✐❜✉❧❧ ♠❛r❣✐♥❛❧ ❡ ✉s✉❛❧✱ ❝♦♠ ✺✵✵ r❡♣❧✐❝❛çõ❡s✱ s♦❜ ✉♠ ❝❡♥ár✐♦ ✐♥❢♦r♠❛t✐✈♦✱ ❝♦♠φ= 1✱ ♣❛r❛ ❢✉♥çã♦ r✐s❝♦ ❝♦♥✈❡①❛✳ ✺✹

❇✳✾ ❊st✐♠❛t✐✈❛ ❞♦s ♣❛râ♠❡tr♦s ♣❡❧♦s ♠♦❞❡❧♦s ❲❡✐❜✉❧❧ ♠❛r❣✐♥❛❧ ❡ ✉s✉❛❧✱ ❝♦♠ ✺✵✵ r❡♣❧✐❝❛çõ❡s✱ s♦❜ ✉♠ ❝❡♥ár✐♦ ✐♥❢♦r♠❛t✐✈♦✱ ❝♦♠ φ = 0,5✱ ♣❛r❛ ❢✉♥çã♦ r✐s❝♦

❞❡❝r❡s❝❡♥t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹

❇✳✶✵ ❊st✐♠❛t✐✈❛ ❞♦s ♣❛râ♠❡tr♦s ♣❡❧♦s ♠♦❞❡❧♦s ❲❡✐❜✉❧❧ ♠❛r❣✐♥❛❧ ❡ ✉s✉❛❧✱ ❝♦♠ ✺✵✵ r❡♣❧✐❝❛çõ❡s✱ s♦❜ ✉♠ ❝❡♥ár✐♦ ✐♥❢♦r♠❛t✐✈♦✱ ❝♦♠φ = 1✱ ♣❛r❛ ❢✉♥çã♦ r✐s❝♦ ❞❡❝r❡s✲

❝❡♥t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺

❇✳✶✶ ❉✐stâ♥❝✐❛s ♠é❞✐❛s ❞❛s ❢✉♥çõ❡s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❞♦ ♠♦❞❡❧♦ ❡①♣♦♥❡♥❝✐❛❧ ✐♥❢♦r✲ ♠❛t✐✈♦ ❡ ✉s✉❛❧✱ ❝♦♠ ❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ✈❡r❞❛❞❡✐r❛✱ s♦❜ ✉♠ ❝❡♥ár✐♦ ✐♥❢♦r♠❛t✐✈♦✱ ❝♦♠ φ= 1✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺

❇✳✶✷ ❉✐stâ♥❝✐❛s ♠é❞✐❛s ❞❛s ❢✉♥çõ❡s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❞♦ ♠♦❞❡❧♦ ✇❡✐❜✉❧❧ ✐♥❢♦r♠❛t✐✈♦ ❡ ✉s✉❛❧✱ ❝♦♠ ❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ✈❡r❞❛❞❡✐r❛✱ s♦❜ ✉♠ ❝❡♥ár✐♦ ✐♥❢♦r♠❛t✐✈♦✱ ❝♦♠ φ= 1✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺

❇✳✶✸ ❉✐stâ♥❝✐❛s ♠é❞✐❛s ❞❛s ❢✉♥çõ❡s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❞♦ ♠♦❞❡❧♦ ✇❡✐❜✉❧❧ ✐♥❢♦r♠❛✲ t✐✈♦ ❡ ✉s✉❛❧✱ ❝♦♠ ❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ✈❡r❞❛❞❡✐r❛✱ s♦❜ ✉♠ ❝❡♥ár✐♦ ♥ã♦✲ ✐♥❢♦r♠❛t✐✈♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻

❇✳✶✹ ❉✐stâ♥❝✐❛s ♠é❞✐❛s ❞❛s ❢✉♥çõ❡s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❞♦ ♠♦❞❡❧♦ ✇❡✐❜✉❧❧ ✐♥❢♦r♠❛t✐✈♦ ❡ ✉s✉❛❧✱ ❝♦♠ ❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ✈❡r❞❛❞❡✐r❛✱ s♦❜ ✉♠ ❝❡♥ár✐♦ ✐♥❢♦r♠❛t✐✈♦✱ ❝♦♠ φ= 0,5✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻

(14)

▲■❙❚❆ ❉❊ ❚❆❇❊▲❆❙ ①✐✐

❇✳✶✻ ❉✐stâ♥❝✐❛s ♠é❞✐❛s ❞❛s ❢✉♥çõ❡s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❞♦ ♠♦❞❡❧♦ ✇❡✐❜✉❧❧ ✐♥❢♦r♠❛t✐✈♦ ❡ ✉s✉❛❧✱ ❝♦♠ ❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ✈❡r❞❛❞❡✐r❛✱ s♦❜ ✉♠ ❝❡♥ár✐♦ ✐♥❢♦r♠❛t✐✈♦✱ ❝♦♠ φ= 1✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻

❇✳✶✼ ❉✐stâ♥❝✐❛s ♠é❞✐❛s ❞❛s ❢✉♥çõ❡s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❞♦ ♠♦❞❡❧♦ ✇❡✐❜✉❧❧ ✐♥❢♦r♠❛✲ t✐✈♦ ❡ ✉s✉❛❧✱ ❝♦♠ ❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ✈❡r❞❛❞❡✐r❛✱ s♦❜ ✉♠ ❝❡♥ár✐♦ ♥ã♦✲ ✐♥❢♦r♠❛t✐✈♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼

❇✳✶✽ ❉✐stâ♥❝✐❛s ♠é❞✐❛s ❞❛s ❢✉♥çõ❡s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❞♦ ♠♦❞❡❧♦ ✇❡✐❜✉❧❧ ✐♥❢♦r♠❛t✐✈♦ ❡ ✉s✉❛❧✱ ❝♦♠ ❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ✈❡r❞❛❞❡✐r❛✱ s♦❜ ✉♠ ❝❡♥ár✐♦ ✐♥❢♦r♠❛t✐✈♦✱ ❝♦♠ φ= 0,5✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼

(15)

❈❛♣ít✉❧♦ ✶

■♥tr♦❞✉çã♦

❉❡ ❛❝♦r❞♦ ❝♦♠❈♦❧♦s✐♠♦ ❡ ●✐♦❧♦✭✷✵✵✻✮ ❛ ❛♥á❧✐s❡ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ é ✉♠❛ ❞❛s ár❡❛s ❞❛ ❡st❛tíst✐❝❛ q✉❡ ♠❛✐s ❝r❡s❝❡✉ ♥❛s ✉❧t✐♠❛s ❞é❝❛❞❛s✱ ✉♠❛ ❞❛s r❛③õ❡s ❞❡ t❛❧ é ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❡ ♠❡❧❤♦r❛♠❡♥t♦ ❞❡ ♣r♦❝❡❞✐♠❡♥t♦s ❡st❛tíst✐❝♦s ❡ ❝♦♠♣✉t❛❝✐♦♥❛✐s✳ ❊♠ ❛♥á❧✐s❡ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❛ ✈❛r✐á✈❡❧ r❡s♣♦st❛ é ♦ t❡♠♣♦ ❛té ❛ ♦❝♦rrê♥❝✐❛ ❞❡ ✉♠ ❡✈❡♥t♦ ❞❡ ✐♥t❡r❡ss❡✱ t❛❧ ❝♦♠♦ ♦ t❡♠♣♦ ❛té ❛ ♠♦rt❡ ❞❡ ✉♠ ♣❛❝✐❡♥t❡✱ ❛té ❛ ❝✉r❛ ♦✉ r❡❝✐❞✐✈❛ ❞❡ ✉♠❛ ❞♦❡♥ç❛✱ ♦✉ ❛té ❛ ♦❝♦rrê♥❝✐❛ ❞❡ ✉♠❛ ❢❛❧❤❛ ❡♠ ✉♠ ❡q✉✐♣❛♠❡♥t♦ ❡t❝✳

