❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❙ã♦ ❈❛r❧♦s
❈❡♥tr♦ ❞❡ ❈✐ê♥❝✐❛s ❊①❛t❛s ❡ ❞❡ t❡❝♥♦❧♦❣✐❛
❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❊st❛tíst✐❝❛
❆✈❛❧✐❛çã♦ ❊s♣♦rt✐✈❛ ❯t✐❧✐③❛♥❞♦ ❚é❝♥✐❝❛s ▼✉❧t✐✈❛r✐❛❞❛s✿
❈♦♥str✉çã♦ ❞❡ ■♥❞✐❝❛❞♦r❡s ❡ ❙✐st❡♠❛ ❖♥❧✐♥❡
❆❧❡①❛♥❞r❡ ❈r✐st♦✈ã♦ ▼❛✐♦r❛♥♦
❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❙ã♦ ❈❛r❧♦s
❈❡♥tr♦ ❞❡ ❈✐ê♥❝✐❛s ❊①❛t❛s ❡ ❞❡ ❚❡❝♥♦❧♦❣✐❛
❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❊st❛tíst✐❝❛
❆✈❛❧✐❛çã♦ ❊s♣♦rt✐✈❛ ❯t✐❧✐③❛♥❞♦ ❚é❝♥✐❝❛s ▼✉❧t✐✈❛r✐❛❞❛s✿
❈♦♥str✉çã♦ ❞❡ ■♥❞✐❝❛❞♦r❡s ❡ ❙✐st❡♠❛ ❖♥❧✐♥❡
❆❧❡①❛♥❞r❡ ❈r✐st♦✈ã♦ ▼❛✐♦r❛♥♦
❖r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❉r✳ ❋r❛♥❝✐s❝♦ ▲♦✉③❛❞❛ ◆❡t♦
❉✐ss❡rt❛çã♦ ❞❡ ▼❡str❛❞♦ ❛♣r❡s❡♥t❛❞❛ ❛♦ Pr♦❣r❛♠❛ ❞❡ Pós ●r❛❞✉❛çã♦ ❡♠ ❊st❛tíst✐❝❛ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❙ã♦ ❈❛r❧♦s✱ ❝♦♠♦ ♣❛rt❡ ❞♦s r❡q✉✐s✐t♦s ♣❛r❛ ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ▼❡str❡ ❡♠ ❊st❛tíst✐❝❛✳
Ficha catalográfica elaborada pelo DePT da Biblioteca Comunitária da UFSCar
M227ae
Maiorano, Alexandre Cristovão.
Avaliação esportiva utilizando técnicas multivariadas: construção de indicadores e sistemas online/ Alexandre Cristovão Maiorano. -- São Carlos : UFSCar, 2015. 61 f.
Dissertação (Mestrado) -- Universidade Federal de São Carlos, 2015.
1. Estatística. 2. Avaliação esportiva. 3. Métodos univariados e multivriados. 4. Metodologia. I. Título.
❆❣r❛❞❡❝✐♠❡♥t♦s
❆❣r❛❞❡ç♦ ♣r✐♠❡✐r❛♠❡♥t❡ à ❉❡✉s ♣♦r t❡r ✐❧✉♠✐♥❛❞♦ ♠✐♥❤❛ tr❛❥❡tór✐❛ ❡ ❢❡✐t♦ ❝♦♠ q✉❡ ❡✉ t❡♥❤❛ ❡s❝♦❧❤✐❞♦ ♦s ♠❡❧❤♦r❡s ❝❛♠✐♥❤♦s ❞✉r❛♥t❡ t♦❞❛ ♠✐♥❤❛ ✈✐❞❛✱ ❛❧é♠ ❞❡ t❡r ♠❡ ❞❛❞♦ s❛ú❞❡ ❡ ❞❡t❡r♠✐♥❛çã♦ ♣❛r❛ ❝♦♥s❡❣✉✐r ✜♥❛❧✐③❛r ♠✐♥❤❛ ❞✐ss❡rt❛çã♦✳
➚ ♠✐♥❤❛ ❢❛♠í❧✐❛✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♠❡✉s ♣❛✐s✱ ▲✉✐③ ❡ ❲✐❧♥❡✐❞❡✱ ♣♦r t♦❞♦ ❡s❢♦rç♦✱ ❛♠♦r✱ ❝♦♠♣r❡❡♥sã♦ ❡ ❛♣♦✐♦ ♣❛r❛ ❞❛r ❝♦♥t✐♥✉✐❞❛❞❡ ❛♦s ♠❡✉s ❡st✉❞♦s✳ ➚ ♠✐♥❤❛ ✐r♠ã ❆♠❛♥❞❛ ♣❡❧♦ ❝♦♠♣❛♥❤❡✐r✐s♠♦ ❡ ♠♦t✐✈❛çã♦ ❞❡s❞❡ q✉❛♥❞♦ ér❛♠♦s ♣❡q✉❡♥♦s✳
➚ ♠✐♥❤❛ ♥❛♠♦r❛❞❛ ❇ár❜❛r❛✱ q✉❡ ❛♠♦ t❛♥t♦✱ ♣❡❧♦ ❛♠♦r✱ ❝❛r✐♥❤♦✱ ❝♦♠♣❛♥❤❡✐r✐s♠♦ ❡ ❣r❛♥❞❡ ❛♣♦✐♦ ❡♠ t♦❞♦ ❡ss❡ t❡♠♣♦ q✉❡ ❡st❛♠♦s ❥✉♥t♦s✳
❆♦ ♠❡✉ ♦r✐❡♥t❛❞♦r ❋r❛♥❝✐s❝♦ ▲♦✉③❛❞❛ ◆❡t♦ ♣❡❧❛s ♦♣♦rt✉♥✐❞❛❞❡s ❡ t♦❞❛ ❛ ❡①♣❡r✐ê♥❝✐❛ q✉❡ t❡♠ ♠❡ ♣❛ss❛❞♦ ♥❡ss❡s ❛♥♦s ❞❡ tr❛❜❛❧❤♦✳
❆❣r❛❞❡ç♦ ❛♦ ❆♥❞❡rs♦♥ ❆r❛ ♣❡❧❛ ❛❥✉❞❛ ♥♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞♦ ✐❙♣♦rts✱ ♣❡❧❛ ❛♠✐③❛❞❡ ❡ ❝♦♥❤❡❝✐♠❡♥t♦ q✉❡ s❡♠♣r❡ t❡♠ ♠❡ ♣❛ss❛❞♦✳
➚ t♦❞♦s ♦s ❛❧✉♥♦s ❞♦ ●r✉♣♦ ❈❊❘ q✉❡ ♣❛rt✐❝✐♣❛r❛♠ ❞❛ ❝♦❧❡t❛ ❞❡ ❞❛❞♦s ♣❛r❛ r❡❛❧✐③❛çã♦ ❞❛ ♣❡sq✉✐s❛✱ ❜❡♠ ❝♦♠♦ ❛ ❡q✉✐♣❡ ❞❛ ❡s❝♦❧✐♥❤❛ ▼❡♥✐♥♦s ❞❛ ❱✐❧❛ ✲ ❙ã♦ ❈❛r❧♦s ♣♦r t❡r ❞✐s♣♦♥✐❜✐❧✐③❛❞♦ s✉❛s ❞❡♣❡♥❞ê♥❝✐❛s ♣❛r❛ ❛♣❧✐❝❛çã♦ ❞♦s t❡st❡s ❞❡ ❢✉t❡❜♦❧✳
❘❡s✉♠♦
❖ ♣r✐♥❝✐♣❛❧ ♦❜❥❡t✐✈♦ ❞♦ tr❛❜❛❧❤♦ é ❛♣r❡s❡♥t❛r ❢❡rr❛♠❡♥t❛s ❡st❛tíst✐❝❛s q✉❡ ♣❡r♠✐t❛♠ ❛ ❝♦♠♣❛r❛çã♦ ❞❡ ✐♥❞✐✈í❞✉♦s ❡♠ ✉♠❛ ❞❡t❡r♠✐♥❛❞❛ ♠♦❞❛❧✐❞❛❞❡ ❡s♣♦rt✐✈❛✳ P❛rt✐❝✉❧❛r♠❡♥t❡✱ ♦ ❡st✉❞♦ ❡①♣♦st♦ é ✈♦❧t❛❞♦ à ❛✈❛❧✐❛çã♦ ❞❡ ❞❡s❡♠♣❡♥❤♦ ❡♠ ❢✉t❡❜♦❧✱ ✉t✐❧✐③❛♥❞♦ ♠ét♦❞♦s ✉♥✐✈❛✲ r✐❛❞♦s ❡ ♠✉❧t✐✈❛r✐❛❞♦s✳ ❆ ❛❜♦r❞❛❣❡♠ ✉♥✐✈❛r✐❛❞❛ é ❞❛❞❛ ♣❡❧❛ ♠❡t♦❞♦❧♦❣✐❛ ❩✲❈❊▲❆❋■❙❈❙✱ ❞❡s❡♥✈♦❧✈✐❞❛ ❝♦♠ ♦ ♣r♦♣ós✐t♦ ❞❡ ✐❞❡♥t✐✜❝❛r t❛❧❡♥t♦s ♥♦ ❡s♣♦rt❡✳ ❆s ❛❜♦r❞❛❣❡♥s ♠✉❧t✐✈❛r✐✲ ❛❞❛s sã♦ ❞❛❞❛s ♣❡❧❛ ❝♦♥str✉çã♦ ❞❡ ✐♥❞✐❝❛❞♦r❡s✱ ♠❛✐s ❡s♣❡❝✐✜❝❛♠❡♥t❡ ♣♦r ♠❡✐♦ ❞❛ ❛♥á❧✐s❡ ❞❡ ❝♦♠♣♦♥❡♥t❡s ♣r✐♥❝✐♣❛✐s✱ ❛♥á❧✐s❡ ❢❛t♦r✐❛❧ ❡ ❝ó♣✉❧❛s✳ ❆ ♦❜t❡♥çã♦ ❞❡ss❡s ✐♥❞✐❝❛❞♦r❡s ♣♦s✲ s✐❜✐❧✐t❛ ❛ r❡❞✉çã♦ ❞❛ ❞✐♠❡♥s✐♦♥❛❧✐❞❛❞❡ ❞♦ ❡st✉❞♦✱ ❢♦r♥❡❝❡♥❞♦ ♠❡❧❤♦r ✐♥t❡r♣r❡t❛çã♦ ❞♦s r❡s✉❧t❛❞♦s ❡ ♠❡❧❤♦r ❝♦♠♣❛r❛❜✐❧✐❞❛❞❡ ❡♥tr❡ ♦ ❞❡s❡♠♣❡♥❤♦ ❡ r❛♥❦❡❛♠❡♥t♦ ❞♦s ✐♥❞✐✈í❞✉♦s✳ P❛r❛ ❢❛❝✐❧✐t❛r ❛ ✉t✐❧✐③❛çã♦ ❞❛ ♠❡t♦❞♦❧♦❣✐❛ ❛q✉✐ ❡st✉❞❛❞❛ ❢♦✐ ❝♦♥str✉í❞♦ ✉♠ s✐st❡♠❛ ❡st❛✲ tíst✐❝♦ ♦♥❧✐♥❡ ❝❤❛♠❛❞♦ ❞❡ ✐✲❙♣♦rts✳
❆❜str❛❝t
❚❤❡ ♠❛✐♥ ♦❜❥❡❝t✐✈❡ ♦❢ t❤✐s r❡s❡❛r❝❤ ✐s t♦ ♣r♦✈✐❞❡ st❛t✐st✐❝❛❧ t♦♦❧s t❤❛t ❛❧❧♦✇ t❤❡ ❝♦♠♣❛✲ r✐s♦♥ ♦❢ ✐♥❞✐✈✐❞✉❛❧s ✐♥ ❛ s♣❡❝✐✜❡❞ s♣♦rts ❝❛t❡❣♦r②✳ P❛rt✐❝✉❧❛r❧②✱ t❤❡ ♣r❡s❡♥t st✉❞② ✐s ❢♦❝✉s❡❞ ♦♥ t❤❡ ♣❡r❢♦r♠❛♥❝❡ ❡✈❛❧✉❛t✐♦♥ ✐♥ ❢♦♦t❜❛❧❧ ✉s✐♥❣ ✉♥✐✈❛r✐❛t❡ ❛♥❞ ♠✉❧t✐✈❛r✐❛t❡ ♠❡t❤♦❞s✳ ❚❤❡ ✉♥✐✈❛r✐❛t❡ ❛♣♣r♦❛❝❤ ✐s ❣✐✈❡♥ ❜② ❩✲❈❊▲❆❋■❙❈❙ ♠❡t❤♦❞♦❧♦❣②✱ ✇❤✐❝❤ ✇❛s ❞❡✈❡❧♦♣❡❞ ✇✐t❤ t❤❡ ♣✉r♣♦s❡ ♦❢ ✐❞❡♥t✐❢②✐♥❣ t❛❧❡♥ts ✐♥ t❤❡ s♣♦rt✳ ❚❤❡ ♠✉❧t✐✈❛r✐❛t❡ ❛♣♣r♦❛❝❤❡s ❛r❡ ❣✐✈❡♥ ❜② t❤❡ ❝♦♥str✉❝t✐♦♥ ♦❢ ✐♥❞✐❝❛t♦rs✱ s♣❡❝✐✜❝❛❧❧② ❜② ♠❡❛♥s ♦❢ ♣r✐♥❝✐♣❛❧ ❝♦♠♣♦♥❡♥t ❛♥❛❧②s✐s✱ ❢❛❝t♦r ❛♥❛❧②s✐s ❛♥❞ ❝♦♣✉❧❛s✳ ❚❤❡s❡ ✐♥❞✐❝❛t♦rs ❛❧❧♦✇s t❤❡ r❡❞✉❝t✐♦♥ ♦❢ t❤❡ ❞✐♠❡♥s✐♦♥❛❧✐t② ♦❢ t❤❡ ❞❛t❛ ✐♥ st✉❞②✐♥❣✱ ♣r♦✈✐❞✐♥❣ ❜❡tt❡r ✐♥t❡r♣r❡t❛t✐♦♥ ♦❢ t❤❡ r❡s✉❧ts ❛♥❞ ✐♠♣r♦✈✐♥❣ ❝♦♠✲ ♣❛r❛❜✐❧✐t② ❜❡t✇❡❡♥ t❤❡ ♣❡r❢♦r♠❛♥❝❡ ❛♥❞ ❛ss♦rt♠❡♥t ♦❢ ✐♥❞✐✈✐❞✉❛❧s✳ ❚♦ ❢❛❝✐❧✐t❛t❡ t❤❡ ✉s❡ ♦❢ t❤❡ ♠❡t❤♦❞♦❧♦❣② st✉❞✐❡❞ ❤❡r❡ ✇❛s ❜✉✐❧t ❛♥ ♦♥❧✐♥❡ st❛t✐st✐❝❛❧ s②st❡♠ ❝❛❧❧❡❞ ✐✲❙♣♦rts✳
❙✉♠ár✐♦