❋♦r♠❛❧✐③❛♥❞♦ ❡st❛s ✐❞❡✐❛s ❞❡✈❡✲s❡ ❝♦♥s✐❞❡r❛r T ❝♦♠♦ s❡♥❞♦ ✉♠❛ ✈❛r✐á✈❡❧ ❛❧❡❛tór✐❛ ♥ã♦✲

♥❡❣❛t✐✈❛✱ q✉❡ r❡♣r❡s❡♥t❛ ♦ t❡♠♣♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❞❡ ✐♥❞✐✈í❞✉♦s ❡♠ ❛❧❣✉♠❛ ♣♦♣✉❧❛çã♦✳ ❚❛❧ ✈❛r✐á✈❡❧ ❛❧❡❛tór✐❛ ♣♦ss✉✐ ❢✉♥çã♦ ❞❡♥s✐❞❛❞❡ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡♥♦t❛❞❛ ♣♦r f(t) ❡ ❢✉♥çã♦ ❞❡ ❞✐str✐❜✉✐çã♦F(t)✳ ❆ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ✉♠ ✐♥❞✐✈í❞✉♦ s♦❜r❡✈✐✈❡r ♠❛✐s q✉❡ ✉♠ t❡♠♣♦ t é ❞❛❞❛

♣❡❧❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛✱

S(t) =P(T > t) =

Z ∞

t

f(u)du= 1−F(t), t >0. ✭✶✳✶✮

❆ ❢✉♥çã♦ ❞❡ t❛①❛ ❞❡ ❢❛❧❤❛✱ ❞❡♥♦t❛❞❛ ♣♦r h(t)✱ r❡♣r❡s❡♥t❛ ❛ t❛①❛ ❞❡ ❢❛❧❤❛ ✭r✐s❝♦✮ ✐♥st❛♥✲

tâ♥❡❛ ♥♦ t❡♠♣♦ t✱ ❡ é ❞❡✜♥✐❞❛ ♣♦r✱

h(t) = lim ∆t→₀

P(t≤T < t+ ∆t|T ≥t)

∆t , t >0. ✭✶✳✷✮

❆s ❢✉♥çõ❡s f(t)✱ F(t)✱ S(t)❡h(t)❢♦r♥❡❝❡♠ ❡s♣❡❝✐✜❝❛çõ❡s ♠❛t❡♠❛t✐❝❛♠❡♥t❡ ❡q✉✐✈❛❧❡♥t❡s ❞❛s ❞✐str✐❜✉✐çõ❡s ❞❡ T✳ P♦❞❡♠♦s ❢❛③❡r ❛❧❣✉♠❛s r❡❧❛çõ❡s✱ ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞❛s ♦✉tr❛s✱ ❝♦♠ S(t) ❡f(t)✱ ❡♠ t❡r♠♦s ❞❡ h(t)✱

h(t) = f(t)

S(t), t >0, ✭✶✳✸✮

❛ss✐♠ ❝♦♠ ❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ S(t)✱

S(t) = exp{−H(t)}, t >0, ✭✶✳✹✮

❡♠ q✉❡ H(t) é ❛ ❢✉♥çã♦ ❞❡ t❛①❛ ❞❡ ❢❛❧❤❛ ❛❝✉♠✉❧❛❞❛✱ ✐st♦ é✱

(16)

✶✳✵ ✷

H(t) =

Z t

0

h(u)du, t >0. ✭✶✳✺✮

❆✉t♦r❡s ❝♦♠♦ ■❜r❛❤✐♠ ❡t ❛❧✳ ✭✷✵✵✶✮ ❡ ❈♦❧❧❡tt ✭✷✵✵✸✮✱ ❡♥tr❡ ♦✉tr♦s✱ ❝✐t❛♠ ❝❧❛ss❡s ❞❡ ♠♦✲ ❞❡❧♦s ♥❛ ❧✐t❡r❛t✉r❛ ❡st❛tíst✐❝❛ ♥♦♠❡❛❞❛s ❝♦♠♦✿ ♣❛r❛♠étr✐❝♦✱ ♥ã♦✲♣❛r❛♠étr✐❝♦ ❡ ♦s s❡♠✐✲ ♣❛r❛♠étr✐❝♦s✳ ◆❡st❡ tr❛❜❛❧❤♦ ✉s❛r❡♠♦s s♦♠❡♥t❡ ❛ ❛❜♦r❞❛❣❡♠ ♣❛r❛♠étr✐❝❛✳ ◆♦ ❝❛s♦ ❞♦s ♠♦❞❡❧♦s ♣❛r❛♠étr✐❝♦s✱ ❛ss♦❝✐❛✲s❡ ✉♠❛ ❞✐str✐❜✉✐çã♦ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ à ✈❛r✐á✈❡❧ ❛❧❡❛tór✐❛ ❚✳ ❆❧é♠ ❞✐ss♦✱ ❣❡r❛❧♠❡♥t❡ ❛ ❞✐str✐❜✉✐çã♦ ❞♦s t❡♠♣♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ é ❛ss✐♠étr✐❝♦ ♥❛ ❞✐r❡çã♦ ❞♦s ♠❛✐♦r❡s t❡♠♣♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛✳ ■st♦ ♦❝♦rr❡ ♣♦rq✉❡ ❛ ♠❛✐♦r ♣❛rt❡ ❞♦s t❡♠♣♦s ♦❜s❡r✈❛✲ ❞♦s tê♠ ✈❛❧♦r❡s ♣❡q✉❡♥♦s ❡ ❛♣r❡s❡♥t❛♠✱ t❛♠❜é♠✱ ♣♦✉❝♦s ✐♥❞✐✈í❞✉♦s q✉❡ r❡❣✐str❛♠ t❡♠♣♦s ❞❡ ❛❝♦♠♣❛♥❤❛♠❡♥t♦ ♠✉✐t♦ ❧♦♥❣♦s✳

❆ ♣r✐♥❝✐♣❛❧ ❝❛r❛❝t❡ríst✐❝❛ ❞❡ ❞❛❞♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ é ❛ ♣r❡s❡♥ç❛ ❞❡ ❝❡♥s✉r❛✱ ❝❛r❛❝t❡r✐③❛❞❛ ♣❡❧❛ ♦❜s❡r✈❛çã♦ ✐♥❝♦♠♣❧❡t❛ ❞❛ ✈❛r✐á✈❡❧ ❞❡ ✐♥t❡r❡ss❡ ♣❛r❛ ❛❧❣✉♥s ✐♥❞✐✈í❞✉♦s ❞♦ ❡st✉❞♦✱ s❡❥❛ ♣♦r ✐♥✐❝✐❛t✐✈❛ ❞♦s ♠❡s♠♦s ❡♠ s❛✐r ❞♦ ❡st✉❞♦✱ ♣❡r❞❛ ❞❡ ❝♦♥t❛t♦ ❞✉r❛♥t❡ ♦ ❛❝♦♠♣❛♥❤❛♠❡♥t♦✱ tér♠✐♥♦ ❞♦ ❡st✉❞♦ s❡♠ ♦❝♦rrê♥❝✐❛ ❞♦ ❡✈❡♥t♦ ❡t❝✳ ❆ ❝❡♥s✉r❛ é ✐♥❝♦r♣♦r❛❞❛ ♥♦s ♠♦❞❡❧♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛✱ ❡ ♣♦❞❡ s❡r ❝❧❛ss✐✜❝❛❞❛ ❝♦♠♦✿

• ❈❡♥s✉r❛ à ❉✐r❡✐t❛✿ ♦ t❡♠♣♦ ❞❡ ♦❝♦rrê♥❝✐❛ ❞♦ ❡✈❡♥t♦ ❞❡ ✐♥t❡r❡ss❡ é ♠❛✐♦r q✉❡ ♦ t❡♠♣♦

r❡❣✐str❛❞♦✳ ✭❈❡♥s✉r❛ ❞♦ t✐♣♦ ■✱ ■■ ❡ ❛❧❡❛tór✐❛ ❝♦♠♦ ❝❛s♦s ♣❛rt✐❝✉❧❛r❡s✮

• ❈❡♥s✉r❛ à ❊sq✉❡r❞❛✿ ♦ t❡♠♣♦ r❡❣✐str❛❞♦ é ♠❛✐♦r q✉❡ ♦ t❡♠♣♦ ❞❡ ♦❝♦rrê♥❝✐❛ ❞♦ ❡✈❡♥t♦

❞❡ ✐♥t❡r❡ss❡✳

• ❈❡♥s✉r❛ ■♥t❡r✈❛❧❛r✿ ♦❝♦rr❡ q✉❛♥❞♦ s❛❜❡✲s❡ ❛♣❡♥❛s q✉❡ ♦ ❡✈❡♥t♦ ❞❡ ✐♥t❡r❡ss❡ ♦❝♦rr❡✉ ❡♠

✉♠ ❝❡rt♦ ✐♥t❡r✈❛❧♦ ❞❡ t❡♠♣♦✳

P❛r❛ ❡st❡ tr❛❜❛❧❤♦ ❞❡ ❞✐ss❡rt❛çã♦✱ ❝♦♥s✐❞❡r❛♠♦s s♦♠❡♥t❡ ♦ ♠❡❝❛♥✐s♠♦ ❞❡ ❝❡♥s✉r❛ à ❞✐✲ r❡✐t❛✳ ❖ ♠❡❝❛♥✐s♠♦ ❞❡ ❝❡♥s✉r❛ é ✉♠ ♣♦♥t♦ ❝r✉❝✐❛❧ ♥❛s ❛♥á❧✐s❡s ❞❡ ❞❛❞♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ✭✈❡r ▲❡✉♥❣ ❡t ❛❧✳ ✭✶✾✾✼✮✮✳ ❆ ♠❛✐♦r✐❛ ❞♦s ♠ét♦❞♦s ❡♠ ❛♥á❧✐s❡ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ s✉♣õ❡ ♦ ♠❡✲ ❝❛♥✐s♠♦ ❞❡ ❝❡♥s✉r❛ ♥ã♦✲✐♥❢♦r♠❛t✐✈♦✱ ♦✉ s❡❥❛✱ ♦s t❡♠♣♦s ❛té ♦ ❡✈❡♥t♦ ❞❡ ✐♥t❡r❡ss❡ ❡ ♦ ❞❡ ❝❡♥s✉r❛ sã♦ ✐♥❞❡♣❡♥❞❡♥t❡s ✭❛ ❞✐str✐❜✉✐çã♦ ❞♦s t❡♠♣♦s ❞❡ ❝❡♥s✉r❛ ♥ã♦ ❝❛rr❡❣❛♠ ✐♥❢♦r♠❛✲ çã♦ ❞♦s ♣❛râ♠❡tr♦s ❞❛ ❞✐str✐❜✉✐çã♦ ❞♦s t❡♠♣♦s ❞❡ ❢❛❧❤❛✮✳ ❊♥tr❡t❛♥t♦✱ ❡♠ ❛❧❣✉♥s ❝❛s♦s ❡ss❛ s✉♣♦s✐çã♦ é ✈✐♦❧❛❞❛✱ ❡ ❛ss✐♠ ♠ét♦❞♦s q✉❡ ✐♥❝♦r♣♦r❡♠ ❡str✉t✉r❛s ♣❛r❛ s✐t✉❛çõ❡s ❡♠ q✉❡ ♦ ♠❡❝❛♥✐s♠♦ ❞❡ ❝❡♥s✉r❛ é ✐♥❢♦r♠❛t✐✈♦ sã♦ ♥❡❝❡ssár✐♦s✳ ❊♠ s✐t✉❛çõ❡s ❡♠ q✉❡ ♣❛❝✐❡♥t❡s s❛❡♠ ❞♦ ❡st✉❞♦ ♣♦r r❛③õ❡s r❡❧❛❝✐♦♥❛❞❛s ❛♦ t✐♣♦ ❞❡ t❡r❛♣✐❛ ❡ ❝♦♥s❡q✉❡♥t❡♠❡♥t❡ t❡♠ ♦ ✜♠ ❞♦ s❡✉ ❛❝♦♠♣❛♥❤❛♠❡♥t♦✱ ♣♦❞❡✲s❡ ❝♦♥s✐❞❡r❛r q✉❡ ❛ ❝❡♥s✉r❛ é ✐♥❢♦r♠❛t✐✈❛✱ ♣♦✐s ❛ r❛③ã♦ ❞❛ ❝❡♥s✉r❛ ❡stá r❡❧❛❝✐♦♥❛❞❛ ❝♦♠ ♦ t❡♠♣♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❢✉t✉r♦✳ ❖✉tr♦s ❡①❡♠♣❧♦s sã♦ s✐t✉❛çõ❡s ❡♠ q✉❡ ❛ ❢❛❧❤❛ é ❝❛✉s❛❞❛ ♣♦r ❡✈❡♥t♦s s❡❝✉♥❞ár✐♦s ❡ ❛ss✐♠ r❡❣✐str❛❞❛s ❝♦♠♦ ♦❜s❡r✈❛çõ❡s ❝❡♥s✉r❛❞❛s ❬▲❛❣❛❦♦s ✭✶✾✼✾✮❪✳ ❇❛s✐❝❛♠❡♥t❡✱ ❛ ❝❡♥s✉r❛ ✐♥❢♦r♠❛t✐✈❛ ♦❝♦rr❡ q✉❛♥❞♦ ♦❜s❡r✈❛çõ❡s ❝❡♥s✉r❛✲ ❞❛s sã♦ ♠❛✐s ✭♦✉ ♠❡♥♦s✮ ♣r♦♣❡♥s❛s ❛ ❡①♣❡r✐♠❡♥t❛r ✉♠ ❡✈❡♥t♦ ❡s♣❡❝í✜❝♦ ❞❛s ♦❜s❡r✈❛çõ❡s r❡st❛♥t❡s ♥♦ ❢✉t✉r♦ ✭❈♦❧❧❡tt✱ ✷✵✵✸✮✳

❆ss✐♠✱ ❛❧❣✉♥s ❛✉t♦r❡s ❞❡s❡♥✈♦❧✈❡r❛♠ ♣r♦♣♦st❛s ♣❛r❛ ♠♦❞❡❧❛r ❞❛❞♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ s♦❜ ❛ s✉♣♦s✐çã♦ ❞❡ q✉❡ ♦ ♠❡❝❛♥✐s♠♦ ❞❡ ❝❡♥s✉r❛ é ✐♥❢♦r♠❛t✐✈♦✳ ▲❛❣❛❦♦s ❡ ❲✐❧❧✐❛♠s ✭✶✾✼✽✮ ♣r♦♣✉s❡r❛♠ ✉♠ ♠♦❞❡❧♦ q✉❡ ♣❡r♠✐t❡ q✉❡ ✉♠ ♣❛râ♠❡tr♦ ❡s❝❛❧❛r θ ✭✈❛r✐❛♥❞♦ ❞❡ ✵ ❛ ✶✮ ♠❡ç❛

♦ q✉❛♥t♦ ♦ t❡♠♣♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❡stá s❡♥❞♦ ❛❢❡t❛❞♦ ♣❡❧❛ ❝❡♥s✉r❛✳ ❆ss✐♠ ♣❛r❛ ✈❛❧♦r❡s ❞❡

θ ♣ró①✐♠♦s ❞❡ ✶ ❛ ❢✉♥çã♦ ❞❡ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ♥ã♦ é ❛❢❡t❛❞❛✱ ♠❛s q✉❛♥❞♦ s❡ ❛♣r♦①✐♠❛♠ ❞❡ ✵