✶ ■♥tr♦❞✉çã♦ ✶
✶✳✶ ❖❜❥❡t✐✈♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸
✶✳✷ ❖r❣❛♥✐③❛çã♦ ❞♦s ❈❛♣ít✉❧♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸
✷ ▼❛t❡r✐❛✐s ❡ ▼ét♦❞♦s ✹
✷✳✶ ❚❡st❡s Prát✐❝♦s ♣❛r❛ ❆✈❛❧✐❛çã♦ ❞❡ ❉❡s❡♠♣❡♥❤♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹
✷✳✶✳✶ ❚❡st❡ ❞❡ P❛ss❡ ❞❡ ▼♦r ❡ ❈❤r✐st✐❛♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺
✷✳✶✳✷ ❚❡st❡ ❞❡ ❉r✐❜❧❡ ❞❡ ❈✐♥❝♦ ❈♦♥❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺
✷✳✶✳✸ ❚❡st❡ ❞❡ ❈❤✉t❡ ❛♣ós P❛ss❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻
✷✳✶✳✹ ❚❡st❡ ❞❡ ✶✵✵✵ ▼❡tr♦s ❡♠ P✐st❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼
✷✳✶✳✺ ❚❡st❡ ❞❡ ❱❡❧♦❝✐❞❛❞❡ ❈í❝❧✐❝❛ ❞❡ ✷✵ ▼❡tr♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽
✷✳✶✳✻ ❚❡st❡ ❞❡ P♦tê♥❝✐❛ ❆♥❛❡ró❜✐❝❛ ✭❘✳❆✳❙✳❚✳✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾
✷✳✷ ❙✉♠❛r✐③❛çã♦ ❞❡ ❉❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵ ✷✳✷✳✶ ▼ét♦❞♦ ❩ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✷✳✷✳✷ ❆♥á❧✐s❡ ❞❡ ❈♦♠♣♦♥❡♥t❡s Pr✐♥❝✐♣❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷ ✷✳✷✳✸ ❆♥á❧✐s❡ ❋❛t♦r✐❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹ ✷✳✷✳✹ ❚❡♦r✐❛ ❞❡ ❈ó♣✉❧❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼
✸ ❘❡s✉❧t❛❞♦s ✷✸
❙✉♠ár✐♦ ✐
✸✳✹ ❏♦❣❛❞♦r❡s ❝♦♠ ▼❡❧❤♦r❡s ❆✈❛❧✐❛çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷
✹ ❙✐st❡♠❛ ✐✲❙♣♦rts ✹✹
✹✳✶ ❆❜♦r❞❛❣❡♠ ❲❡❜ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✹✳✷ ■♠♣❧❡♠❡♥t❛çã♦ ❡ ❆✈❛❧✐❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺
✺ ❈♦♥s✐❞❡r❛çõ❡s ❋✐♥❛✐s ✺✻
❘❡❢❡rê♥❝✐❛s ❇✐❜❧✐♦❣rá✜❝❛s ✺✼
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✸✳✶ ▼❡❞✐❞❛s ❞❡s❝r✐t✐✈❛s ♣❛r❛ ❛s ✈❛r✐á✈❡✐s ❝♦❧❡t❛❞❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✸✳✷ ▼❛tr✐③ ❞❡ ❝♦rr❡❧❛çã♦ ♦❜s❡r✈❛❞❛ ♣❛r❛ ♦s t❡st❡s ❢ís✐❝♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✸✳✸ ❆✉t♦✈❛❧♦r❡s ❡ ✪ ❞❡ ✈❛r✐❛❜✐❧✐❞❛❞❡ ❡①♣❧✐❝❛❞❛ ♦❜t✐❞❛ ♣♦r ♠❡✐♦ ❞❛ ❆✳❈✳P✳ ♣❛r❛
t❡st❡s ❢ís✐❝♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✸✳✹ ❆✉t♦✈❡t♦r❡s ♦❜t✐❞♦s ♣♦r ♠❡✐♦ ❞❛ ❆✳❈✳P✳ ♣❛r❛ t❡st❡s ❢ís✐❝♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✸✳✺ ▼❛tr✐③ ❞❡ ❝♦rr❡❧❛çã♦ ♦❜s❡r✈❛❞❛ ♣❛r❛ ♦s t❡st❡s té❝♥✐❝♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✸✳✻ ❆✉t♦✈❛❧♦r❡s ❡ ✪ ❞❡ ✈❛r✐❛❜✐❧✐❞❛❞❡ ❡①♣❧✐❝❛❞❛ ♦❜t✐❞❛ ♣♦r ♠❡✐♦ ❞❛ ❆✳❈✳P✳ ♣❛r❛
t❡st❡s té❝♥✐❝♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✸✳✼ ❆✉t♦✈❡t♦r❡s ♦❜t✐❞♦s ♣♦r ♠❡✐♦ ❞❛ ❆✳❈✳P✳ ♣❛r❛ t❡st❡s té❝♥✐❝♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✸✳✽ ▼❛tr✐③ ❞❡ ❝♦rr❡❧❛çã♦ ❞♦s t❡st❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✸✳✾ ❘❡s✉❧t❛❞♦ ❞♦ t❡st❡ ❇❛rt❧❡tt ❞❡ ❡s❢❡r✐❝✐❞❛❞❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✸✳✶✵ ▼❡❞✐❞❛ ❞❡ ❛❞❡q✉❛çã♦ ❞❛ ❛♠♦str❛ ✲ ▼❙❆✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✸✳✶✶ ❆✉t♦✈❛❧♦r✱ ♣r♦♣♦rçã♦ ❞❡ ✈❛r✐❛❜✐❧✐❞❛❞❡ ❡①♣❧✐❝❛❞❛ ❡ ❛❝✉♠✉❧❛❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✸✳✶✷ ❈❛r❣❛s ❢❛t♦r✐❛✐s r♦t❛❝✐♦♥❛❞❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✸✳✶✸ ❱❛r✐â♥❝✐❛ ❡①♣❧✐❝❛❞❛ ♣♦r ❝❛❞❛ ❢❛t♦r r♦t❛❝✐♦♥❛❞♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✸✳✶✹ ❈♦♠✉♥❛❧✐❞❛❞❡ ✜♥❛❧ ❡st✐♠❛❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✸✳✶✺ ❈♦❡✜❝✐❡♥t❡s ❞♦s ❡s❝♦r❡s ❢❛t♦r✐❛✐s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✸✳✶✻ ❆❥✉st❡ ❞❛ ❝ó♣✉❧❛ ◆♦r♠❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✸✳✶✼ ❚❡st❡ ❞❡ q✉❛❧✐❞❛❞❡ ❞❡ ❛❥✉st❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✸✳✶✽ ■♥❞✐✈í❞✉♦s ♠❛✐s ❝♦♥s✐st❡♥t❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾ ✸✳✶✾ ❚❡st❡ ❞❡ ✐♥❞❡♣❡♥❞ê♥❝✐❛ ♠✉❧t✐✈❛r✐❛❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✸✳✷✵ ❋❛♠í❧✐❛ ❞❡ ❝ó♣✉❧❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✸✳✷✶ ❆❥✉st❡ ❞❛ ❝ó♣✉❧❛ ◆♦r♠❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✸✳✷✷ ■♥❞✐✈í❞✉♦s q✉❡ ♠❛✐s s❡ ❞❡st❛❝❛r❛♠ ♥♦ ❈❍❯❚❊ s❡❣✉♥❞♦ ❛ ♠❡t♦❞♦❧♦❣✐❛ ❩✳ ✳ ✹✶ ✸✳✷✸ ■♥❞✐✈í❞✉♦s q✉❡ ♠❛✐s s❡ ❞❡st❛❝❛r❛♠ ♥♦ ❉❘■❇▲❊ s❡❣✉♥❞♦ ❛ ♠❡t♦❞♦❧♦❣✐❛ ❩✳ ✳ ✹✶
▲✐st❛ ❞❡ ❚❛❜❡❧❛s ✐✐✐
✸✳✷✹ ■♥❞✐✈í❞✉♦s q✉❡ ♠❛✐s s❡ ❞❡st❛❝❛r❛♠ ♥♦ P❆❙❙❊ s❡❣✉♥❞♦ ❛ ♠❡t♦❞♦❧♦❣✐❛ ❩✳ ✳ ✳ ✹✶ ✸✳✷✺ ■♥❞✐✈í❞✉♦s q✉❡ ♠❛✐s s❡ ❞❡st❛❝❛r❛♠ ❡♠ P❘ s❡❣✉♥❞♦ ❛ ♠❡t♦❞♦❧♦❣✐❛ ❩✳ ✳ ✳ ✳ ✹✶ ✸✳✷✻ ■♥❞✐✈í❞✉♦s q✉❡ ♠❛✐s s❡ ❞❡st❛❝❛r❛♠ ❡♠ ❱❖✷▼❆❳ s❡❣✉♥❞♦ ❛ ♠❡t♦❞♦❧♦❣✐❛ ❩✳ ✹✶ ✸✳✷✼ ■♥❞✐✈í❞✉♦s q✉❡ ♠❛✐s s❡ ❞❡st❛❝❛r❛♠ ❡♠ ❈▲✷✵ s❡❣✉♥❞♦ ❛ ♠❡t♦❞♦❧♦❣✐❛ ❩✳ ✳ ✳ ✹✷ ✸✳✷✽ ▼❡❧❤♦r❡s ❥♦❣❛❞♦r❡s ✜s✐❝❛♠❡♥t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✸✳✷✾ ❏♦❣❛❞♦r❡s ❝♦♠ ♠❛✐♦r ❤❛❜✐❧✐❞❛❞❡ té❝♥✐❝❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✸✳✸✵ ❏♦❣❛❞♦r❡s ❝♦♠ ♠❡❧❤♦r❡s ❛✈❛❧✐❛çõ❡s ✲ ❊s❝♦r❡ ❣❡r❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✸✳✸✶ ■♥❞✐✈í❞✉♦s ♠❛✐s ❝♦♥s✐st❡♥t❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✷✳✶ ❉✐s♣♦s✐çã♦ ❡ ♦r❞❡♠ ❞❡ ❛♣❧✐❝❛çã♦ ❞♦s t❡st❡s ❛♣❧✐❝❛❞♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺
✷✳✷ ■❧✉str❛çã♦ ❞♦ t❡st❡ ❞❡ ♣❛ss❡ ❞❡ ▼♦r ❡ ❈❤r✐st✐❛♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻
✷✳✸ ■❧✉str❛çã♦ ❞♦ t❡st❡ ❞❡ ❞r✐❜❧❡ ❞❡ ✺ ❝♦♥❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻
✷✳✹ ■❧✉str❛çã♦ ❞♦ t❡st❡ ❞❡ ❝❤✉t❡ ❛♣ós ♣❛ss❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼
✷✳✺ ■❧✉str❛çã♦ ❞♦ t❡st❡ ❞❡ ✶✵✵✵ ♠❡tr♦s ❡♠ ♣✐st❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾
✷✳✻ ■❧✉str❛çã♦ ❞♦ t❡st❡ ❞❡ ✈❡❧♦❝✐❞❛❞❡ ❝í❝❧✐❝❛ ❞❡ ✷✵ ♠❡tr♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾
✷✳✼ ■❧✉str❛çã♦ ❞♦ t❡st❡ ❞❡ ♣♦tê♥❝✐❛ ❛♥❛❡ró❜✐❝❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵
✷✳✽ P♦s✐çã♦ ❞❡ ✉♠ ✐♥❞✐✈í❞✉♦ ❝♦♠ Z = 1 ❡♠ r❡❧❛çã♦ ❛♦s ❞❡♠❛✐s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶
✷✳✾ ❖❜t❡♥çã♦ ❞♦s ✐♥❞✐❝❛❞♦r❡s ♣♦r ♠❡✐♦ ❞❛ ❆✳❈✳P✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸
✸✳✶ ❍✐st♦❣r❛♠❛ ✲ ❞❡s❝r✐çã♦ ❣❡r❛❧ ❞♦s ✐♥❞✐✈í❞✉♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✸✳✷ ❍✐st♦❣r❛♠❛ ✲ ❞❡s❡♠♣❡♥❤♦ ♥♦s t❡st❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✸✳✸ ●rá✜❝♦ ❞❛s ❞✉❛s ♣r✐♠❡✐r❛s ❝♦♠♣♦♥❡♥t❡s ✲ ❊s❝♦r❡ té❝♥✐❝♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✸✳✹ ●rá✜❝♦ ❞❡ ❝♦t♦✈❡❧♦ ❡ ♣r♦♣♦rçã♦ ❞❡ ✈❛r✐â♥❝✐❛ ❡①♣❧✐❝❛❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✸✳✺ ❈r✉③❛♠❡♥t♦ ❡♥tr❡ ♣r✐♠❡✐r♦ ❡ s❡❣✉♥❞♦ ❢❛t♦r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✸✳✻ ❈r✉③❛♠❡♥t♦ ❡♥tr❡ ♣r✐♠❡✐r♦ ❡ t❡r❝❡✐r♦ ❢❛t♦r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✸✳✼ ❈r✉③❛♠❡♥t♦ ❡♥tr❡ s❡❣✉♥❞♦ ❡ t❡r❝❡✐r♦ ❢❛t♦r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✸✳✽ ❈r✉③❛♠❡♥t♦ ❡♥tr❡ t♦❞❛s ❛s ✈❛r✐á✈❡✐s ❞❛ ❛♥á❧✐s❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻
✸✳✾ ◆♦r♠❛❧ ❜✐✈❛r✐❛❞❛ ✭r= 1
2✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼
✸✳✶✵ ❈ó♣✉❧❛ ◆♦r♠❛❧ ✭r = 12✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼
✸✳✶✶ ❉❛❞♦s ♦r✐❣✐♥❛✐s ✭❡sq✉❡r❞❛✮ ❡ tr❛♥s❢♦r♠❛❞♦s ♣❡❧♦ r❛♥❦ ✭❞✐r❡✐t❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✸✳✶✷ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ♣♦ssí✈❡✐s ❝ó♣✉❧❛s s✐♠✉❧❛❞❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾
✸✳✶✸ ◗◗♣❧♦t ♣❛r❛ ❝♦♠♣❛r❛çã♦ ❡♥tr❡ ❝ó♣✉❧❛ ❡♠♣ír✐❝❛ ❡ ❝ó♣✉❧❛ ◆♦r♠❛❧ ✭θ =
0,7813✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾
✹✳✶ ❊str✉t✉r❛ ❣❡r❛❧ ❞♦ s✐st❡♠❛✱ ❜❡♠ ❝♦♠♦ ❛s ❧✐♥❣✉❛❣❡♥s ✉t✐❧✐③❛❞❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻
▲✐st❛ ❞❡ ❋✐❣✉r❛s ✈
✹✳✷ ❆❝❡ss♦ ❞✐s♣♦♥í✈❡❧ ♣❛r❛ ❝❛❞❛ t✐♣♦ ❞❡ ✉s✉ár✐♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✹✳✸ ➪r❡❛ ❞❡ ❧♦❣✐♥ ❞❛ ❡s❝♦❧❛ ❝❛❞❛str❛❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✹✳✹ ❋♦r♠✉❧ár✐♦ ❞❡ ❝❛❞❛str♦ ❞❡ ❛❧✉♥♦✴❛t❧❡t❛ ♥♦ s✐st❡♠❛ ✐✲❙♣♦rts✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✹✳✺ ▼❡♥✉ ❞❡ r❡❧❛tór✐♦s ♣❛r❛ ❛ ❡s❝♦❧❛ ▼❡♥✐♥♦s ❞❛ ❱✐❧❛ ♥♦ ✐✲❙♣♦rts✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✹✳✻ ❘❡❧❛tór✐♦ ❣❡r❛❧ ❞♦s ❛❧✉♥♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✹✳✼ ❘❡❧❛tór✐♦ ❣❡r❛❧ ❞♦s t❡st❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ✹✳✽ ▼❡❧❤♦r❡s ❥♦❣❛❞♦r❡s ✜s✐❝❛♠❡♥t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷ ✹✳✾ ❏♦❣❛❞♦r❡s ❝♦♠ ♠❛✐♦r ❤❛❜✐❧✐❞❛❞❡ té❝♥✐❝❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷ ✹✳✶✵ ❏♦❣❛❞♦r❡s ❝♦♠ ♠❡❧❤♦r❡s ❛✈❛❧✐❛çõ❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✹✳✶✶ ❏♦❣❛❞♦r❡s ♠❛✐s ❝♦♥s✐st❡♥t❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✹✳✶✷ ❆❧✉♥♦ ❝♦♠ ♠❛✐♦r ❡s❝♦r❡ ❣❡r❛❧ ❡ ♠❛✐♦r ❝♦♥s✐stê♥❝✐❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✹✳✶✸ ❆❧✉♥♦ ❝♦♠ ♠❡♥♦r ❡s❝♦r❡ ❣❡r❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺
❈❛♣ít✉❧♦ ✶
■♥tr♦❞✉çã♦
❊♠ t❡♠♣♦s ❞❡ ❡✈❡♥t♦s ❡s♣♦rt✐✈♦s ♠✉♥❞✐❛✐s r❡❛❧✐③❛❞♦s ♥♦ ♣❛ís ❞♦ ❋✉t❡❜♦❧✱ ♦ ❇r❛s✐❧✱ ❝❛❞❛ ✈❡③ ♠❛✐s ♦ ❛ss✉♥t♦ ❡s♣♦rt❡ s❡ t♦r♥❛ ♦ ❝❡♥tr♦ ❞❛s ❛t❡♥çõ❡s✳ ◆❡ss❡ s❡♥t✐❞♦✱ s✉r❣❡♠ ❞✐✈❡rs❛s ❛❜♦r❞❛❣❡♥s ❡st❛tíst✐❝❛s s♦❜r❡ ♦ t❡♠❛ ❡✱ ❞❡♥tr❡ ❡❧❛s✱ ❛ ✉t✐❧✐③❛çã♦ ❞❡ ✐♥❞✐❝❛❞♦r❡s ♣❛r❛ ❝♦♠♣❛r❛r ♦ ❞❡s❡♠♣❡♥❤♦ ❞❡ ✐♥❞✐✈í❞✉♦s✴❛t❧❡t❛s✳