♦s ❡❢❡✐t♦s ❞❛ ❝❡♥s✉r❛ s❡r✐❛♠ r❡❧❡✈❛♥t❡s ♥❛s ❡st✐♠❛t✐✈❛s ❞♦s ♣❛râ♠❡tr♦s ❞♦ ♠♦❞❡❧♦✳

(17)

✶✳✶ ❈❖◆❙■❉❊❘❆➬Õ❊❙ P❘❊▲■▼■◆❆❘❊❙ ✸

❡ ❞❡ ❝❡♥s✉r❛✱ ❡ ♠♦str❛r❛♠ q✉❡ ♦s ❡st✐♠❛❞♦r❡s ❞❡ ♠á①✐♠❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ♣❛r❛ ❛ ❞✐str✐❜✉✐çã♦ ❝♦♥❥✉♥t❛ sã♦ ❝♦♥s✐st❡♥t❡s✳ ◆♦ ❛rt✐❣♦ ❞❡ ❙❝❤❛r❢st❡✐♥ ❡ ❘♦❜✐♥s✭✷✵✵✷✮ ❢♦✐ ♣r♦♣♦st♦ ✉♠❛ ❢♦r♠❛ s❡♠✐♣❛r❛♠étr✐❝❛ ♣❛r❛ r❡❛❧✐③❛r ✉♠❛ ❛♥á❧✐s❡ ❞❡ s❡♥s✐❜✐❧✐❞❛❞❡ s♦❜r❡ ❛ ❞✐str✐❜✉✐çã♦ ❞♦ t❡♠♣♦ ❞❡ ❢❛❧❤❛✱ ❛tr❛✈és ❞❡ ✉♠❛ ❢✉♥çã♦ ♥ã♦ ❡s♣❡❝✐✜❝❛❞❛✱ ❝♦♠ ♦ ♦❜❥❡t✐✈♦ ❞❡ ❡st✐♠❛r ❛ ❞✐str✐❜✉✐çã♦ ❞❡ t❡♠♣♦ ❞❡ ❢❛❧❤❛✱ ❝♦♠ ❝❡rt❛ ❞❡♣❡♥❞ê♥❝✐❛✳ ◆✉♠ ❝❡♥ár✐♦ ❞❡ r✐s❝♦s ❝♦♠♣❡t✐t✐✈♦s ✭❡♠ q✉❡ ❡①✐st❡ ♠❛✐s ❞❡ ✉♠❛ ❝❛✉s❛ ♣❛r❛ ♦ ❛❝♦♠❡t✐♠❡♥t♦ ❞♦ ❡✈❡♥t♦ ❞❡ ✐♥t❡r❡ss❡✮✱❙✐❛♥♥✐s✭✷✵✵✹✮ ❢❡③ ❛♣❧✐❝❛çõ❡s ❝♦♠ ✉♠ ♠♦❞❡❧♦ ♣❛r❛♠étr✐❝♦ ❝♦♠ s✉♣♦s✐çã♦ ❞❡ ❝❡♥s✉r❛ ✐♥❢♦r♠❛t✐✈❛✱ ❡ ❡♠ s❡❣✉✐❞❛ r❡❛❧✐③♦✉ ✉♠❛ ❛♥á❧✐s❡ ❞❡ s❡♥s✐❜✐❧✐❞❛❞❡ ❞❡st❡ ♠❡❝❛♥✐s♠♦ ❞❡ ❝❡♥s✉r❛ ♥♦ ♠❡s♠♦ ♠♦❞❡❧♦ ❡♠❙✐❛♥♥✐s ❡t ❛❧✳

✭✷✵✵✺✮✳❇r❛❡❦❡rs✭✷✵✵✹✮ r❡❛❧✐③♦✉ ✉♠❛ ❡①♣❛♥sã♦ ❞♦ ♠♦❞❡❧♦ ❝❧áss✐❝♦ ❞❡ r❡❣r❡ssã♦ ❞❡ ❈♦① ✭❈♦①✱

✶✾✼✷✮ ♣❛r❛ ❧❡✈❛r ❡♠ ❝♦♥t❛ ❝❡♥s✉r❛ ♣❛r❝✐❛❧♠❡♥t❡ ✐♥❢♦r♠❛t✐✈❛✱ ❡♠ q✉❡ sã♦ ❝♦♥s✐❞❡r❛❞♦s ❞♦✐s t❡♠♣♦s ❞❡ ❝❡♥s✉r❛ ✭✐♥❢♦r♠❛t✐✈♦ ❡ ♥ã♦✲✐♥❢♦r♠❛t✐✈♦✮✳

❙✐t✉❛çõ❡s ❡♠ q✉❡ s❡ ❞❡s❡❥❛ ❢❛③❡r ✐♥❢❡rê♥❝✐❛s s♦❜r❡ ❛ s♦❜r❡✈✐✈ê♥❝✐❛ ❞❡ ✉♠❛ ❛♠♦str❛ ❞❡ ✐r♠ã♦s ♦s q✉❛✐s ❝♦♠♣❛rt✐❧❤❛♠ ✉♠❛ ❝❛r❛❝t❡ríst✐❝❛ ❣❡♥ét✐❝❛ ❡♠ ❝♦♠✉♠❀ ❡st✉❞❛r ❛ s♦❜r❡✈✐✲ ✈ê♥❝✐❛ ❞❡ ✉♠❛ ❛♠♦str❛ ❞❡ ❝❛s❛✐s q✉❡ ❝♦♠♣❛rt✐❧❤❛♠ ✉♠ ♠❡s♠♦ ❛♠❜✐❡♥t❡ ✭♥ã♦ ♠❡♥s✉rá✈❡❧✮❀ ♦✉ ❡st✉❞❛r t❡♠♣♦s ❞❡ ♦❝♦rrê♥❝✐❛s ❞❡ ❞✐❢❡r❡♥t❡s ❞♦❡♥ç❛s ❞❡♥tr♦ ❞❡ ✉♠ ♠❡s♠♦ ✐♥❞✐✈í❞✉♦✱ sã♦ ❝❡♥ár✐♦s ❡♠ q✉❡ ♣r♦✈❛✈❡❧♠❡♥t❡ ❡①✐st❡ ❛❧❣✉♠❛ ❛ss♦❝✐❛çã♦ ❡♥tr❡ t❡♠♣♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❞❡♥✲ tr♦ ❞❡ ❣r✉♣♦s ❡♠ ✉♠❛ ❛♠♦str❛ ♦❜s❡r✈❛❞❛✳ ❖ ♠♦❞❡❧♦ ❞❡ ❢r❛❣✐❧✐❞❛❞❡ s❡ t♦r♥♦✉ ♠✉✐t♦ ♣♦♣✉❧❛r ❞❡♥tr♦ ❞❛ ❧✐t❡r❛t✉r❛ ❡st❛tíst✐❝❛✱ ♣♦r ♠♦❞❡❧❛r ❛ ❛ss♦❝✐❛çã♦ ❡♥tr❡ t❡♠♣♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❞❡♥tr♦ ❞❡ s✉❜❣r✉♣♦s ❝♦♠ ♦ ✉s♦ ❞❡ ✉♠❛ ❢r❛❣✐❧✐❞❛❞❡✳ ❚❛❧ t❡r♠♦✱ ✐♥tr♦❞✉③✐❞♦ ♣❡❧❛ ♣r✐♠❡✐r❛ ✈❡③ ♣♦r❱❛✉♣❡❧ ❡t ❛❧✳ ✭✶✾✼✾✮✱ é ✉♠ ❡❢❡✐t♦ ❛❧❡❛tór✐♦ ❝♦♠♣❛rt✐❧❤❛❞♦ ♣♦r ♦❜s❡r✈❛çõ❡s ❞❡♥tr♦ ❞❡ ✉♠ s✉❜❣r✉♣♦✳ ❖ ♠♦❞❡❧♦ ❞❡ ❢r❛❣✐❧✐❞❛❞❡ ♠❛✐s s✐♠♣❧❡s é ♦ ❝♦♠ ❡❢❡✐t♦ ❛❧❡❛tór✐♦ ❝♦♠✉♠ q✉❡ ❛t✉❛ ❞❡ ❢♦r♠❛ ♠✉❧t✐♣❧✐❝❛t✐✈❛ ♥❛s t❛①❛s ❞❡ ❢❛❧❤❛ ❞❡ t♦❞♦s ♦s ♠❡♠❜r♦s ❞♦ s✉❜❣r✉♣♦✳ ▼❛✐s ❞❡t❛❧❤❡s ♣♦❞❡♠ s❡r ✈✐st♦s ❡♠ ❑❧❡✐♥ ✭✷✵✵✸✮✱ ❉✉❝❤t❡❛✉ ✭✷✵✵✽✮ ❡ ❍❛♥❛❣❛❧ ✭✷✵✵✸✮✳ ❆ ❡①♣r❡ssã♦ ♣❛r❛ ❛ ❢✉♥çã♦ ❞❡ t❛①❛ ❞❡ ❢❛❧❤❛ ❝♦♠ ❛ ❢r❛❣✐❧✐❞❛❞❡ ❛t✉❛♥❞♦ ❞❡ ❢♦r♠❛ ♠✉❧t✐♣❧✐❝❛t✐✈❛ é