◆♦ ❡s❝♦♣♦ ❣❡r❛❧ ❞❛ ❝♦♠♣♦s✐çã♦ ❞❡ ✉♠ ❛t❧❡t❛✱ t❡♠♦s q✉❡ s✉❛ ❝♦♥❞✐çã♦ ❢ís✐❝❛ é ✐♠♣r❡s❝✐♥✲ ❞í✈❡❧ ♣❛r❛ q✉❡ s❡✉ r❡♥❞✐♠❡♥t♦ ❡♠ ❞❡t❡r♠✐♥❛❞♦ ❡s♣♦rt❡ s❡❥❛ ❞❡ ❡①❝❡❧ê♥❝✐❛ ❬✶✱ ✷✱ ✸✱ ✹✱ ✺✱ ✻❪✳ ❯♠ ❛t❧❡t❛ ❝♦♠ ❝♦♥❞✐çã♦ ❢ís✐❝❛ ❛♣✉r❛❞❛ t❡♥❞❡ ❛ ♦❜t❡r r❡s✉❧t❛❞♦s ♠❛✐s s❛t✐s❢❛tór✐♦s q✉❛♥❞♦ ❝♦♠♣❛r❛❞♦s ❝♦♠ ❛q✉❡❧❡s q✉❡ sã♦ ❞❡s♣r♦✈✐❞♦s ❞❡ss❛ ❝❛r❛❝t❡ríst✐❝❛✱ ♣♦✐s ❛ ❛❧t❛ ❝❛♣❛❝✐❞❛❞❡ ❢ís✐❝❛ ❡stá r❡❧❛❝✐♦♥❛❞❛ ❝♦♠ ♦ ❛❧t♦ ❞❡s❡♠♣❡♥❤♦ ❡♠ ✐♥❞✐❝❛❞♦r❡s ❞❡ ♣❡r❢♦r♠❛♥❝❡✱ ♠❡♥♦r ❢❛✲ ❞✐❣❛ ❞❡ ❥♦❣♦ ❡ ❛té ♠❡s♠♦ ❝♦♠ ♦ ❞❡s❡♠♣❡♥❤♦ ❞♦ ♣ró♣r✐♦ t✐♠❡ ❬✼❪✳ ❆❧é♠ ❞✐ss♦✱ ♦s ♠❡❧❤♦r❡s ❥♦❣❛❞♦r❡s ❞❡✈❡♠ ❝♦♥s❡❣✉✐r s❡ ❛❞❛♣t❛r ❛ ❞❡♠❛♥❞❛ ❢ís✐❝❛ ❞♦ ❥♦❣♦✱ q✉❡ é ♠✉❧t✐❢❛t♦r✐❛❧✳ ❊❧❡s ♥ã♦ ♣r❡❝✐s❛♠ t❡r ✉♠❛ ❝❛r❛❝t❡ríst✐❝❛ ❡①tr❛♦r❞✐♥ár✐❛ ❡♠ ✉♠❛ ú♥✐❝❛ ár❡❛✱ ♠❛s s✐♠ ♣♦ss✉✐r ✉♠ ♥í✈❡❧ ❡❧❡✈❛❞♦ ❡♠ t♦❞❛s ❡❧❛s ❬✶❪✳
P♦ré♠✱ ❡st❡ ♥ã♦ é ♦ ú♥✐❝♦ ❢❛t♦r q✉❡ ✐♥✢✉❡♥❝✐❛ ❡♠ s❡✉ ❞❡s❡♠♣❡♥❤♦✳ ❆ ❝❛♣❛❝✐❞❛❞❡ q✉❡ ✉♠ ❛t❧❡t❛✴❡q✉✐♣❡ ♣♦ss✉✐ ❡stá r❡❧❛❝✐♦♥❛❞❛ ❝♦♠ ♠✉✐t❛s ♦✉tr❛s ✈❛r✐á✈❡✐s ❝♦♠♦ ❛ ❝❛♣❛❝✐❞❛❞❡ ♣s✐❝♦❧ó❣✐❝❛ ♣❛r❛ s✉♣♦rt❛r ❛❧t❛s ♣r❡ssõ❡s✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡ q✉❛♥❞♦ ❡♥✈♦❧✈❡♠ ❝♦♥s❡q✉ê♥❝✐❛s ♥❡❣❛t✐✈❛s ❬✸❪✱ ❡ ❝❛r❛❝t❡ríst✐❝❛s ❞❡ ♣❡rs♦♥❛❧✐❞❛❞❡ q✉❡ ❢❛❝✐❧✐t❛♠ ♦ ❛♣r❡♥❞✐③❛❞♦✱ tr❡✐♥❛♠❡♥t♦ ❡ ❝♦♠♣❡t✐çã♦ ❬✷❪✳ P♦❞❡♠♦s ♦❜s❡r✈❛r t❛♠❜é♠ ❛ ❡①✐stê♥❝✐❛ ❞❡ ❢❛t♦r❡s ❝♦❣♥✐t✐✈♦s ❡ ❞❡ ✐♥✲ t❡❧✐❣ê♥❝✐❛ ❞❡ ❥♦❣♦ ❝♦♠♦ ❛♥t❡❝✐♣❛çã♦✱ t♦♠❛❞❛ ❞❡ ❞❡❝✐sã♦ ❡ ❛té ✐♥t❡❧✐❣ê♥❝✐❛ ❡ ❝r✐❛t✐✈✐❞❛❞❡ ❬✷✱ ✽✱ ✾❪✳ ❆✐♥❞❛✱ ❞❡✈❡♠♦s ❧❡✈❛r ❡♠ ❝♦♥t❛ ❛ ♠❛t✉r❛çã♦ ❞♦ ❛t❧❡t❛ ❬✺✱ ✶✵❪✱ ❢❛t♦r❡s ❣❡♥ét✐❝♦s ❬✷✱ ✶✶❪ ❡ s♦❝✐♦❧ó❣✐❝♦s ❬✷❪ ❝♦♠♦✱ ♣♦r ❡①❡♠♣❧♦✱ ❛ ✐♥✢✉ê♥❝✐❛ ❢❛♠✐❧✐❛r✱ ♦ ♣❛♣❡❧ ❞♦ tr❡✐♥❛❞♦r ❡ ❛ ♣r❡✈❡♥çã♦ ❡ ❞❡t❡❝çã♦ ❞❡ ❧❡sõ❡s✳
✷
t❡st❡s ❞❡ ❝❛♠♣♦ ❡s♣❡❝í✜❝♦s ♣♦❞❡♠ s❡r ✉s❛❞♦s ❡ ❡♠♣✐r✐❝❛♠❡♥t❡ ❛♥❛❧✐s❛❞♦s✱ ❛ ✜♠ ❞❡ ❞❡✲ t❡❝t❛r ✐♥❞✐✈í❞✉♦s q✉❡ s❡ ❞❡st❛q✉❡♠ ❞❡♥tr❡ ♦s ❞❡♠❛✐s✳ ❊ss❡s t❡st❡s sã♦ ❝♦♥s✐❞❡r❛❞♦s ✉♠❛ ❛❧t❡r♥❛t✐✈❛ s❛t✐s❢❛tór✐❛ ❡♠ r❡❧❛çã♦ ❛♦s t❡st❡s ❧❛❜♦r❛t♦r✐❛✐s ❬✶✷❪✱ ♣♦✐s ❣❡r❛❧♠❡♥t❡ sã♦ s✐♠✲ ♣❧❡s✱ ♣♦♣✉❧❛r❡s ❡♥tr❡ ❥♦❣❛❞♦r❡s ❡ té❝♥✐❝♦s ❡ ♥ã♦ ♥❡❝❡ss✐t❛♠ ❞❡ ❡q✉✐♣❛♠❡♥t♦s ♣❛r❛ s✉❛ ❛♣❧✐❝❛çã♦ ❬✼❪✳
❖✉tr♦ ❢❛t♦r q✉❡ ❝♦♥tr✐❜✉✐ ♥❛ ✉t✐❧✐③❛çã♦ ❞❡ss❡s t❡st❡s é q✉❡ ♦s t❡st❡s ❧❛❜♦r❛t♦r✐❛✐s ❡♥✲ ✈♦❧✈❡♠ ❡①❡r❝í❝✐♦s q✉❡ ♥ã♦ sã♦ ❡s♣❡❝í✜❝♦s ❞♦ ❢✉t❡❜♦❧ ❡ ♦s ♣r♦t♦❝♦❧♦s ✉s❛❞♦s ✐♠♣❛❝t❛♠ ♥❛ ♠♦t✐✈❛çã♦ ❞♦s ❥♦❣❛❞♦r❡s ❬✶✷❪✳ ❆❧é♠ ❞✐ss♦✱ t❛✐s t❡st❡s ❣❡r❛❧♠❡♥t❡ sã♦ ❝❛r♦s ❬✼❪✳
❉❡ss❛ ❢♦r♠❛✱ ♣❛r❛ ❝♦♠♣❛r❛r♠♦s ♦ ❞❡s❡♠♣❡♥❤♦ ❞❡ ❛t❧❡t❛s✴✐♥❞✐✈í❞✉♦s ❡♠ ❞❡t❡r♠✐♥❛❞♦ ❡s♣♦rt❡✱ ❞❡✈❡♠♦s ✉t✐❧✐③❛r ✐♥❞✐❝❛❞♦r❡s q✉❡ r❡✢✐t❛♠ ❡s♣❡❝✐❛❧♠❡♥t❡ ❛ r❡❛❧✐❞❛❞❡ ❞❛ ❛♣t✐❞ã♦ ❢ís✐❝❛ ❡ té❝♥✐❝❛✳ ❈♦♠♦ ✉♠❛ ❞❛s ♣r✐♥❝✐♣❛✐s ❝❛r❛❝t❡ríst✐❝❛s ❞❡ ✉♠ ❜♦♠ ✐♥❞✐❝❛❞♦r✱ t❡♠♦s q✉❡ ❡st❡ ❞❡✈❡ s❡r ❝❛❧❝✉❧❛❞♦ ❞❡ ❢♦r♠❛ s✐♠♣❧❡s ❡ t❛♠❜é♠ s❡r ❞❡ ❢á❝✐❧ ✐♥t❡r♣r❡t❛çã♦✳
◆❡st❡ ❝♦♥t❡①t♦✱ ❛♥á❧✐s❡s ❡st❛tíst✐❝❛s sã♦ ✉t✐❧✐③❛❞❛s ♣❛r❛ ♠❡♥s✉r❛r ❛s ❤❛❜✐❧✐❞❛❞❡s ❢ís✐✲ ❝❛s ❡ té❝♥✐❝❛s ❞❡ ✐♥❞✐✈í❞✉♦s✱ ♣❡r♠✐t✐♥❞♦ ❛ ❝♦♠♣❛r❛❜✐❧✐❞❛❞❡ ❞♦s ♠❡s♠♦s✳ P❛r❛ ❡st❡ ✜♠✱ ♣r♦♣♦♠♦s ✉♠ ♣r♦❜❧❡♠❛ ❞❡ ❝❛rát❡r s♦❝✐❛❧✱ ❛ ❝♦♠♣❛r❛çã♦ ❞♦ ❞❡s❡♠♣❡♥❤♦ ❞❡ ❛t❧❡t❛s ❡♠ ❞✐❢❡r❡♥t❡s t❡st❡s ❛♣❧✐❝❛❞♦s✱ ✉t✐❧✐③❛♠♦s ✉♠❛ ♠❡t♦❞♦❧♦❣✐❛ ♣r♦♣♦st❛ ♣♦r ❬✶✸❪✱ ❛ ❝♦♥str✉çã♦ ❞❡ ✐♥❞✐❝❛❞♦r❡s ♣♦r ♠❡✐♦ ❞❛ ❆♥á❧✐s❡ ❞❡ ❈♦♠♣♦♥❡♥t❡s Pr✐♥❝✐♣❛✐s✱ ❞❛ ❆♥á❧✐s❡ ❋❛t♦r✐❛❧ ❡ t❛♠❜é♠ ♣❡❧❛ ♠❡t♦❞♦❧♦❣✐❛ ❞❡ ❈ó♣✉❧❛s ❡ ❞❡s❡♥✈♦❧✈❡♠♦s ✉♠ s✐st❡♠❛ ♦♥❧✐♥❡ ❡ ✐♥♦✈❛❞♦r ❢❡✐t♦ ❛ ♣❛rt✐r ❞❡ s♦❢t✇❛r❡s ❧✐✈r❡s ❡ ❣r❛t✉✐t♦s✳
◆♦ ♥♦ss♦ ❝♦♥❤❡❝✐♠❡♥t♦✱ ♥ã♦ ❡①✐st❡ ♥❛ ❧✐t❡r❛t✉r❛ tr❛❜❛❧❤♦s q✉❡ tr❛t❛♠ ❞❡ ❢♦r♠❛ s✐s✲ t❡♠át✐❝❛ ♣r♦❝❡❞✐♠❡♥t♦s ❞❡ t❡st❡s ❡s♣❡❝í✜❝♦s ✐♥✐❝✐❛♥❞♦✲s❡ ❝♦♠ ❛ ❝♦❧❡t❛ ❞♦s ❞❛❞♦s✱ ❞❡✲ s❡♥✈♦❧✈✐♠❡♥t♦ t❡ór✐❝♦✱ ❛♣❧✐❝❛çã♦ ❡ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ✉♠ s♦❢t✇❛r❡ q✉❡ ♣♦ss✐❜✐❧✐t❛ ✉♠❛ ❡str✉t✉r❛ ✐♥t❡❣r❛❞❛✳ ■ss♦ ♥♦s r❡♣♦rt❛ ❛ ✉♠❛ ❡str✉t✉r❛ ❞❡ ✐♥♦✈❛çã♦ ❡♠ ❡st❛tíst✐❝❛ ❛♣❧✐❝❛❞❛ ❛♦ ❡s♣♦rt❡ q✉❡ ♣♦ss✐✈❡❧♠❡♥t❡ ❞❡✈❡rá s❡r ❝♦♠✉♠ ♥♦ ❢✉t✉r♦ ♣ró①✐♠♦✱ ✐♥❝❧✉s✐✈❡ ♣❛r❛ ♦✉tr❛s ár❡❛s ❞♦ ❝♦♥❤❡❝✐♠❡♥t♦✳
❚r❛❜❛❧❤♦ s❡♠❡❧❤❛♥t❡ ❢♦✐ ❛♣r❡s❡♥t❛❞♦ ♣♦r ❬✶✹❪✱ ❡♠ q✉❡ ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞♦ ✉♠ s✐st❡♠❛ ♦♥❧✐♥❡ ✉t✐❧✐③❛♥❞♦ ♠ét♦❞♦s ❋✉③③② ♣❛r❛ ✐❞❡♥t✐✜❝❛çã♦ ❞❡ ❛♣t✐❞ã♦ ❞♦ ✐♥❞✐✈í❞✉♦ ❡♠ ✉♠❛ ❧✐st❛ ❡s♣❡❝í✜❝❛ ❞❡ ❡s♣♦rt❡s✳ ◆♦ss♦ tr❛❜❛❧❤♦ s❡ ❜❛s❡✐❛ ♥❛ ❡str✉t✉r❛ ❡♠♣r❡❣❛❞❛ ♣❡❧♦s ❛✉t♦r❡s✱ ♠❛s ❡♥❣❧♦❜❛ ♠ét♦❞♦s ❡st❛tíst✐❝♦s ✉♥✐ ❡ ♠✉❧t✐✈❛r✐❛❞♦s✱ ❞✐❢❡r❡♥t❡s ❧✐♥❣✉❛❣❡♥s ❡ s♦❢t✇❛r❡s ❡ ❛ ❡①❝❧✉s✐✈❛ ✉t✐❧✐③❛çã♦ ❞♦ s♦❢t✇❛r❡ ❘ ❬✶✺❪ ❝♦♠♦ ♠❡✐♦ ❞❡ ❝á❧❝✉❧♦ ❞♦s r❡s✉❧t❛❞♦s ❡♠ ✉♠ s✐st❡♠❛ ❞✐♥â♠✐❝♦ ❞❡ ❝♦♥❡①ã♦ ❝♦♠ ♦ s❡r✈✐❞♦r✳
P❛r❛ ❡①❡♠♣❧✐✜❝❛r ❛s ♠❡t♦❞♦❧♦❣✐❛s ✉t✐❧✐③❛❞❛s✱ ✜③❡♠♦s ❛ ❛♣❧✐❝❛çã♦ ❞❡ t❡st❡s ♣❛r❛ ❛✈❛✲ ❧✐❛çã♦ ❞❡ ❞❡s❡♠♣❡♥❤♦ ❡♠ ❢✉t❡❜♦❧ ❡♠ ✉♠❛ ❡s❝♦❧❛ ❞❡ ❢✉t❡❜♦❧ ❞❡ ❝❛♠♣♦ ❞❛ ❝✐❞❛❞❡ ❞❡ ❙ã♦
✶✳✶✳ ❖❜❥❡t✐✈♦s ✸
❈❛r❧♦s ✲ ❙P ❡ ❛♣r❡s❡♥t❛♠♦s ♦s ❞✐❢❡r❡♥t❡s r❡❧❛tór✐♦s ❣❡r❛❞♦s ♣❡❧♦ s✐st❡♠❛ ❝r✐❛❞♦✱ ♦ ✐✲❙♣♦rts ✭❞✐s♣♦♥í✈❡❧ ❡♠ ❤tt♣✿✴✴✇✇✇✳♠✇st❛t✳❝♦♠✴✐s♣♦rts✮✳
✶✳✶ ❖❜❥❡t✐✈♦s
❖ ♦❜❥❡t✐✈♦ ♣r✐♥❝✐♣❛❧ ❞❡st❡ tr❛❜❛❧❤♦ é ❛♣r❡s❡♥t❛r ❢❡rr❛♠❡♥t❛s ❡st❛tíst✐❝❛s q✉❡ ♣❡r♠✐t❛♠ ❛ ❝♦♠♣❛r❛çã♦ ❞❡ ✐♥❞✐✈í❞✉♦s ❡♠ q✉❛❧q✉❡r ♠♦❞❛❧✐❞❛❞❡ ❡s♣♦rt✐✈❛✳ ■♥✐❝✐❛❧♠❡♥t❡✱ ♦ ❡st✉❞♦ ❛♣r❡s❡♥t❛❞♦ é ✈♦❧t❛❞♦ à ❛✈❛❧✐❛çã♦ ❞❡ ❞❡s❡♠♣❡♥❤♦ ♥♦ ❢✉t❡❜♦❧✱ s❡♥❞♦ q✉❡ sã♦ ❛♣r❡s❡♥t❛❞❛s ❛❜♦r❞❛❣❡♥s ✉♥✐✈❛r✐❛❞❛s ❡ ♠✉❧t✐✈❛r✐❛❞❛s✳
❈♦♠♦ r❡s✉❧t❛❞♦✱ ❛♣r❡s❡♥t❛♠♦s ❛s ❡t❛♣❛s ❞❡ ❝r✐❛çã♦ ❞♦s ✐♥❞✐❝❛❞♦r❡s ✉t✐❧✐③❛❞♦s✱ ❡①✐❜✐✲ ♠♦s ♦s ✐♥❞✐✈í❞✉♦s q✉❡ s❡ ❞❡st❛❝❛r❛♠ ❞♦s ❞❡♠❛✐s ♥♦s t❡st❡s ❡ ♠♦str❛♠♦s ❛ ✉t✐❧✐③❛çã♦ ❞♦s ✐♥❞✐❝❛❞♦r❡s ❝r✐❛❞♦s ❡♠ ✉♠ s✐st❡♠❛ ❡st❛tíst✐❝♦ ♦♥❧✐♥❡✳
✶✳✷ ❖r❣❛♥✐③❛çã♦ ❞♦s ❈❛♣ít✉❧♦s
❖ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦ ❡stá ♦r❣❛♥✐③❛❞♦ ❝♦♠♦ s❡❣✉❡✿ ♥♦ ❈❛♣ít✉❧♦ ✷ ❛♣r❡s❡♥t❛♠♦s ❛ ♠❡t♦✲ ❞♦❧♦❣✐❛ ❞❡ ❛♣❧✐❝❛çã♦ ❡ ❝♦❧❡t❛ ❞❡ ❞❛❞♦s✱ ❜❡♠ ❝♦♠♦ ❛s té❝♥✐❝❛s ❡st❛tíst✐❝❛s ✉t✐❧✐③❛❞❛s✳ ◆♦ ❈❛♣ít✉❧♦ ✸ ❡①✐❜✐♠♦s ♦s r❡s✉❧t❛❞♦s ❞❛ ❝r✐❛çã♦ ❞♦s ✐♥❞✐❝❛❞♦r❡s ❞✐r❡❝✐♦♥❛❞♦s à ♠♦❞❛❧✐❞❛❞❡ ❞❡ ❢✉t❡❜♦❧ ❞❡ ❝❛♠♣♦ ❡ ♥♦ ❈❛♣ít✉❧♦ ✹ ❛ ❝♦♥str✉çã♦ ❡ ❢✉♥❝✐♦♥❛♠❡♥t♦ ❞♦ s✐st❡♠❛ ✐✲❙♣♦rts✳ P♦r ✜♠✱ ♥♦ ❈❛♣ít✉❧♦ ✺ ❛♣r❡s❡♥t❛♠♦s ❛s ❝♦♥s✐❞❡r❛çõ❡s ✜♥❛✐s ❡ tr❛❜❛❧❤♦s ❢✉t✉r♦s✳
❈❛♣ít✉❧♦ ✷
▼❛t❡r✐❛✐s ❡ ▼ét♦❞♦s
❊st❛ s❡çã♦ ❛♣r❡s❡♥t❛ ❛ ♠❡t♦❞♦❧♦❣✐❛ ❞❡ ❝♦❧❡t❛ ❞❡ ❞❛❞♦s ❜❛s❡❛❞❛ ❡♠ t❡st❡s ❞❡ ❞❡s❡♠✲ ♣❡♥❤♦ ✈♦❧t❛❞♦ ❛♦ ❢✉t❡❜♦❧✱ ❜❡♠ ❝♦♠♦ ❛s ❢❡rr❛♠❡♥t❛s ❡st❛tíst✐❝❛s ✉t✐❧✐③❛❞❛s ♣❛r❛ ❛ ❛♥á❧✐s❡ ❞❛s ✐♥❢♦r♠❛çõ❡s r❡❧❛t✐✈❛s ❛♦s t❡st❡s ♣rát✐❝♦s✳
✷✳✶ ❚❡st❡s Prát✐❝♦s ♣❛r❛ ❆✈❛❧✐❛çã♦ ❞❡ ❉❡s❡♠♣❡♥❤♦
❈♦♠♦ ❝✐t❛❞♦ ❛♥t❡r✐♦r♠❡♥t❡ t❡st❡s ❞❡ ❝❛♠♣♦ ❡s♣❡❝í✜❝♦s t❡♠ s✐❞♦ ❜❛st❛♥t❡ ✉t✐❧✐③❛❞♦s ♣❛r❛ ❛✈❛❧✐❛r ♦ ❞❡s❡♠♣❡♥❤♦ ❡♠ ❢✉t❡❜♦❧ ❬✶✱ ✻✱ ✼✱ ✶✷✱ ✶✻✱ ✶✼✱ ✶✽✱ ✶✾✱ ✷✵✱ ✷✶✱ ✷✷✱ ✷✸✱ ✷✹❪✳ ❚❛✐s t❡st❡s sã♦ ❛❧✈♦s ❞❡ ♣❡sq✉✐s❛ t❛♥t♦ ♣❛r❛ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ♥♦✈♦s t❡st❡s ❬✷✺✱ ✷✻❪ q✉❛♥t♦ ♣❛r❛ ✈❛❧✐❞❛çã♦ ❞♦s ♠❡s♠♦s ❬✷✺✱ ✷✼✱ ✷✽❪✳
P❛r❛ s❡❧❡❝✐♦♥❛r♠♦s ♦s t❡st❡s ❞❡ ❛✈❛❧✐❛çã♦ ❞❡ ❞❡s❡♠♣❡♥❤♦ ❛ s❡r❡♠ ✉t✐❧✐③❛❞♦s ♥♦ s✐st❡♠❛✱ ✉♠❛ ❝♦❧❡çã♦ ❞❡ t❡st❡s ❛♣❧✐❝❛❞♦s à ❛✈❛❧✐❛çã♦ ❞❡ ❛t❧❡t❛s ❞❡ ❢✉t❡❜♦❧ ❞❡ ❝❛♠♣♦ ❢♦✐ ❡①✐❜✐❞❛ ❛ ✉♠ ❡s♣❡❝✐❛❧✐st❛ ❞❡st❡ ❡s♣♦rt❡✱ ❛ ✜♠ ❞❡ q✉❡ s❡❧❡❝✐♦♥❛ss❡ ♦s t❡st❡s ❢ís✐❝♦s ❡ té❝♥✐❝♦s ❛ s❡r❡♠ ✉t✐❧✐③❛❞♦s✳
❖s t❡st❡s ❞❡ ❤❛❜✐❧✐❞❛❞❡ té❝♥✐❝❛ s❡❧❡❝✐♦♥❛❞♦s ❢♦r❛♠✿ t❡st❡ ❞❡ ♣❛ss❡ ❞❡ ▼♦r ❡ ❈❤r✐st✐❛♥✱ t❡st❡ ❞❡ ❞r✐❜❧❡ ❞❡ ❝✐♥❝♦ ❝♦♥❡s ❡ t❡st❡ ❞❡ ❝❤✉t❡ ❛♣ós ♣❛ss❡✳
❏á ♦s t❡st❡s ❢ís✐❝♦s ❢♦r❛♠✿ t❡st❡ ❞❡ ✶✵✵✵ ♠❡tr♦s ❡♠ ♣✐st❛✱ t❡st❡ ❞❡ ✈❡❧♦❝✐❞❛❞❡ ❝í❝❧✐❝❛ ❞❡ ✷✵ ♠❡tr♦s ❡ ♦ t❡st❡ ❞❡ ♣♦tê♥❝✐❛ ❛♥❛❡ró❜✐❝❛ ✭❘✳❆✳❙✳❚✳✮✳
✷✳✶✳ ❚❡st❡s Prát✐❝♦s ♣❛r❛ ❆✈❛❧✐❛çã♦ ❞❡ ❉❡s❡♠♣❡♥❤♦ ✺
❋✐❣✉r❛ ✷✳✶✿ ❉✐s♣♦s✐çã♦ ❡ ♦r❞❡♠ ❞❡ ❛♣❧✐❝❛çã♦ ❞♦s t❡st❡s ❛♣❧✐❝❛❞♦s✳
✷✳✶✳✶ ❚❡st❡ ❞❡ P❛ss❡ ❞❡ ▼♦r ❡ ❈❤r✐st✐❛♥
❖ t❡st❡ ❞❡ ♣❛ss❡ ❞❡ ▼♦r ❡ ❈❤r✐st✐❛♥ ❬✷✾❪ ❝♦♥s✐st❡ ♥❛ ❞❡♠❛r❝❛çã♦ ❞❡ ✉♠❛ ♣❡q✉❡♥❛ ♠❡t❛✱ ❞❡ ✾✶ ❝❡♥tí♠❡tr♦s ❞❡ ❧❛r❣✉r❛ ❡ ✹✻ ❝❡♥tí♠❡tr♦s ❞❡ ❛❧t✉r❛✱ ❢❡✐t❛ ♣♦r ❞♦✐s ❝♦♥❡s ❡ ✉♠❛ ❤❛st❡ ❞❡ ♠❛♥❡✐r❛ q✉❡ ❡st❛rá ❧✐♠✐t❛♥❞♦ ❛ ❛❧t✉r❛ ❞♦ ✏❣♦❧✑✳ ❖s ✐♥❞✐✈í❞✉♦s ♣❛rt✐❝✐♣❛♥t❡s ❞♦
t❡st❡ ✜❝❛♠ ❛ ✉♠❛ ❞✐stâ♥❝✐❛ ❞❡ ✶✹ ♠❡tr♦s✱ ❡♠ três â♥❣✉❧♦s ❞✐❢❡r❡♥t❡s✿ 45◦✱ 90◦ ❡ 135◦✱ ❞❡
♠❛♥❡✐r❛ q✉❡ ❝❛❞❛ ✉♠ t❡rá ❛ ❞✐s♣♦s✐çã♦ q✉❛tr♦ t❡♥t❛t✐✈❛s ❡♠ ❝❛❞❛ â♥❣✉❧♦✱ r❡s✉❧t❛♥❞♦ ❡♠ ❞♦③❡ ♥♦ t♦t❛❧✳ ❈♦♠♣✉t❛✲s❡ ✶ ♣♦♥t♦ ♣❛r❛ ❝❛❞❛ ❛❝❡rt♦✱ q✉❡ é ❝♦♥s✐❞❡r❛❞♦ ✈á❧✐❞♦ q✉❛♥❞♦ ❛ ❜♦❧❛ ♣❛ss❛ ♣♦r ❞❡ ❞❡♥tr♦ ❞❛ ♠❡t❛✱ ♠❡s♠♦ q✉❡ t❡♥❤❛ t♦❝❛❞♦ ♦s ❝♦♥❡s ❡✴♦✉ ♥❛ ❤❛st❡✳ ❉❡ss❛ ❢♦r♠❛✱ ❛ ♠❡♥♦r ♣♦♥t✉❛çã♦ ♣♦ssí✈❡❧ é ✵ ❡ ❛ ♠❛✐♦r é ✶✷✳ ❆ ❞✐s♣♦s✐çã♦ ❞♦s ❝♦♥❡s é ❡①♣♦st❛ ♥❛ ❋✐❣✉r❛ ✷✳✷✳
❆s ♦❜s❡r✈❛çõ❡s ❞❡st❡ t❡st❡ ❢♦r❛♠ ✐♥❞❡①❛❞❛s à ✈❛r✐á✈❡❧ P❆❙❙❊✳
✷✳✶✳✷ ❚❡st❡ ❞❡ ❉r✐❜❧❡ ❞❡ ❈✐♥❝♦ ❈♦♥❡s
❊ss❡ t❡st❡ ❝♦♥s✐st❡ ❡♠ ✉♠❛ ❛❞❛♣t❛çã♦ ❞♦ t❡st❡ ❞❡ ❛❣✐❧✐❞❛❞❡ ❞❡ ❬✶✾❪✳ ❈✐♥❝♦ ❝♦♥❡s sã♦ ❞✐s♣♦st♦s ❛ ✷✱✼ ♠❡tr♦s ✉♠ ❞♦ ♦✉tr♦ ❡♠ ❧✐♥❤❛ r❡t❛ ❡ ♦ ✐♥❞✐✈í❞✉♦ ❞❡✈❡✱ ❞❛❞♦ ✉♠ ❧❛❞♦ ❞❡ ♣❛rt✐❞❛✱ ✐r ❡ ✈♦❧t❛r ❞r✐❜❧❛♥❞♦ ♦s ❝♦♥❡s ❡♠ ✏③✐❣✉❡③❛❣✉❡✑✳ ❊st❡ ♣r♦❝❡ss♦ é r❡❛❧✐③❛❞♦ ❞✉❛s ✈❡③❡s ❡ ❛ ♣♦♥t✉❛çã♦ ♦❜t✐❞❛ é ❛ s♦♠❛ ❞♦s t❡♠♣♦s r❡❛❧✐③❛❞♦s ♥❛s ❞✉❛s t❡♥t❛t✐✈❛s✱ ❞❡ ♠♦❞♦ q✉❡ q✉❛♥t♦ ♠❡♥♦r ❢♦r ❡ss❛ s♦♠❛✱ ♠❛✐♦r s❡rá ♦ ♥í✈❡❧ ❞❡ ❞r✐❜❧❡ ❡ ❝♦♥tr♦❧❡ ❞❡ ❜♦❧❛ ❞♦ ❛❧✉♥♦ ✭✈✐st♦ s❡r❡♠ ❛♠❜♦s ❝❛♣❛❝✐❞❛❞❡s té❝♥✐❝❛s ❡ss❡♥❝✐❛✐s ❛♦ ❢✉t❡❜♦❧ ♣r♦✜ss✐♦♥❛❧✮✳ ❆ ❞✐s♣♦s✐çã♦
✷✳✶✳ ❚❡st❡s Prát✐❝♦s ♣❛r❛ ❆✈❛❧✐❛çã♦ ❞❡ ❉❡s❡♠♣❡♥❤♦ ✻
❋✐❣✉r❛ ✷✳✷✿ ■❧✉str❛çã♦ ❞♦ t❡st❡ ❞❡ ♣❛ss❡ ❞❡ ▼♦r ❡ ❈❤r✐st✐❛♥✳
❞♦s ❝♦♥❡s é ❡①♣♦st❛ ♥❛ ❋✐❣✉r❛ ✷✳✸✳
❋✐❣✉r❛ ✷✳✸✿ ■❧✉str❛çã♦ ❞♦ t❡st❡ ❞❡ ❞r✐❜❧❡ ❞❡ ✺ ❝♦♥❡s✳
❆s ♦❜s❡r✈❛çõ❡s ❞❡st❡ t❡st❡ ❢♦r❛♠ ✐♥❞❡①❛❞❛s à ✈❛r✐á✈❡❧ ❉❘■❇▲❊✳
✷✳✶✳✸ ❚❡st❡ ❞❡ ❈❤✉t❡ ❛♣ós P❛ss❡
❖ t❡st❡ ❞❡ ❝❤✉t❡ ❛♣ós ♣❛ss❡ ❬✷✾❪ ❝♦♥s✐st❡ ❡♠ ✉♠ ❣♦❧ r❡❣✉❧❛♠❡♥t❛r ❞❡ ❢✉t❡❜♦❧ ✭✼✱✸✷ ♠❡tr♦s ① ✷✱✹ ♠❡tr♦s✮ ❞✐✈✐❞✐❞♦ ❡♠ ár❡❛s ❞❡ ♣♦♥t✉❛çã♦ ♣♦r ❞✉❛s ❝♦r❞❛s ✜①❛❞❛s ♥♦ tr❛✈❡ssã♦
✷✳✶✳ ❚❡st❡s Prát✐❝♦s ♣❛r❛ ❆✈❛❧✐❛çã♦ ❞❡ ❉❡s❡♠♣❡♥❤♦ ✼
❛ ✶✱✷ ♠❡tr♦s ❞❡ ❝❛❞❛ tr❛✈❡✳ ❈❛❞❛ ❧❛❞♦ ❝♦♥té♠ ❞♦✐s ❜❛♠❜♦❧ês ❞❡ ✶✱✷ ♠❡tr♦s ❞❡ ❞✐â♠❡tr♦✱ ❞✐s♣♦st♦s ❞❡ ❢♦r♠❛ q✉❡ ✉♠ ✜q✉❡ ❡♠ ❝✐♠❛ ❡ ♦ ♦✉tr♦ ❡♠❜❛✐①♦✳ ❆ss✐♠✱ t❡♠♦s q✉❛tr♦ ③♦♥❛s ❞❡ ♣♦♥t✉❛çã♦✱ ❢♦r♠❛❞❛s ♣♦r q✉❛tr♦ ❝✐r❝✉♥❢❡rê♥❝✐❛s ❞❡ ✶✱✷ ♠❡tr♦s ❞❡ ❞✐â♠❡tr♦✳