h(y) = h0(y)Z.

Pr♦♣♦st❛s ❡♠ ✉t✐❧✐③❛r ♠♦❞❡❧♦s ❞❡ ❢r❛❣✐❧✐❞❛❞❡ s♦❜ ❛ s✉♣♦s✐çã♦ ❞❡ ❝❡♥s✉r❛ ✐♥❢♦r♠❛t✐✈❛ t❛♠❜é♠ ❢♦r❛♠ ❝♦♥s✐❞❡r❛❞❛s✳ ❆ss✐♠✱ ▲✐♥❦ ✭✶✾✽✾✮ ❢❡③ ✉♠❛ ❛♥á❧✐s❡ ❞❡ s❡♥s✐❜✐❧✐❞❛❞❡ ✉s❛♥❞♦ ✉♠ ♠♦❞❡❧♦ ❞❡ ❢r❛❣✐❧✐❞❛❞❡✱ ❝♦♠ ❝❡♥s✉r❛ ✐♥❢♦r♠❛t✐✈❛✳ ❙❡✉ ♠♦❞❡❧♦ ♣r❡ss✉♣õ❡ q✉❡ ❛ ❝❡♥s✉r❛ ♦❝♦rr❡ s♦♠❡♥t❡ ❡♠ ✉♠❛ s✉❜✲♣♦♣✉❧❛çã♦ ❞❡✜♥✐❞❛ ♣❡❧❛ ❞✐str✐❜✉✐çã♦ ❞❛ ❢r❛❣✐❧✐❞❛❞❡ ❛tr✐❜✉í❞❛✳ ◆♦ ❡♥t❛♥t♦✱ ✉s♦✉ ❞❛❞♦s ❞❡ ✐♥❞✐✈í❞✉♦s ✐♥❞❡♣❡♥❞❡♥t❡s✳ ◆♦ tr❛❜❛❧❤♦ ❞❡❍✉❛♥❣ ❡ ❲♦❧❢❡ ✭✷✵✵✷✮ ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞♦ ♦✉tr♦ ♠♦❞❡❧♦ ❞❡ ❢r❛❣✐❧✐❞❛❞❡ ♣❛r❛ ❞❛❞♦s ❡♠ ❝♦♥❣❧♦♠❡r❛❞♦s✱ q✉❡ ♣❡r♠✐t❡ ✉♠❛ ♠❛✐♦r ✢❡①✐❜✐❧✐❞❛❞❡ ❡ ❣r❛✉ ❞❡ ❞❡♣❡♥❞ê♥❝✐❛ ❡♥tr❡ ❛ ❢❛❧❤❛ ❡ ❝❡♥s✉r❛✱ ❡ ♠❛✐s t❛r❞❡ ❡♠

❍✉❛♥❣ ❡t ❛❧✳✭✷✵✵✹✮✱ ❛ ♣r♦♣♦st❛ ❞❡ ✉♠ t❡st❡ ♣❛r❛ ✈❡r✐✜❝❛r ❛ ♣r❡s❡♥ç❛ ❞❛ ❝❡♥s✉r❛ ✐♥❢♦r♠❛t✐✈❛ ❡♠ ❞❛❞♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❡♠ ❝♦♥❣❧♦♠❡r❛❞♦s✳

✶✳✶ ❈♦♥s✐❞❡r❛çõ❡s Pr❡❧✐♠✐♥❛r❡s

◆❡ss❡ tr❛❜❛❧❤♦ ❞❡ ❞✐ss❡rt❛çã♦✱ s❡rá ❛ss✉♠✐❞♦ q✉❡ ♦s t❡♠♣♦s ❞❡ ❢❛❧❤❛ ❚ ❡ ❝❡♥s✉r❛ ❈ sã♦ ❝♦♥❞✐❝✐♦♥❛❧♠❡♥t❡ ✐♥❞❡♣❡♥❞❡♥t❡s ❞❛❞♦ ✉♠❛ ❢r❛❣✐❧✐❞❛❞❡Z ✭❡❢❡✐t♦ ❛❧❡❛tór✐♦✮✳ ❆ ❢r❛❣✐❧✐❞❛❞❡

(18)

✶✳✸ ❖❇❏❊❚■❱❖❙ ✹

♥ã♦✲♣❛r❛♠étr✐❝❛✳ ❙✐t✉❛çã♦ ❞✐❢❡r❡♥t❡ ❞♦ q✉❡ é ♣r♦♣♦st♦ ♥❡st❡ tr❛❜❛❧❤♦ ❞❡ ❞✐ss❡rt❛çã♦✱ ♣♦✐s ❛ss✉♠✐♠♦s ❛ ❞✐str✐❜✉✐çã♦ ❞❛ ❢r❛❣✐❧✐❞❛❞❡ ❝♦♠♦ s❡♥❞♦ ●❛♠❛ ❡ r❡❛❧✐③❛r❡♠♦s ✉♠ ❡st✉❞♦ s♦❜ ✉♠❛ ❛❜♦r❞❛❣❡♠ ♣❛r❛♠étr✐❝❛✱ ❝♦♠ ♦ ✉s♦ ❞♦s ♠♦❞❡❧♦s ❊①♣♦♥❡♥❝✐❛❧ ❡ ❲❡✐❜✉❧❧✳ ❘❡s✉♠✐♥❞♦✱ ❛s ❡st✐♠❛t✐✈❛s ❞❡ ♠á①✐♠❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ sã♦ ♦❜t✐❞❛s ✈✐❛ ❢✉♥çã♦ ❞❡ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ♠❛r❣✐♥❛❧✱ ❝♦♥str✉í❞❛ s❡❣✉♥❞♦ ❛ s✉♣♦s✐çã♦ ❛ss✉♠✐❞❛✳ ❆ ✐♠♣❧❡♠❡♥t❛çã♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ ❢♦✐ t♦❞❛ r❡❛❧✐✲ ③❛❞❛ ♥♦ s♦❢t✇❛r❡OxMetrics 6✳ ❙♦❜ ❡st❛s ❝♦♥❞✐çõ❡s✱ ♦❜❥❡t✐✈♦s s❡rã♦ ❞❡s❝r✐t♦s ♥❛ ♣ró①✐♠❛

s❡çã♦✳

✶✳✷ ❖❜❥❡t✐✈♦s

❊st❡ tr❛❜❛❧❤♦ ❞❡ ❞✐ss❡rt❛çã♦ t❡♠ ❝♦♠♦ ♦❜❥❡t✐✈♦ ♣r✐♥❝✐♣❛❧✱ ✉t✐❧✐③❛r ❛ s✉♣♦s✐çã♦ ❞❡ q✉❡ ❚ ❡ ❈ sã♦ ❝♦♥❞✐❝✐♦♥❛❧♠❡♥t❡ ✐♥❞❡♣❡♥❞❡♥t❡s ❞❛❞♦ ❩✱ ♦✉ s❡❥❛✱ ♠♦❞❡❧❛r ❞❛❞♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❝♦♠ ♦ ♠❡❝❛♥✐s♠♦ ❞❡ ❝❡♥s✉r❛ ✐♥❢♦r♠❛t✐✈♦✱ ✈✐❛ ❢✉♥çã♦ ❞❡ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ♠❛r❣✐♥❛❧✳