❖ ♦❜❥❡t✐✈♦ é ❝❤✉t❛r ❛ ❜♦❧❛ ❡♠ ♠♦✈✐♠❡♥t♦✱ q✉❡ é ♣❛ss❛❞❛ ♣♦r ✉♠ ✐♥str✉t♦r ❛ ❝❡r❝❛ ❞❡ ✶✶ ♠❡tr♦s ❞❡ ❞✐stâ♥❝✐❛ ❞♦ ❛❧✈♦✱ ❛❝❡rt❛♥❞♦ ❛s ③♦♥❛s ❞❡ ♣♦♥t✉❛çã♦ ❞❡ ♠♦❞♦ q✉❡ ♦ ❥♦❣❛❞♦r ♦❜t❡♥❤❛ ✻ ♣♦♥t♦s ♣❛r❛ ❝❛❞❛ ❛❝❡rt♦ ♥❛s ③♦♥❛s s✉♣❡r✐♦r❡s✱ ✶ ♣♦♥t♦ ♣❛r❛ ❝❛❞❛ ❛❝❡rt♦ ♥❛s ③♦♥❛s ✐♥❢❡r✐♦r❡s ❡ ♥❡♥❤✉♠ ♣♦♥t♦ ♣❛r❛ q✉❛❧q✉❡r ♦✉tr♦ ❝❛s♦✳ ❖ ❛t❧❡t❛ t❡♠ ❞✐r❡✐t♦ ❛ ✺ t❡♥t❛t✐✈❛s✱ s❡♥❞♦ q✉❡ s❡ ❢♦r ♣r❡❝✐s♦✱ ✉♠❛ t❡♥t❛t✐✈❛ ♣♦❞❡ s❡r ❢❡✐t❛ ♥♦✈❛♠❡♥t❡✳ ❆❧é♠ ❞✐ss♦✱ ♦ ❥♦❣❛❞♦r ♣♦❞❡ t❡r ✉♠❛ ❝❤❛♥❝❡ ♣❛r❛ tr❡✐♥♦ ❛♥t❡s ❞♦ ✐♥í❝✐♦ ❞❛ ❛✈❛❧✐❛çã♦✳ ❆♣❡♥❛s ❛❝❡rt❛r ♦ ❜❛♠❜♦❧ê ❥á é ✈✐st♦ ❝♦♠♦ ❛❝❡rt♦✱ ♦✉ s❡❥❛✱ ❛ ❜♦❧❛ ♥ã♦ ♣r❡❝✐s❛ ♥❡❝❡ss❛r✐❛♠❡♥t❡ ♣❛ss❛r ♣♦r ❞❡♥tr♦ ❞❛s ❝✐r❝✉♥❢❡rê♥❝✐❛s✳ ❆ ❞✐s♣♦s✐çã♦ ❞♦s ❜❛♠❜♦❧ês é ❡①♣♦st❛ ♥❛ ❋✐❣✉r❛ ✷✳✹✳
❋✐❣✉r❛ ✷✳✹✿ ■❧✉str❛çã♦ ❞♦ t❡st❡ ❞❡ ❝❤✉t❡ ❛♣ós ♣❛ss❡✳
❆s ♦❜s❡r✈❛çõ❡s ❞❡st❡ t❡st❡ ❢♦r❛♠ ✐♥❞❡①❛❞❛s à ✈❛r✐á✈❡❧ ❈❍❯❚❊✳
✷✳✶✳✹ ❚❡st❡ ❞❡ ✶✵✵✵ ▼❡tr♦s ❡♠ P✐st❛
❊ss❡ t❡st❡ é ✉t✐❧✐③❛❞♦ ♣❛r❛ ♠❡❞✐r ❛ ♣♦tê♥❝✐❛ ❛❡ró❜✐❝❛ ❞♦ ❛t❧❡t❛✱ ✉♠❛ ❞❛s ❝❛♣❛❝✐❞❛❞❡s ❢ís✐❝❛s q✉❡ ♠❛✐s ✐♥✢✉❡♥❝✐❛♠ ♥♦ ❞❡s❡♠♣❡♥❤♦ ❞♦s ❥♦❣❛❞♦r❡s✱ ♣♦✐s ❡♠ ✉♠❛ ♣❛rt✐❞❛ ❞❡ ❢✉t❡❜♦❧✱ ♦s ❥♦❣❛❞♦r❡s✱ ❝♦♠ ❡①❝❡çã♦ ❞♦ ❣♦❧❡✐r♦✱ ♣❡r❝♦rr❡♠ ❝❡r❝❛ ❞❡ ✶✵ q✉✐❧ô♠❡tr♦s ❝♦♠ ✈❡❧♦❝✐❞❛❞❡s
✷✳✶✳ ❚❡st❡s Prát✐❝♦s ♣❛r❛ ❆✈❛❧✐❛çã♦ ❞❡ ❉❡s❡♠♣❡♥❤♦ ✽
❜❛✐①❛s ❡ ♠♦❞❡r❛❞❛s ❡♠ ♠❛✐s ❞❡ ✸✵✪ ❞♦ t❡♠♣♦ ❞❡ ❥♦❣♦ ❬✸✵❪✳
❖ t❡st❡ ❞❡ ✶✵✵✵ ♠❡tr♦s ❡♠ ♣✐st❛ é ✐♥❞✐r❡t♦ ✭❣❡r❛❧♠❡♥t❡ ❞❡ ❝❛♠♣♦✮✱ ♦✉ s❡❥❛✱ ❡❧❡ ❢♦r✲ ♥❡❝❡ ❛♣❡♥❛s ✉♠❛ ❡st✐♠❛t✐✈❛ ❞♦ ✈♦❧✉♠❡ ♠á①✐♠♦ ❞❡ ♦①✐❣ê♥✐♦✱ ❞✐❢❡r❡♥t❡♠❡♥t❡ ❞❡ ✉♠ t❡st❡ ❧❛❜♦r❛t♦r✐❛❧ ✭❣♦❧❞ st❛♥❞❛r❞ ✲ ♣❛❞rã♦ ♦✉r♦✮✱ q✉❡ ❡✈✐❞❡♥t❡♠❡♥t❡ ♣♦ss✉✐ ♠❛✐s r❡❝✉rs♦s q✉❡ ♦ ❞❡ ❝❛♠♣♦✳ ❊♥tr❡t❛♥t♦✱ ❛ ✈❛❧✐❞❛çã♦ ❞♦s ✶✵✵✵ ♠❡tr♦s ❡♠ ♣✐st❛ ❢♦✐ ❝♦♠♣r♦✈❛❞❛ ♣♦r ❬✸✶❪✳
❆ ❛♣❧✐❝❛çã♦ ❞♦ t❡st❡ ❞❡ ✶✵✵✵ ♠❡tr♦s é s✐♠♣❧❡s✿ ♦s ❛t❧❡t❛s ❞❡✈❡♠ ❝♦rr❡r ✉♠❛ ❞✐stâ♥❝✐❛ ❞❡ ✶✵✵✵ ♠❡tr♦s ♥♦ ♠❡♥♦r t❡♠♣♦ ♣♦ssí✈❡❧✱ ♣r❡❢❡r✐✈❡❧♠❡♥t❡ ❡♠ ✉♠❛ ♣✐st❛ ❞❡ ❛t❧❡t✐s♠♦ ♦✉ ♥✉♠ ❝❛♠♣♦ ❞❡ ❢✉t❡❜♦❧✱ ♣❡r♠✐t✐♥❞♦ ♦ r❡❣✐str♦ ❞♦ t❡♠♣♦ ✭❡♠ s❡❣✉♥❞♦s✮ ❣❛st♦ ♣❡❧♦ ❛❧✉♥♦ ♣❛r❛ ❛ ❡①❡❝✉çã♦ ❞❛ t❛r❡❢❛✳ ❆ss✐♠✱ ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞♦ ✈❛❧♦r ❞♦ ❝♦♥s✉♠♦ ♠á①✐♠♦ ❞❡ ♦①✐❣ê♥✐♦ ✭❱❖✷▼❆❳✮✱ é ✉t✐❧✐③❛❞❛ ❛ s❡❣✉✐♥t❡ ❢ór♠✉❧❛✿
X = 652,17−Y
6,762 ✭✷✳✶✮
❡♠ q✉❡Xr❡♣r❡s❡♥t❛ ♦ ❝♦♥s✉♠♦ ♠á①✐♠♦ ❞❡ ♦①✐❣ê♥✐♦ ✭♠❧✴❦❣✴♠✐♥✮✱Y é ♦ t❡♠♣♦ ❞❡ ❝♦rr✐❞❛
✭❡♠ s❡❣✉♥❞♦s✮ ♥♦s ✶✵✵✵ ♠❡tr♦s ❡ ✻✺✷✱✶✼ ❡ ✻✱✼✻✷ sã♦ ❝♦♥st❛♥t❡s✳
P❛r❛ ❛ ♠❡❞✐çã♦ ❞♦ t❡♠♣♦ q✉❡ é ✉t✐❧✐③❛❞♦ ♥❛ ❡①♣r❡ssã♦ ✭✷✳✶✮ sã♦ ♥❡❝❡ssár✐♦s ❝r♦♥ô♠❡✲ tr♦s ♦✉ ❝â♠❡r❛s q✉❡ ❝♦♥s✐❣❛♠ ❝❛❧❝✉❧❛r ❞❡ ❢♦r♠❛ ♣r❡❝✐s❛ ♦ t❡♠♣♦ ❞❡ ❝❛❞❛ ✐♥❞✐✈í❞✉♦✳ ❆❧é♠ ❞✐ss♦✱ t❛❧ ❛t✐✈✐❞❛❞❡ ❞❡✈❡ s❡r ❛♣❧✐❝❛❞❛ ❡♠ ❤♦rár✐♦s ❛❞❡q✉❛❞♦s s❡♠ ❡①♣♦r ♦s ♣❛rt✐❝✐♣❛♥t❡s ❛ ♣❡rí♦❞♦s ❞❡ ❛❧t❛ t❡♠♣❡r❛t✉r❛✱ ♣♦ss✐❜✐❧✐t❛♥❞♦ ❛ ♣r❡✈❡♥çã♦ ❞❡ ♣r♦❜❧❡♠❛s ❢ís✐❝♦s ❞❡✈✐❞♦ à ✐♥t❡♥s✐❞❛❞❡ ❞❛ ❛t✐✈✐❞❛❞❡✳
◆❛ ❋✐❣✉r❛ ✷✳✺ t❡♠♦s ❝♦♠♦ ❡①❡♠♣❧♦ ✉♠ ❝❛♠♣♦ ❞❡ ❢✉t❡❜♦❧ ❞❡ ✶✵✵ ♠❡tr♦s ① ✻✺ ♠❡tr♦s✱ ♥❛ q✉❛❧ s❡r✐❛♠ ♥❡❝❡ssár✐❛s ❛♣r♦①✐♠❛❞❛♠❡♥t❡ três ✈♦❧t❛s ❝♦♠♣❧❡t❛s ♣❛r❛ ❛ ❡①❡❝✉çã♦ ❞♦s ✶✵✵✵ ♠❡tr♦s✳
❆s ♦❜s❡r✈❛çõ❡s ❞❡st❡ t❡st❡ ❢♦r❛♠ ✐♥❞❡①❛❞❛s à ✈❛r✐á✈❡❧ ❱❖✷▼❆❳✳
✷✳✶✳✺ ❚❡st❡ ❞❡ ❱❡❧♦❝✐❞❛❞❡ ❈í❝❧✐❝❛ ❞❡ ✷✵ ▼❡tr♦s
◆❡ss❡ t❡st❡ ♦ ❛❧✉♥♦ ❞❡✈❡ ♣❛rt✐r ❞❛ ❧✐♥❤❛ ❞❡ s❛í❞❛✱ ❛♣ós ♦✉✈✐r ♦ ❛♣✐t♦✱ ❡ ♣❡r❝♦rr❡r ♦s ✷✵ ♠❡tr♦s ♥♦ ♠❡♥♦r t❡♠♣♦ ♣♦ssí✈❡❧✱ r❡❣✐str❛♥❞♦✲s❡ ♦ t❡♠♣♦ ❣❛st♦ ♣❛r❛ ❝♦♠♣❧❡t❛r ♦ ♣❡r❝✉rs♦✳ ❊♠ ♦✉tr❛s ♣❛❧❛✈r❛s✱ ♦ t❡st❡ ❞❡ ✈❡❧♦❝✐❞❛❞❡ ❝í❝❧✐❝❛ ❞❡ ✷✵ ♠❡tr♦s ❝♦♥s✐st❡ ♥✉♠❛ ❝♦rr✐❞❛ ❝í❝❧✐❝❛✱ ♥❛ q✉❛❧ ♦ ❝♦♠♣r✐♠❡♥t♦ ❞❛ ❝✐r❝✉♥❢❡rê♥❝✐❛ ❞❡✈❡ t❡r ❛♣r♦①✐♠❛❞❛♠❡♥t❡ ✻✱✸✼ ♠❡tr♦s ❞❡ ❞✐â♠❡tr♦ ✭♣♦ss✐❜✐❧✐t❛♥❞♦ q✉❡ ❛ ❝✐r❝✉♥❢❡rê♥❝✐❛ t❡♥❤❛ s❡✉s ✷✵ ♠❡tr♦s✮✳
❖ ♦❜❥❡t✐✈♦ é r❡❣✐str❛r ♦ t❡♠♣♦ q✉❡ ♦ ✐♥❞✐✈í❞✉♦ ❣❛st❛ ♣❛r❛ ❝♦♠♣❧❡t❛r ♦ t❡st❡✳ ❆ ❞✐s♣♦s✐çã♦ ❞♦ t❡st❡ é ❡①✐❜✐❞❛ ♥❛ ❋✐❣✉r❛ ✷✳✻ ❡ ❛s ♦❜s❡r✈❛çõ❡s ❞❡st❡ t❡st❡ ❢♦r❛♠ ✐♥❞❡①❛❞❛s
✷✳✶✳ ❚❡st❡s Prát✐❝♦s ♣❛r❛ ❆✈❛❧✐❛çã♦ ❞❡ ❉❡s❡♠♣❡♥❤♦ ✾
❋✐❣✉r❛ ✷✳✺✿ ■❧✉str❛çã♦ ❞♦ t❡st❡ ❞❡ ✶✵✵✵ ♠❡tr♦s ❡♠ ♣✐st❛✳
à ✈❛r✐á✈❡❧ ❈▲✷✵✳
❋✐❣✉r❛ ✷✳✻✿ ■❧✉str❛çã♦ ❞♦ t❡st❡ ❞❡ ✈❡❧♦❝✐❞❛❞❡ ❝í❝❧✐❝❛ ❞❡ ✷✵ ♠❡tr♦s✳
✷✳✶✳✻ ❚❡st❡ ❞❡ P♦tê♥❝✐❛ ❆♥❛❡ró❜✐❝❛ ✭❘✳❆✳❙✳❚✳✮
❊ss❡ t❡st❡ ❬✸✷❪ é ✉t✐❧✐③❛❞♦ ♣❛r❛ ♠❡❞✐r ❛ ♣♦tê♥❝✐❛ ❛♥❛❡ró❜✐❝❛ ❞♦ ❛t❧❡t❛✱ ♦✉tr❛ ❣r❛♥❞❡③❛ ❞❡ ❡①tr❡♠❛ ✐♠♣♦rtâ♥❝✐❛✱ ✉♠❛ ✈❡③ q✉❡ ❡❧❛ ❡stá ♣r❡s❡♥t❡ ❡♠ ❞✐✈❡rs❛s s✐t✉❛çõ❡s ❡♠ ✉♠❛ ♣❛rt✐❞❛ ❞❡ ❢✉t❡❜♦❧ ❝♦♠♦✱ ♣♦r ❡①❡♠♣❧♦✱ q✉❛♥❞♦ ✉♠ ③❛❣✉❡✐r♦ ❛❧t♦✱ ♠❛s ❧❡♥t♦✱ ❞❡✈❡ ❛❝♦♠♣❛♥❤❛r
✷✳✷✳ ❙✉♠❛r✐③❛çã♦ ❞❡ ❉❛❞♦s ✶✵
✐♥❝❛♥s❛✈❡❧♠❡♥t❡ ✉♠ ❛t❛❝❛♥t❡ ❜❛st❛♥t❡ rá♣✐❞♦ ❡ ❞r✐❜❧❛❞♦r ♥✉♠ ❝♦♥tr❛✲❛t❛q✉❡ ❞✉r❛♥t❡ ❛ ♣❛rt❡ ✜♥❛❧ ❞♦ ❥♦❣♦✳ ➱ ♣♦ssí✈❡❧ q✉❡ t❛♥t♦ ♦ ③❛❣✉❡✐r♦ q✉❛♥t♦ ♦ ❛t❛❝❛♥t❡ ❥á t❡♥❤❛♠ ❛t✐♥❣✐❞♦ ♦ ❧✐♠✐t❡ ❞❡ ❝♦♥s✉♠♦ ❞❡ ♦①✐❣ê♥✐♦ ♥❛ ♣r♦❞✉çã♦ ❡♥❡r❣ét✐❝❛✱ ♣r♦♣♦r❝✐♦♥❛♥❞♦ ✉♠ ❡st❛❞♦ ♥♦ q✉❛❧ ❛ r❡s✐stê♥❝✐❛ é ✐♥❞✐s♣❡♥sá✈❡❧✳ ➱ ❛♣❡♥❛s ✉♠❛ ❝✐r❝✉♥stâ♥❝✐❛ q✉❡ ♥ã♦ só é ❜❛st❛♥t❡ r❡❛❧✱ ♠❛s t❛♠❜é♠ r❡♣r❡s❡♥t❛ ❝❛t❡❣♦r✐❝❛♠❡♥t❡ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ ✐♥❝❧✉✐r t❛❧ ✈❛r✐á✈❡❧ ❡♥tr❡ ❛q✉❡❧❛s q✉❡ sã♦ ♣r♦✈❛✈❡❧♠❡♥t❡ ❛s ♠❛✐s ✐♥✢✉❡♥t❡s ♥♦ ♠❡✐♦ ❢✉t❡❜♦❧íst✐❝♦✳ ❆ ❞✐s♣♦s✐çã♦ ❞♦ t❡st❡ é ❡①✐❜✐❞❛ ♥❛ ❋✐❣✉r❛ ✷✳✼✳
❋✐❣✉r❛ ✷✳✼✿ ■❧✉str❛çã♦ ❞♦ t❡st❡ ❞❡ ♣♦tê♥❝✐❛ ❛♥❛❡ró❜✐❝❛✳
◆❡st❡ t❡st❡✱ ♦ ❛❧✉♥♦ ❞❡✈❡ ❝♦rr❡r s❡✐s ✈❡③❡s ❛ ❞✐stâ♥❝✐❛ ❞❡ ✸✺ ♠❡tr♦s✱ ♥❛ ♠❛✐♦r ✈❡❧♦❝✐❞❛❞❡ ♣♦ssí✈❡❧✱ ❝♦♠ ✉♠ ✐♥t❡r✈❛❧♦ ❞❡ ✶✵ s❡❣✉♥❞♦s ❡♥tr❡ ❝❛❞❛ ❞❡s❧♦❝❛♠❡♥t♦✳ ❆ss✐♠✱ ♣♦❞❡✲s❡
❝❛❧❝✉❧❛r ❛ ♣♦tê♥❝✐❛ ♥♦ t✐r♦ ✐✿ Pi = P❡s♦×(352/(ti)3)✱ ❡♠ q✉❡ ti é ♦ t❡♠♣♦ ♥♦ t✐r♦ ✐✳
❆ P♦tê♥❝✐❛ ▼é❞✐❛ ✭P▼✮ ❡ ❛ P♦tê♥❝✐❛ ❘❡❧❛t✐✈❛ ✭P❘✮ sã♦ ❞❛❞❛s ♣♦r✿ P▼ =
P6
j=1Pi
6 ❡
P❘= P♦t❡♥❝✐❛ ▼é❞✐❛P❡s♦ ✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳
✷✳✷ ❙✉♠❛r✐③❛çã♦ ❞❡ ❉❛❞♦s
◆❡st❛ s❡çã♦ sã♦ ❡①✐❜✐❞❛s ❛s ❢❡rr❛♠❡♥t❛s ❡st❛tíst✐❝❛s ✉t✐❧✐③❛❞❛s ♣❛r❛ ❛ ❛♥á❧✐s❡ ❞❛s ✐♥✲ ❢♦r♠❛çõ❡s r❡❧❛t✐✈❛s ❛♦s t❡st❡s ♣rát✐❝♦s ❞❡ ❞❡s❡♠♣❡♥❤♦✳
❯♠ ❝♦♥❥✉♥t♦ ❞❡ té❝♥✐❝❛s ❡st❛tíst✐❝❛s ✉♥✐ ❡ ♠✉❧t✐✈❛r✐❛❞❛s ❢♦✐ ❛♣❧✐❝❛❞♦ ❝♦♠ ♦ ✐♥t✉✐t♦ ❞❡ ❝r✐❛r♠♦s ✐♥❞✐❝❛❞♦r❡s ❝❛♣❛③❡s ❞❡ ❛✈❛❧✐❛r ❡ ❝♦♠♣❛r❛r ❛s ❤❛❜✐❧✐❞❛❞❡s ❞♦s ✐♥❞✐✈í❞✉♦s✳
✷✳✷✳ ❙✉♠❛r✐③❛çã♦ ❞❡ ❉❛❞♦s ✶✶
✷✳✷✳✶ ▼ét♦❞♦ ❩
❯♠❛ ♣r♦♣♦st❛ ♣❛r❛ ✐❞❡♥t✐✜❝❛r ❛t❧❡t❛s q✉❡ s❡ ❞❡st❛❝❛♠ ❡♠ ❞❡t❡r♠✐♥❛❞❛ ♣rát✐❝❛ ❡s♣♦r✲ t✐✈❛✱ ❞❡♥♦♠✐♥❛❞❛ ✏❡str❛té❣✐❛ ❩✲❈❊▲❆❋■❙❈❙✑✱ ❢♦✐ ❛♣r❡s❡♥t❛❞❛ ♣♦r ❬✶✸❪✳ ❊ss❡ ✐♥str✉♠❡♥t♦ ♣❡r♠✐t❡ ❞✐❛❣♥♦st✐❝❛r ♦ ♣❡r✜❧ ❞❡ ❛♣t✐❞ã♦ ❢ís✐❝❛ ♦✉ té❝♥✐❝❛ ❡ ❞❡t❡r♠✐♥❛r✱ ❡♠ t❡r♠♦s ♣❡r❝❡♥✲ t✉❛✐s✱ ♦ q✉❛♥t♦ ✉♠ ❞❡t❡r♠✐♥❛❞♦ ✐♥❞✐✈í❞✉♦ s❡ ❛♣r♦①✐♠❛ ♦✉ s❡ ❛❢❛st❛ ❞❛ ♠é❞✐❛ ♣♦♣✉❧❛❝✐♦♥❛❧✳ ❖ ✏❩✑ q✉❡ ❛♣❛r❡❝❡ ♥♦ tít✉❧♦ ✈❡♠ ❞❛ ♣❛❞r♦♥✐③❛çã♦ ❞❛ ❞✐str✐❜✉✐çã♦ ◆♦r♠❛❧✿
Z = x−µ
σ , ✭✷✳✷✮
❡♠ q✉❡x=✈❛❧♦r ♦❜s❡r✈❛❞♦ ♣❛r❛ ✉♠ ✐♥❞✐✈í❞✉♦ ❡s♣❡❝í✜❝♦✱ µ=♠é❞✐❛ ♣♦♣✉❧❛❝✐♦♥❛❧ ❡ σ=
❞❡s✈✐♦ ♣❛❞rã♦ ♣♦♣✉❧❛❝✐♦♥❛❧✳
P♦r ❡①❡♠♣❧♦✱ s❡ ❩ ❢♦r ✐❣✉❛❧ ❛ ✶ ✐♥❞✐❝❛ q✉❡ t❛❧ ✐♥❞✐✈í❞✉♦ ❡st❛rá ✉♠ ❞❡s✈✐♦ ♣❛❞rã♦ ❛❝✐♠❛ ❞❛ ♠é❞✐❛ ♣♦♣✉❧❛❝✐♦♥❛❧ q✉❡✱ ❡♠ t❡r♠♦s ♣❡r❝❡♥t✉❛✐s✱ s✐❣♥✐✜❝❛r✐❛ t❡r ✉♠ ❞❡s❡♠♣❡♥❤♦ ♠❡❧❤♦r q✉❡ ✽✹✱✶✸✪ ❞❛ ♣♦♣✉❧❛çã♦ ❞❡ s✉❛ ❝❛r❛❝t❡ríst✐❝❛ ❡♠ ❞❡t❡r♠✐♥❛❞❛ ✈❛r✐á✈❡❧✳ ❆ ❋✐❣✉r❛ ✷✳✽ ❡①✐❜❡ ❛ ♣♦s✐çã♦ ❞❡ss❡ ✐♥❞✐✈í❞✉♦ ♥♦ ❣rá✜❝♦ ❞❛ ❞❡♥s✐❞❛❞❡ ❞❛ ❞✐str✐❜✉✐çã♦ ◆♦r♠❛❧✳
❋✐❣✉r❛ ✷✳✽✿ P♦s✐çã♦ ❞❡ ✉♠ ✐♥❞✐✈í❞✉♦ ❝♦♠ Z = 1 ❡♠ r❡❧❛çã♦ ❛♦s ❞❡♠❛✐s✳
❊st❛ ❡str❛té❣✐❛ é ✉♠ ♠ét♦❞♦ ✐♥t❡r❡ss❛♥t❡✱ ♣♦✐s ♣♦❞❡ s❡r ❝♦♥s✐❞❡r❛❞❛ ❝♦♠♦ ✉♠ ✐♥str✉✲ ♠❡♥t♦ ❞❡ ❢á❝✐❧ ❛♣❧✐❝❛çã♦ ❡ ❜❛✐①♦ ❝✉st♦✱ ♣♦❞❡♥❞♦ s❡r ✉t✐❧✐③❛❞❛ ❡♠ ❧❛r❣❛ ❡s❝❛❧❛✳ P♦r ♦✉tr♦ ❧❛❞♦✱ s✉❛ ❡✜❝á❝✐❛ ♣♦❞❡ s❡r q✉❡st✐♦♥❛❞❛✱ ♣♦✐s s❡ tr❛t❛ ❞❡ ✉♠❛ ❛♥á❧✐s❡ ✉♥✐✈❛r✐❛❞❛ ✭q✉❡ ❝♦♥s✐✲ ❞❡r❛ ❛♣❡♥❛s ❛ ✐♥❢♦r♠❛çã♦ ❞❡ ✉♠❛ ú♥✐❝❛ ✈❛r✐á✈❡❧✮✳ ❉❡ss❛ ❢♦r♠❛✱ ♥ã♦ ❝♦♥s✐❞❡r❛ ❛s r❡❧❛çõ❡s ❡①✐st❡♥t❡s ❡♥tr❡ ❛s ✈❛r✐á✈❡✐s ❡ ♥❡♠ ❧❡✈❛ ❡♠ ❝♦♥s✐❞❡r❛çã♦ ❛s ❞✐❢❡r❡♥ç❛s ❞❛s ✐♠♣♦rtâ♥❝✐❛s r❡❧❛t✐✈❛s ❞❡ss❛s ✈❛r✐á✈❡✐s ❡♠ ❝❛❞❛ ❝❛t❡❣♦r✐❛✳ ❊ss❡s ❞♦✐s ❡❧❡♠❡♥t♦s sã♦ ❢✉♥❞❛♠❡♥t❛✐s ♥❛ ❛♥á❧✐s❡ ❞❡ ❞❡s❡♠♣❡♥❤♦ ❞♦ ❛t❧❡t❛✳
❆ss✐♠✱ ❛ ✉t✐❧✐③❛çã♦ ❞❡ ❡s❝♦r❡s ♣❛❞r♦♥✐③❛❞♦s ♥♦s ♣r♦❝❡ss♦s ❞❡ ♣r♦♠♦çã♦ ❞❡ t❛❧❡♥t♦s ❡s♣♦rt✐✈♦s ♣❛r❡❝❡ s❡r ✉♠ ♣❛ss♦ ✐♠♣♦rt❛♥t❡ ❢r❡♥t❡ à s✉❜❥❡t✐✈✐❞❛❞❡ ❛✐♥❞❛ ♣r❡s❡♥t❡ ♥❡ss❡s
✷✳✷✳ ❙✉♠❛r✐③❛çã♦ ❞❡ ❉❛❞♦s ✶✷
♣r♦❝❡ss♦s✳ ❈♦♥t✉❞♦✱ ❛ ❜✉s❝❛ ♣♦r ❛♥á❧✐s❡s ♠❛✐s s♦✜st✐❝❛❞❛s s❡ ❢❛③ ❞❡s❡❥á✈❡❧ ♣❛r❛ q✉❡ s❡ ♣♦ss❛ ❝❛♠✐♥❤❛r ❡♠ ❞✐r❡çã♦ ❛ ✉♠❛ té❝♥✐❝❛ q✉❡ ♣❡r♠✐t❛ ❛❜♦r❞❛r ❛s r❡❧❛çõ❡s ❡♥tr❡ ❛s ✈❛r✐á✈❡✐s ❡ ❛ ✐♠♣♦rtâ♥❝✐❛ ❞❛s ♠❡s♠❛s ♥♦s ❞✐❢❡r❡♥t❡s ♣❡rí♦❞♦s q✉❡ ❡♥✈♦❧✈❡♠ ♦ tr❡✐♥❛♠❡♥t♦ ❡♠ ❧♦♥❣♦ ♣r❛③♦✳
✷✳✷✳✷ ❆♥á❧✐s❡ ❞❡ ❈♦♠♣♦♥❡♥t❡s Pr✐♥❝✐♣❛✐s
❆ ❆♥á❧✐s❡ ❞❡ ❈♦♠♣♦♥❡♥t❡s Pr✐♥❝✐♣❛✐s ✭❆✳❈✳P✳✮ é ✉♠❛ té❝♥✐❝❛ ❞❡ ❛♥á❧✐s❡ ♠✉❧t✐✈❛r✐❛❞❛ q✉❡ ❝♦♥s✐st❡ ❡♠ ❡st✉❞❛r ❛ ❡str✉t✉r❛ ❞❡ ✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛ ❞❡ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ✈❛r✐á✈❡✐s ♦❜s❡r✈❛❞❛s ❡♠ ✉♠ ❞❡t❡r♠✐♥❛❞♦ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s✳ ❖ ❡st✉❞♦ ❞❡st❛ ✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛ ❝♦♥s✐❞❡r❛ ❛ ❛♥á❧✐s❡ ❞❛ ❡str✉t✉r❛ ❞❡ ✈❛r✐â♥❝✐❛s ❡ ❝♦✈❛r✐â♥❝✐❛s ❞❛s ✈❛r✐á✈❡✐s✱ ❜✉s❝❛♥❞♦ ❛ ♦❜t❡♥çã♦ ❞❡ ❝♦♠❜✐♥❛çõ❡s ❧✐♥❡❛r❡s q✉❡ r❡t❡♥❤❛♠ ♦ ♠á①✐♠♦ ♣♦ssí✈❡❧ ❞❡ ✐♥❢♦r♠❛çã♦ ❝♦♥t✐❞❛ ♥❛s ✈❛r✐á✈❡✐s ♦r✐❣✐♥❛✐s✳ ❊ss❛s ❝♦♠❜✐♥❛çõ❡s sã♦ ♦s ❝❤❛♠❛❞♦s ❝♦♠♣♦♥❡♥t❡s ♣r✐♥❝✐♣❛✐s ❡ ♣♦r ♠❡✐♦ ❞❡❧❡s ♣♦❞❡♠♦s r❡❞✉③✐r ❛ ❞✐♠❡♥s✐♦♥❛❧✐❞❛❞❡ ❞♦ ♣r♦❜❧❡♠❛ ❡♠ ❡st✉❞♦✱ ❢❛❝✐❧✐t❛♥❞♦ ❛ ❛♥á❧✐s❡ ❡ ✐♥t❡r♣r❡t❛çã♦ ❞❛s r❡❧❛çõ❡s ❡♥tr❡ ❛s ✈❛r✐á✈❡✐s ❡st✉❞❛❞❛s✳
❙❡♥❞♦Σ❛ ♠❛tr✐③ ❞❡ ❝♦✈❛r✐â♥❝✐❛s ❛ss♦❝✐❛❞❛ ❛♦ ✈❡t♦r ❛❧❡❛tór✐♦ ❳′ = [X1, X2, . . . , Xp]❡
(λi,❡i)♦s ♣❛r❡s ❞❡ ❛✉t♦✈❛❧♦r✲❛✉t♦✈❡t♦r ❞❡Σ♣❛r❛ i= 1,2, . . . , p✱ ❡♠ q✉❡ λ1 ≥λ2 ≥. . .≥
λp ≥0✱ ♦ ✐✲és✐♠♦ ❝♦♠♣♦♥❡♥t❡ ♣r✐♥❝✐♣❛❧ é ❞❛❞♦ ♣♦r✿
Yi =❡
′
i❳ =ei1X1+ei2X2+· · ·+eipXp, i= 1,2, . . . , p. ✭✷✳✸✮
❙✉❛s ♣r✐♥❝✐♣❛✐s ❝❛r❛❝t❡ríst✐❝❛s sã♦✿ V ar(Yi) = ❡
′
iΣ❡i ❡ Cov(Yi, Yk) = ❡
′
iΣ❡k = 0✱
♣❛r❛ i 6= k ❡ ❡i = (ei1. . . , eip)✱ ❡ P p
i=1V ar(Yi) = λ1+λ2+. . .+λp = P p
i=1V ar(Xi) =
σ11+σ22+. . .+σpp✳
❆❧é♠ ❞✐ss♦✱ ♣♦❞❡♠♦s ♦❜t❡r ♦s ❝♦❡✜❝✐❡♥t❡s ❞❡ ❝♦rr❡❧❛çã♦ ❡♥tr❡ ♦s ❝♦♠♣♦♥❡♥t❡sYi ❡ ❛s
✈❛r✐á✈❡✐s Xk ❞❛ s❡❣✉✐♥t❡ ♠❛♥❡✐r❛✿
ρXk,Yi =
eik √
λi
√σ
kk
, ♣❛r❛ i, k= 1,2, . . . , p.