❖s ♦❜❥❡t✐✈♦s ❡s♣❡❝í✜❝♦s sã♦ ♦s s❡❣✉✐♥t❡s✿

• ■♥❝♦r♣♦r❛r ♦ ♠❡❝❛♥✐s♠♦ ❞❡ ❝❡♥s✉r❛ ✐♥❢♦r♠❛t✐✈♦ ❡♠ ♠♦❞❡❧♦s ♣❛r❛♠étr✐❝♦s ✭❊①♣♦♥❡♥❝✐❛❧

❡ ❲❡✐❜✉❧❧✮✱ ✉t✐❧✐③❛♥❞♦ ❛ s✉♣♦s✐çã♦ ❡st❛❜❡❧❡❝✐❞❛✳

• ❘❡❛❧✐③❛r ✉♠ ❡st✉❞♦ ❝♦♠ ❞❛❞♦s s✐♠✉❧❛❞♦s✱ ❝♦♠ ♦ ♦❜❥❡t✐✈♦ q✉❡ ✈❡r✐✜❝❛r ♦ ❞❡s❡♠♣❡♥❤♦

❞❛ ♠❡t♦❞♦❧♦❣✐❛ ♣r♦♣♦st❛✱ ❣❡r❛♥❞♦ ❝❡♥ár✐♦s ❡♠ q✉❡ ♦ ♠❡❝❛♥✐s♠♦ é ♥ã♦✲✐♥❢♦r♠❛t✐✈♦ ❡ ✐♥❢♦r♠❛t✐✈♦✳

• ❆♥❛❧✐s❛r ❝♦♠♣♦rt❛♠❡♥t♦ ❞❛ ♠❡t♦❞♦❧♦❣✐❛ ❡st✉❞❛❞❛ ❡♠ ❞❛❞♦s r❡❛✐s✱ ❡♠ ❝♦♠♣❛r❛çã♦ ❝♦♠

❛ ♠❡t♦❞♦❧♦❣✐❛ ✉s✉❛❧ ✭♠❡❝❛♥✐s♠♦ ❞❡ ❝❡♥s✉r❛ ♥ã♦✲✐♥❢♦r♠❛t✐✈♦✮✳

✶✳✸ ❖r❣❛♥✐③❛çã♦ ❞♦ ❚r❛❜❛❧❤♦

❆ ♦r❣❛♥✐③❛çã♦ ❞♦ tr❛❜❛❧❤♦ é r❡❛❧✐③❛❞❛ ❞❛ s❡❣✉✐♥t❡ ♠❛♥❡✐r❛✱ ♥♦ ❈❛♣ít✉❧♦ ✷ ♠♦str❛r❡♠♦s ❛ ♠❡t♦❞♦❧♦❣✐❛ q✉❡ s❡rá ✉s❛❞❛ ♥❡st❡ tr❛❜❛❧❤♦ ❞❡ ❞✐ss❡rt❛çã♦✳ ■♥✐❝✐❛❧♠❡♥t❡✱ ✉♠❛ ✐♥tr♦❞✉çã♦ ❜ás✐❝❛ s♦❜r❡ ❛❧❣✉♥s ❝♦♥❝❡✐t♦s ❡ ❛ ♠❡t♦❞♦❧♦❣✐❛ ♣❛r❛ ♦ ❝❛s♦ ❡♠ q✉❡ ♦ ♠❡❝❛♥✐s♠♦ ❞❡ ❝❡♥s✉r❛ é ♥ã♦✲✐♥❢♦r♠❛t✐✈♦✳ ❊♠ s❡❣✉✐❞❛✱ s❡rá ❛♣r❡s❡♥t❛❞❛ ❛ ♣r♦♣♦st❛ ♣❛r❛ tr❛❜❛❧❤❛r ❝♦♠ ♦ ♠❡❝❛♥✐s♠♦ ❞❡ ❝❡♥s✉r❛ ✐♥❢♦r♠❛t✐✈♦✱ ❞❡✜♥✐❞♦ ❛❧❣✉♠❛s ❢✉♥çõ❡s ✐♠♣♦rt❛♥t❡s✱ s♦❜ ❛ s✉♣♦s✐çã♦ t♦♠❛❞❛✳ ▲♦❣♦ ❛♣ós✱ ❞❡ ✉♠❛ ♠❛♥❡✐r❛ ❣❡r❛❧✱ s❡rá ❛♣r❡s❡♥t❛❞♦ ❛ ❝♦♥str✉çã♦ ❞❛ ❢✉♥çã♦ ❞❡ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ♠❛r❣✐♥❛❧ ♣❛r❛ ♦ ❝❛s♦ ❡♠ q✉❡ ♦ ♠❡❝❛♥✐s♠♦ ❞❡ ❝❡♥s✉r❛ é ✐♥❢♦r♠❛t✐✈♦✳ ❆♣ós ✐ss♦✱ ❛♣❧✐❝❛r❡♠♦s ♦ ♣r♦❝❡❞✐♠❡♥t♦ ♣❛r❛ ❞♦✐s ❝❛s♦s ♣❛rt✐❝✉❧❛r❡s✱ ♠♦❞❡❧♦s ❊①♣♦♥❡♥❝✐❛❧ ❡ ❲❡✐❜✉❧❧✳

◆♦ ❈❛♣ít✉❧♦ ✸ r❡❛❧✐③❛♠♦s ✉♠ ❡st✉❞♦ ❞❡ s✐♠✉❧❛çõ❡s ▼♦♥t❡ ❈❛r❧♦ ♣❛r❛ ♠♦❞❡❧❛❣❡♠ ♣❛r❛✲ ♠étr✐❝❛ ❛♣r❡s❡♥t❛❞❛ ♥♦ ❈❛♣ít✉❧♦✷✳ ❈♦♠♣❛r❛♠♦s ♦ ❞❡s❡♠♣❡♥❤♦ ❞❛ ♠❡t♦❞♦❧♦❣✐❛ ❛❧t❡r♥❛t✐✈❛ ❝♦♠ ♦ ♣r♦❝❡❞✐♠❡♥t♦ ✉s✉❛❧ ❞❡ ❛♥á❧✐s❡ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛✱ ❝♦♠ ♦ ♦❜❥❡t✐✈♦ ❞❡ ❛✈❛❧✐❛r ♦ ✐♠♣❛❝t♦ ♥❛s ❡st✐♠❛t✐✈❛s ❞♦s ♣❛râ♠❡tr♦s ❞❡ ✐♥t❡r❡ss❡✱ ❡♠ ❝❡♥ár✐♦s q✉❛♥❞♦ ♦ ♠❡❝❛♥✐s♠♦ ❞❡ ❝❡♥s✉r❛ ♥ã♦✲✐♥❢♦r♠❛t✐✈♦ ❡ ✐♥❢♦r♠❛t✐✈♦✱ ♣❛r❛ ❛♠❜♦s ♠♦❞❡❧♦s✳ ❆❧é♠ ❞♦s ❝❡♥ár✐♦s ♣❛r❛ ♦s ♠❡❝❛♥✐s♠♦ ❞❡ ❝❡♥s✉r❛✱ ❞✐❢❡r❡♥t❡s ♣r♦♣♦rçõ❡s ❞❡ ❢❛❧❤❛ ❡ ❞✐❢❡r❡♥t❡s t❛♠❛♥❤♦s ❛♠♦str❛✐s s❡rã♦ ❝♦♥s✐❞❡r❛❞♦s✳ ❘❡❛❧✐③❛♠♦s ♥♦ ❈❛♣ít✉❧♦ ✹ ✉♠❛ ✐❧✉str❛çã♦ ❞♦ ♣r♦❝❡❞✐♠❡♥t♦ ❝♦♠ ♠❡❝❛♥✐s♠♦ ❞❡ ❝❡♥s✉r❛ ✐♥❢♦r♠❛t✐✈♦ ❞❡s❝r✐t♦ ♥♦ ❈❛♣ít✉❧♦ ✷✱ ❥✉♥t❛♠❡♥t❡ ❝♦♠ ♦ ♣r♦❝❡❞✐♠❡♥t♦ ✉s✉❛❧✱❡♠ ❞❛❞♦s ❞❡ ♣❛❝✐❡♥t❡s q✉❡ r❡❛❧✐③❛r❛♠ tr❛♥s♣❧❛♥t❡ ♥♦ ❍♦s♣✐t❛❧ ❞❛s ❈❧í♥✐❝❛s ❞❛ ❯❋▼●✳