❉❡ss❛ ❢♦r♠❛✱ ❛ ❆✳❈✳P✳ ✐❞❡♥t✐✜❝❛ ✉♠ ♥♦✈♦ ❝♦♥❥✉♥t♦ ❞❡ ❡✐①♦s ♦rt♦❣♦♥❛✐s✱ ❝✉❥♦s ♥♦✈♦s ❡✐①♦s sã♦ ♦s ❝♦♠♣♦♥❡♥t❡s ♣r✐♥❝✐♣❛✐s ❡ ♦s s❡✉s ✈❛❧♦r❡s sã♦ ♦s ❡s❝♦r❡s✳ ❈❛❞❛ ♥♦✈❛ ✈❛r✐á✲ ✈❡❧ é ✉♠❛ ❝♦♠❜✐♥❛çã♦ ❧✐♥❡❛r ❞❛s ✈❛r✐á✈❡✐s ♦r✐❣✐♥❛✐s✱ s❡♥❞♦ q✉❡ ❛ ♣r✐♠❡✐r❛ ♥♦✈❛ ✈❛r✐á✈❡❧
s❡♠♣r❡ ❡①♣❧✐❝❛rá ❛ ♠❛✐♦r ♣❛rt❡ ❞❛ ✈❛r✐â♥❝✐❛ ❞♦s ❞❛❞♦s ❡ ❛s p ♥♦✈❛s ✈❛r✐á✈❡✐s s❡rã♦ ♥ã♦
❝♦rr❡❧❛❝✐♦♥❛❞❛s✳
✷✳✷✳ ❙✉♠❛r✐③❛çã♦ ❞❡ ❉❛❞♦s ✶✸
❊st❛ ♠❡t♦❞♦❧♦❣✐❛ é ❢r❡q✉❡♥t❡♠❡♥t❡ ✉t✐❧✐③❛❞❛✱ ✉♠❛ ✈❡③ q✉❡ é ✉♠ ♣❛ss♦ ✐♥t❡r♠❡❞✐á✲ r✐♦ ❡♠ ♠✉✐t❛s ✐♥✈❡st✐❣❛çõ❡s ❝♦♠♦✱ ♣♦r ❡①❡♠♣❧♦✱ ❡♠ r❡❣r❡ssã♦ ♠ú❧t✐♣❧❛✱ ❡♠ ❛♥á❧✐s❡ ❞❡ ❛❣r✉♣❛♠❡♥t♦s✱ ❡t❝✳
❋✐❣✉r❛ ✷✳✾✿ ❖❜t❡♥çã♦ ❞♦s ✐♥❞✐❝❛❞♦r❡s ♣♦r ♠❡✐♦ ❞❛ ❆✳❈✳P✳
❆ ❋✐❣✉r❛ ✷✳✾ r❡♣r❡s❡♥t❛ ♦ ❡sq✉❡♠❛ ❞❛ ♦❜t❡♥çã♦ ❞♦ ✐♥❞✐❝❛❞♦r ♣♦r ♠❡✐♦ ❞❛ ❆✳❈✳P✳ ❖s ✐♥❞✐❝❛❞♦r❡s ❝r✐❛❞♦s ❢♦r❛♠ ❢♦r♠✉❧❛❞♦s ❛ ♣❛rt✐r ❞❛ s♦♠❛ ❞♦s ❡s❝♦r❡s ❢❛t♦r✐❛✐s ♣❛❞r♦♥✐③❛❞♦s✱ ♣♦♥❞❡r❛❞♦s ♣❡❧❛s r❡s♣❡❝t✐✈❛s ♣♦r❝❡♥t❛❣❡♥s ❞❡ ✈❛r✐❛❜✐❧✐❞❛❞❡ ❡①♣❧✐❝❛❞❛ ❞❡ ❝❛❞❛ ❝♦♠♣♦♥❡♥t❡✳ ❆ ❢ór♠✉❧❛ ♠❛t❡♠át✐❝❛ r❡s✉❧t❛♥t❡ ❞❡ss❡ ♣r♦❝❡ss♦ é ❞❛❞❛ ♣♦r✿
Im =
k
X
j=1
λj
tr(R)CPjm, ✭✷✳✹✮
❡♠ q✉❡ Im ❂ ✈❛❧♦r ❞♦ ✐♥❞✐❝❛❞♦r ❞♦ ♠✲és✐♠♦ ❥♦❣❛❞♦r✱ λj ❂ ❥ ✲és✐♠❛ r❛✐③ ❝❛r❛❝t❡ríst✐❝❛ ❞❛
♠❛tr✐③ ❞❡ ❝♦rr❡❧❛çã♦Rpxp ❞❛s ✈❛r✐á✈❡✐s ✉t✐❧✐③❛❞❛s✱ ❦ ❂ ♥ú♠❡r♦ ❞❡ ❝♦♠♣♦♥❡♥t❡s ♣r✐♥❝✐♣❛✐s
❡s❝♦❧❤✐❞❛s✱ CPjm❂ ❡s❝♦r❡ ❢❛t♦r✐❛❧ ❞♦ ♠✲és✐♠♦ ❥♦❣❛❞♦r✱ ♥❛ ❝♦♠♣♦♥❡♥t❡ ❥ ❡ tr ❂ tr❛ç♦ ❞❛
♠❛tr✐③ ❞❡ ❝♦rr❡❧❛çã♦Rpxp✳
❇✉s❝❛♥❞♦ ❢❛❝✐❧✐t❛r ❛ ❝♦♠♣❛r❛çã♦ ❞♦s ✐♥❞✐❝❛❞♦r❡s ❝r✐❛❞♦s✱ tr❛♥s❢♦r♠❛♠♦s ❛ ❜❛s❡ ❞♦s ♠❡s♠♦s✱ ❞❡ ♠♦❞♦ q✉❡ ♦s ♥♦✈♦s ✈❛❧♦r❡s s❡❥❛♠ ❛♣r❡s❡♥t❛❞♦s ❞❡♥tr♦ ❞♦ ✐♥t❡r✈❛❧♦ ❡♥tr❡ ✵ ❡ ✶✵✵✿
I∗
m =
(Im−Imin)
(Imax−Imin) ×
100, ✭✷✳✺✮
❡♠ q✉❡ ■∗
m❂ ✈❛❧♦r ❞♦ ✐♥❞✐❝❛❞♦r tr❛♥s❢♦r♠❛❞♦ ❞♦ ♠✲és✐♠♦ ❥♦❣❛❞♦r✱ ■m❂ ✈❛❧♦r ❞♦ ✐♥❞✐❝❛❞♦r
♦❜s❡r✈❛❞♦ ♥♦ ♠✲és✐♠♦ ❥♦❣❛❞♦r✱ ■max❂ ✐♥❞✐❝❛❞♦r ♠á①✐♠♦ ♦❜s❡r✈❛❞♦ ♥❛ ❛♠♦str❛ ❡ ■min❂
✐♥❞✐❝❛❞♦r ♠í♥✐♠♦ ♦❜s❡r✈❛❞♦ ♥❛ ❛♠♦str❛✳
❯t✐❧✐③❛♥❞♦ ❛ ❆✳❈✳P✳✱ ♦s s❡❣✉✐♥t❡s í♥❞✐❝❡s ❞❡ ❞❡s❡♠♣❡♥❤♦ ❢♦r❛♠ ❝r✐❛❞♦s✿
❊s❝♦r❡ ❋ís✐❝♦
❖ ❡s❝♦r❡ ❢ís✐❝♦ é ✉♠ ✐♥❞✐❝❛❞♦r q✉❡ ♠❡❞❡ ♦ ❞❡s❡♠♣❡♥❤♦ ❞♦ ✐♥❞✐✈í❞✉♦ ♥♦s t❡st❡s ❢ís✐❝♦s✳ ❯t✐❧✐③❛♥❞♦ ❛ ❆♥á❧✐s❡ ❞❡ ❈♦♠♣♦♥❡♥t❡s Pr✐♥❝✐♣❛✐s✱ ♣♦❞❡✲s❡ r❡❞✉③✐r ❛ ❞✐♠❡♥sã♦ ❞❡ ✈❛r✐á✈❡✐s ❡♠ ❡st✉❞♦ ❧❡✈❛♥❞♦ ❡♠ ❝♦♥t❛ ❛ ❡str✉t✉r❛ ❞❡ ✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛ ❞❛s ✈❛r✐á✈❡✐s q✉❡ ♠❡❞❡♠ ❛ ❝❛♣❛❝✐❞❛❞❡ ❢ís✐❝❛ ❞♦ ✐♥❞✐✈í❞✉♦✳ ❆ss✐♠✱ ♣♦r ♠❡✐♦ ❞❛ ❝♦♠❜✐♥❛çã♦ ❞❡ss❛s ✈❛r✐á✈❡✐s✱ ♦❜té♠✲s❡
✷✳✷✳ ❙✉♠❛r✐③❛çã♦ ❞❡ ❉❛❞♦s ✶✹
✉♠ ❝♦♥❥✉♥t♦ ♠❡♥♦r ❞❡ ✈❛r✐á✈❡✐s q✉❡ ❡①♣❧✐q✉❡♠ ✉♠ ♠❡s♠♦ ❢❡♥ô♠❡♥♦✳ ❖s t❡st❡s ❛♣❧✐❝❛❞♦s ♣❛r❛ ✈❡r✐✜❝❛r ❛ ❝❛♣❛❝✐❞❛❞❡ ❢ís✐❝❛ ❢♦r❛♠ ♦ t❡st❡ ❞❡ ♣♦tê♥❝✐❛ ❛♥❛❡ró❜✐❝❛ ✭❘✳❆✳❙✳❚✳✮✱ s✉✲ ♠❛r✐③❛❞♦ ♣❡❧❛ ♣♦tê♥❝✐❛ r❡❧❛t✐✈❛ ✭P❘✮✱ ♦ t❡st❡ ❞❡ ✶✵✵✵ ♠❡tr♦s ❡♠ ♣✐st❛✱ s✉♠❛r✐③❛❞♦ ♣❡❧♦ ❝♦♥s✉♠♦ ♠á①✐♠♦ ❞❡ ♦①✐❣ê♥✐♦ ✭❱❖✷▼❆❳✮ ❡ ♦ t❡st❡ ❞❡ ✈❡❧♦❝✐❞❛❞❡ ❝í❝❧✐❝❛ ❞❡ ✷✵ ♠❡tr♦s ✭❈▲✷✵✮✳
❊s❝♦r❡ ❚é❝♥✐❝♦
❖ ❡s❝♦r❡ té❝♥✐❝♦ é ✉♠ ✐♥❞✐❝❛❞♦r q✉❡ ❛✈❛❧✐❛ ♦ ❞❡s❡♠♣❡♥❤♦ ❞♦s ✐♥❞✐✈í❞✉♦s ♥♦s t❡st❡s ❞❡ ❤❛❜✐❧✐❞❛❞❡s té❝♥✐❝❛s✳ ❊st❡ ✐♥❞✐❝❛❞♦r t❛♠❜é♠ ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞♦ ❛ ♣❛rt✐r ❞❛ ❆✳❈✳P✳ ❡✱ ♣❛r❛ ♠❡❞✐r♠♦s ❛ ❤❛❜✐❧✐❞❛❞❡ té❝♥✐❝❛ ❞♦ ✐♥❞✐✈í❞✉♦✱ ✉t✐❧✐③❛♠♦s ♦ t❡st❡s ❞❡ ❝❤✉t❡ ❡ ♣❛ss❡ ❞❡ ▼♦r ❡ ❈❤r✐st✐❛♥ ✭P❆❙❙❊✮✱ t❡st❡ ❞❡ ❞r✐❜❧❡ ❞❡ ✺ ❝♦♥❡s ✭❉❘■❇▲❊✮ ❡ ♦ t❡st❡ ❞❡ ❝❤✉t❡ ❛♣ós ♦ ♣❛ss❡ ✭❈❍❯❚❊✮✳
✷✳✷✳✸ ❆♥á❧✐s❡ ❋❛t♦r✐❛❧
❙❡❣✉♥❞♦ ❬✸✸❪✱ ❛ ❆♥á❧✐s❡ ❋❛t♦r✐❛❧ t❡♠ ❝♦♠♦ ♣r✐♥❝✐♣❛❧ ♦❜❥❡t✐✈♦ ❞❡s❝r❡✈❡r ❛ ✈❛r✐❛❜✐❧✐❞❛❞❡ ❞❡ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s ✉t✐❧✐③❛♥❞♦ ✉♠ ♥ú♠❡r♦ ♠❡♥♦r ❞❡ ✈❛r✐á✈❡✐s ♥ã♦ ♦❜s❡r✈á✈❡✐s✱ ❞❡♥♦♠✐♥❛❞♦s ❢❛t♦r❡s ❝♦♠✉♥s✱ q✉❡ ❡stã♦ r❡❧❛❝✐♦♥❛❞❛s ❛♦ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s ♣♦r ♠❡✐♦ ❞❡ ✉♠ ♠♦❞❡❧♦ ❧✐♥❡❛r✳ ◆❡st❡ ♠♦❞❡❧♦✱ ♣❛rt❡ ❞❛ ✈❛r✐❛❜✐❧✐❞❛❞❡ ❞♦s ❞❛❞♦s é ❛tr✐❜✉í❞❛ ❛♦s ❢❛t♦r❡s ❝♦♠✉♥s ❡ ♦ r❡st❛♥t❡ é ❛tr✐❜✉í❞❛ às ✈❛r✐á✈❡✐s q✉❡ ♥ã♦ ❢♦r❛♠ ✐♥❝❧✉í❞❛s ♥♦ ♠♦❞❡❧♦✱ ♦✉ s❡❥❛✱ ♦ ❡rr♦ ❛❧❡❛tór✐♦✳
❉❛❞♦ q✉❡ ♦ ✈❡t♦r ❛❧❡❛tór✐♦ ❳✱ ❛ss♦❝✐❛❞♦ ❛♦s ❞❛❞♦s✱ ❝♦♠ p ❝♦♠♣♦♥❡♥t❡s ✭✈❛r✐á✈❡✐s✮
t❡♠ ✈❡t♦r ❞❡ ♠é❞✐❛s µ ❡ ♠❛tr✐③ ❞❡ ❝♦✈❛r✐â♥❝✐❛ Σ✱ ♦ ♠♦❞❡❧♦ ❢❛t♦r✐❛❧ ♣♦st✉❧❛ q✉❡ ❳ é
❧✐♥❡❛r♠❡♥t❡ ❞❡♣❡♥❞❡♥t❡ ❞❡ ❛❧❣✉♠❛s ✈❛r✐á✈❡✐s ❛❧❡❛tór✐❛s ♥ã♦ ♦❜s❡r✈á✈❡✐s F1, F2, . . . , Fm
❝❤❛♠❛❞❛s ❢❛t♦r❡s ❝♦♠✉♥s ❡p❛❞✐❝✐♦♥❛✐s ❢♦♥t❡s ❞❡ ✈❛r✐❛çã♦ǫ1, ǫ2, . . . , ǫp✱ ❝❤❛♠❛❞♦s ❞❡ ❡rr♦s
♦✉✱ ❛❧❣✉♠❛s ✈❡③❡s ❞❡ ❢❛t♦r❡s ❡s♣❡❝í✜❝♦s✳ ❊♠ ♣❛rt✐❝✉❧❛r ♦ ♠♦❞❡❧♦ ❞❛ ❆♥á❧✐s❡ ❋❛t♦r✐❛❧ é✱ ♥❛ ♥♦t❛çã♦ ♠❛tr✐❝✐❛❧✱ ❞❛❞♦ ♣♦r✿
(❳−µ)p×1 =▲p×m×❋m×1+ǫp×1, ✭✷✳✻✮
❡♠ q✉❡µi ❂ ♠é❞✐❛ ❞❛ ✈❛r✐á✈❡❧ ✐✱ǫi ❂ ✐✲és✐♠♦ ❢❛t♦r ❡s♣❡❝í✜❝♦✱ Fj ❂ ❥ ✲és✐♠♦ ❢❛t♦r ❝♦♠✉♠
❡lij ❂ ❝❛r❣❛ ❢❛t♦r✐❛❧ ❞❛ ✐✲és✐♠❛ ✈❛r✐á✈❡❧ ♥♦ ❥ ✲és✐♠♦ ❢❛t♦r✳
❆ ♠❛tr✐③ ▲ é ❢♦r♠❛❞❛ ♣❡❧♦s ❝♦❡✜❝✐❡♥t❡s lij✱ ❡♠ q✉❡ lij é ❛ ❝❛r❣❛ ❢❛t♦r✐❛❧ ❞❛ ✐✲és✐♠❛
✈❛r✐á✈❡❧ ♥♦ ❥ ✲és✐♠♦ ❢❛t♦r✱ ❞❡ ♠♦❞♦ q✉❡ ❛ ♠❛tr✐③ ▲ é ❛ ♠❛tr✐③ ❞❡ ❝❛r❣❛s ❢❛t♦r✐❛✐s✳ ◆♦t❡