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❈❛♣ít✉❧♦ ✷

▼❡t♦❞♦❧♦❣✐❛

◆❛ ❙❡çã♦ ✷✳✶ ❞❡s❝r❡✈❡r❡♠♦s ❜r❡✈❡♠❡♥t❡ ❛ ♠❡t♦❞♦❧♦❣✐❛ ♣❛r❛ ♦ ♣r♦❝❡❞✐♠❡♥t♦ ♣❛❞rã♦ ❡♠ q✉❡ ♦s t❡♠♣♦s ❞❡ ❢❛❧❤❛ ❡ ❞❡ ❝❡♥s✉r❛ sã♦ ✐♥❞❡♣❡♥❞❡♥t❡s ✭❝❡♥s✉r❛ ♥ã♦✲✐♥❢♦r♠❛t✐✈❛✮✱ ♦♥❞❡ ❞❡t❛❧❤❛r❡♠♦s ❛ ❝♦♥str✉çã♦ ❞❛ ❢✉♥çã♦ ❞❡ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ✉s✉❛❧✱ s❡❣✉♥❞♦ ❈♦❧♦s✐♠♦ ❡ ●✐♦❧♦

✭✷✵✵✻✮✱❈♦❧❧❡tt✭✷✵✵✸✮ ❡❑❛❧❜❡✐s❝❤✭✷✵✵✷✮✳ ❊♠ s❡❣✉✐❞❛✱ ♥❛ ❙❡çã♦✷✳✷✱ ♠♦str❛r❡♠♦s ♦ ♣r♦❝❡❞✐✲ ♠❡♥t♦ ❡♠ q✉❡ ♦s t❡♠♣♦s ❞❡ ❢❛❧❤❛ ❡ ❝❡♥s✉r❛ sã♦ ❝♦♥❞✐❝✐♦♥❛❧♠❡♥t❡ ✐♥❞❡♣❡♥❞❡♥t❡s ❞❛❞♦ ✉♠❛ ❢r❛❣✐❧✐❞❛❞❡✱ ✉t✐❧✐③❛♥❞♦ ✉♠❛ ❢✉♥çã♦ ❞❡ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ♠❛r❣✐♥❛❧ ♣❛r❛ ❛ ♠♦❞❡❧❛❣❡♠ ✭❝❡♥s✉r❛ ✐♥❢♦r♠❛t✐✈❛✮✳ P❛r❛ ❡st❛ ♠❡s♠❛ s❡çã♦✱ ♦s ♠♦❞❡❧♦s ❊①♣♦♥❡♥❝✐❛❧ ❡ ❲❡✐❜✉❧❧ sã♦ ✈✐st♦s ❝♦♠♦ ❝❛✲ s♦s ♣❛rt✐❝✉❧❛r❡s✱ ❡ ✉s❛❞♦s ❞❡ ❢♦r♠❛ ✐❧✉str❛t✐✈❛✱ ❡♠❜♦r❛ ♦✉tr❛s ❞✐str✐❜✉✐çõ❡s s❡❥❛♠ ♣♦ssí✈❡✐s✳ ❈♦♥s✐❞❡r❡ ✉♠❛ ❛♠♦str❛ ❛❧❡❛tór✐❛ ❞❡ ♥ ✐♥❞✐✈í❞✉♦s✱ r❡❢❡r❡♥t❡s ❛ t❡♠♣♦s ❞❡ ❡✈❡♥t♦s ❡ ♦❜✲ s❡r✈❛çõ❡s ❝❡♥s✉r❛❞❛s✱ s♦❜ ♦ ♠❡❝❛♥✐s♠♦ ❞❡ ❝❡♥s✉r❛ à ❞✐r❡✐t❛✱ ❝♦♠♦ ❝♦♠❡♥t❛❞♦ ♥♦ ❈❛♣ít✉❧♦✶✳ ❆ ✈❛r✐á✈❡❧ ❛❧❡❛tór✐❛ ❛ss♦❝✐❛❞❛ ❛♦ t❡♠♣♦ ❛té ♦ ❡✈❡♥t♦ ❞❡ ✐♥t❡r❡ss❡ ✭t❡♠♣♦ ❞❡ ❢❛❧❤❛✮ ♣❛r❛ ♦ ✐✲és✐♠♦ ✐♥❞✐✈í❞✉♦ s❡rá ❞❡♥♦t❛❞❛ ♣♦r Ti✳ ❖s t❡♠♣♦s ❞❡ ❝❡♥s✉r❛ t❛♠❜é♠ s❡rã♦ ❛ss✉♠✐❞♦s

❝♦♠♦ ❛❧❡❛tór✐♦s✱ ❡ C ❞❡♥♦t❛rá ❛ ✈❛r✐á✈❡❧ ❛❧❡❛tór✐❛ ❛ss♦❝✐❛❞❛ ❛♦ t❡♠♣♦ ❛té ❛ ❝❡♥s✉r❛✳

▲♦❣♦✱ ✐rá ❛ss✉♠✐r✲s❡ yi ❝♦♠ ♦ r❡s✉❧t❛❞♦ ❞❛ ✈❛r✐á✈❡❧ ❛❧❡❛tór✐❛ Yi = min(Ti, Ci) r❡♣r❡s❡♥✲

t❛♥❞♦ ♦ t❡♠♣♦ ♦❜s❡r✈❛❞♦ ♣❛r❛ ✐✲és✐♠♦ ✐♥✐✈í❞✉♦ ❡δi =I(Ti < Ci)s❡♥❞♦ ❛ ✈❛r✐á✈❡❧ ✐♥❞✐❝❛❞♦r❛

❞♦ ❡✈❡♥t♦ ❝♦rr❡s♣♦♥❞❡♥t❡✱ ♣❛r❛ i= 1,2, . . . , n✳ ❆ ❢✉♥çã♦ ❞❡♥s✐❞❛❞❡ ❡ s♦❜r❡✈✐✈ê♥❝✐❛ ♣❛r❛ Ti✱

s❡rã♦ ❞❡♥♦t❛❞❛s ♣♦r fT(ti|λ) ❡ ST(ti|λ)✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ P❛r❛ ♦ t❡♠♣♦ ❞❡ ❝❡♥s✉r❛ Ci✱

t❛♠❜é♠ ✉s❛r❡♠♦s ✉♠❛ ❢✉♥çã♦ ❞❡ ❞❡♥s✐❞❛❞❡ ❡ s♦❜r❡✈✐✈ê♥❝✐❛✱fC(ci|θ) ❡SC(ci|θ)✱ r❡s♣❡❝t✐✈❛✲

♠❡♥t❡✱ ❡♠ q✉❡λ❡θ sã♦ ✈❡t♦r❡s ❞❡ ♣❛râ♠❡tr♦s ♣❛r❛ ❛ ❞✐str✐❜✉✐çã♦ ❞♦ t❡♠♣♦ ❚ ❛té ♦ ❡✈❡♥t♦

❞❡ ✐♥t❡r❡ss❡ ❡ ❞♦ t❡♠♣♦ ❈ ❛té ❛ ❝❡♥s✉r❛✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳

➱ ✐♠♣♦rt❛♥t❡ r❡ss❛❧t❛r q✉❡ ✉♠ ❞♦s ♣r✐♥❝✐♣❛✐s ✐♥t❡r❡ss❡s ❡♠ ❛♥á❧✐s❡ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ é ❢❛③❡r ✐♥❢❡rê♥❝✐❛s s♦❜r❡ ♦ ✈❡t♦r ❞❡ ♣❛râ♠❡tr♦s λ✳ ❖✉ s❡❥❛✱ ❛q✉❡❧❡s ♣❛râ♠❡tr♦s q✉❡ ❡stã♦

❛ss♦❝✐❛❞♦s ❛ ❞✐str✐❜✉✐çã♦ ❞♦ t❡♠♣♦ ❛té ❛ ❢❛❧❤❛✳ ◆❡st❡ ❝♦♥t❡①t♦✱ ♦ ✈❡t♦r ❞❡ ♣❛râ♠❡tr♦s θ

❛ss♦❝✐❛❞♦ à ❞✐str✐❜✉✐çã♦ ❞♦ t❡♠♣♦ ❛té ❛ ❝❡♥s✉r❛✱ é ❝♦♥s✐❞❡r❛❞♦ ❞❡ ♣❡rt✉r❜❛çã♦✳

✷✳✶ ▼❡❝❛♥✐s♠♦ ❞❡ ❝❡♥s✉r❛ ♥ã♦ ✐♥❢♦r♠❛t✐✈♦

❈♦♥s✐❞❡r❡ ❛ ❞✐str✐❜✉✐çã♦ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ♣❛r❛ ♦ ♣❛r(Yi, δi)♣❛r❛ ♦❜s❡r✈❛çõ❡s ❝❡♥s✉r❛❞❛s

❡ ♥ã♦✲❝❡♥s✉r❛❞❛s✳ P❛r❛ ♦ ❝❛s♦ ❞❡ ♦❜s❡r✈❛çõ❡s ❝❡♥s✉r❛❞❛s (δi = 0)✱ ❛ ❞✐str✐❜✉✐çã♦ ❝♦♥❥✉♥t❛

❞❡Yi ❡δi é ❞❡s❝r✐t❛ ❞❛ s❡❣✉✐♥t❡ ♠❛♥❡✐r❛

f(yi, δi = 0) =P(C∈(yi, yi+ ∆yi), T > yi).

❙✐♠✐❧❛r♠❡♥t❡✱ ♣❛r❛ ✉♠❛ ♦❜s❡r✈❛çã♦ ♥ã♦ ❝❡♥s✉r❛❞❛✱ t❡♠♦s

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✷✳✷ P❘❖❈❊❉■▼❊◆❚❖ P❆❘❆ ❖ ▼❊❈❆◆■❙▼❖ ❉❊ ❈❊◆❙❯❘❆ ■◆❋❖❘▼❆❚■❱❖ ✻

f(yi, δi = 1) =P(T ∈(yi, yi+ ∆yi), C > yi).

❈♦♠❜✐♥❛♥❞♦ ❛s ❢✉♥çõ❡s ❛❝✐♠❛ ❡ ❞❡✜♥✐♥❞♦ D = {(Yi, δi), i = 1,2, . . . , n}✱ ♣❛r❛ r ❢❛❧❤❛s

❡ ♥✲r ❝❡♥s✉r❛s✱ ❛ ❢✉♥çã♦ ❞❡ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ L(λ_,θ_|_D)✱ ❞❛s _n ♦❜s❡r✈❛çõ❡s✱ _y₁_{, y}₂_{, . . . , y}_n✱ é

❞❛❞❛ ♣♦r

L(λ_,θ_|_D_{) =}

r Y

i=1

{P(T ∈(yi, yi+ ∆yi), C > yi)} n Y

i=r+1

{P(C ∈(yi, yi+ ∆yi), T > yi)},

❘❡❡s❝r❡✈❡♥❞♦ L(λ_,θ_|_D₎ ❡♠ t❡r♠♦s ❞❡ _δ_i✱ t❡♠♦s q✉❡

L(λ_,θ_|_D_{) =}

n Y

i=1

{P(T ∈(yi, yi+ ∆yi), C > yi))}δi{P(C ∈(yi, yi+ ∆yi), T > yi)}1

−δi _{✭✷✳✶✮}

❆ss✉♠✐♥❞♦ q✉❡ ❚ ❡ ❈ sã♦ ✈❛r✐á✈❡✐s ❛❧❡❛tór✐❛s ✐♥❞❡♣❡♥❞❡♥t❡s✱ t❡♠✲s❡

L(λ_,θ_|_D_{) =}

n Y

i=1

P(T ∈(yi, yi+ ∆yi))δiP(T > yi)1

−δi

P(C ∈(yi, yi+ ∆yi))1

−δi

P(C > yi)δi.

=

n Y

i=1

[fT(yi|λ)δiST(yi|λ)1

−δi

][fC(yi|θ)1

−δi

SC(yi|θ)δi]

✭✷✳✷✮ ❙♦❜ ❛ s✉♣♦s✐çã♦ ❞❡ q✉❡ ♦ ♠❡❝❛♥✐s♠♦ ❞❡ ❝❡♥s✉r❛ é ♥ã♦✲✐♥❢♦r♠❛t✐✈♦✱ ♦❜s❡r✈❡ q✉❡ ♦ s❡✲ ❣✉♥❞♦ ♣r♦❞✉t♦ ♥❛ ❡q✉❛çã♦ ✭✷✳✷✮ ♥ã♦ ❡♥✈♦❧✈❡ ♥❡♥❤✉♠ ♣❛râ♠❡tr♦ q✉❡ s❡❥❛ r❡❧❡✈❛♥t❡ ♣❛r❛ ❛ ❞✐str✐❜✉✐çã♦ ❞♦s t❡♠♣♦s ❞❡ ❢❛❧❤❛✳ ❉❡ss❛ ♠❛♥❡✐r❛✱ ❛ ❢✉♥çã♦ ❞❡ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ❡♠ ✭✷✳✷✮ ♣♦❞❡ s❡r r❡❡s❝r✐t❛ ❞❛ s❡❣✉✐♥t❡ ❢♦r♠❛

L(λ_|_D₎ _∝

n Y

i=1

P(Ti ∈(yi, yi+ ∆yi))δiP(Ti > yi)1

−δi

∝ n Y

i=1

fT(yi|λ) δi

ST(yi|λ)1

−δi

,

✭✷✳✸✮

q✉❡ ❝♦rr❡s♣♦♥❞❡ ❛ ❢✉♥çã♦ ❞❡ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ❡♥❝♦♥tr❛❞❛ ♥❛ ❧✐t❡r❛t✉r❛ ✭❞❡t❛❧❤❡s ❡♠❈♦❧♦s✐♠♦ ❡ ●✐♦❧♦

✭✷✵✵✻✮✱ ❈♦❧❧❡tt✭✷✵✵✸✮ ❡ ❑❛❧❜❡✐s❝❤ ✭✷✵✵✷✮✮✳