❉✐str✐❜✉✐çã♦ ◆♦r♠❛❧ ❆ss✐♠étr✐❝❛ ♣❛r❛ ❉❛❞♦s
❞❡ ❊①♣r❡ssã♦ ●ê♥✐❝❛
❉✐str✐❜✉✐çã♦ ◆♦r♠❛❧ ❆ss✐♠étr✐❝❛ ♣❛r❛ ❉❛❞♦s
❞❡ ❊①♣r❡ssã♦ ●ê♥✐❝❛
Pr✐s❝✐❧❛ ❞❛ ❙✐❧✈❛ ●♦♠❡s
❖r✐❡♥t❛❞♦r❡s✿ ❉r❛✳ ❱❡r❛ ▲✳ ❉✳ ❚♦♠❛③③❡❧❛ ❉r✳ ❋r❛♥❝✐s❝♦ ▲♦✉③❛❞❛✲◆❡t♦✳
❚r❛❜❛❧❤♦ ❛♣r❡s❡♥t❛❞♦ ❛♦ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❊s✲ t❛tíst✐❝❛ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❙ã♦ ❈❛r❧♦s ✲ ❉❊s✴❯❋❙❈❛r✱ ❝♦♠♦ ♣❛rt❡ ❞♦s r❡q✉✐s✐t♦s ♣❛r❛ ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ▼❡str❡ ❡♠ ❊st❛tíst✐❝❛✳
Ficha catalográfica elaborada pelo DePT da Biblioteca Comunitária da UFSCar
G633dn
Gomes, Priscila da Silva.
Distribuição normal assimétrica para dados de expressão gênica / Priscila da Silva Gomes. -- São Carlos : UFSCar, 2009.
62 f.
Dissertação (Mestrado) -- Universidade Federal de São Carlos, 2009.
1. Estatística matemática. 2. Expressão gênica. 3. Distribuição normal assimétrica. I. Título.
❆❣r❛❞❡❝✐♠❡♥t♦s
●♦st❛r✐❛ ❞❡ ❛❣r❛❞❡❝❡r✱ ❛♦s ♠❡✉s ♣❛✐s ♣❡❧❛ ♣❛❝✐ê♥❝✐❛ ❡ ♣♦r s❡♠♣r❡ ♠❡ ❛♣♦✐❛r❡♠ ❡♠ t♦❞❛s ❛s ❡s❝♦❧❤❛s ❢❡✐t❛s ♥♦ ❞❡❝♦rr❡r ❞❛ ♠✐♥❤❛ ✈✐❞❛✱ ❝❡rt❛♠❡♥t❡ s❡♠ ❡❧❡s ♥ã♦ ❡st❛r✐❛ ❛q✉✐✳
❆♦s ♠❡✉s ❛♠✐❣♦s✱ q✉❡ s❡♠♣r❡ ❡st✐✈❡r❛♠ ♣r❡s❡♥t❡s ♠❡ ❛❥✉❞❛♥❞♦ ❛ s✉♣❡r❛r ❛ ♣r❡ssã♦ ❡ ✈❡♥❝❡r ♦s ♦❜stá❝✉❧♦s q✉❡ s✉r❣✐r❛♠ ♥♦ ♠❡✐♦ ❞♦ ❝❛♠✐♥❤♦✳
❊s♣❡❝✐❛❧♠❡♥t❡ ❛♦ ❆♥❞ré✱ ♣❡❧♦ ❛♠♦r✱ ❛♠✐③❛❞❡ ❡ t♦t❛❧ ❛♣♦✐♦✱ ❝♦♠♣❛rt✐❧❤❛❞♦s ♥❛s ♣❛❝✐❡♥t❡s ❤♦r❛s ❞❡ tr❛❜❛❧❤♦✱ ❡ ♣♦r ❡st❛r s❡♠♣r❡ ❛♦ ♠❡✉ ❧❛❞♦ ♠❡ ❞❛♥❞♦ ❢♦rç❛ ❡ ♠❡ ✐♥❝❡♥t✐✈❛♥❞♦ ❛ ♥ã♦ ❞❡s✐st✐r✳
❆♦s ♠❡✉s ♦r✐❡♥t❛❞♦r❡s✱ ❱❡r❛ ❡ ◆❡t♦✱ ♣❡❧❛ ♦r✐❡♥t❛çã♦ ❡ ✐♥❝❡♥t✐✈♦ ♥❛ ❡❧❛❜♦r❛çã♦ ❡ ❝♦♥❞✉çã♦ ❞♦ tr❛❜❛❧❤♦✳
❆♦ ♣r♦❢❡ss♦r ▲✉✐s ▼✐❧❛♥✱ ♠❡♠❜r♦ ❞❛ ❜❛♥❝❛ ❞♦ ❡①❛♠❡ ❞❡ q✉❛❧✐✜❝❛çã♦✱ ♣❡❧❛s ❞✐✈❡rs❛s ❝♦♥✈❡rs❛s ❡ ♣❡❧❛s s✉❣❡stõ❡s ❢❡✐t❛s✳
❘❡s✉♠♦
❖s ♠✐❝r♦❛rr❛②s sã♦ ❢❡rr❛♠❡♥t❛s ✉t✐❧✐③❛❞❛s ♣❛r❛ ♠❡❞✐r ♦s ♥í✈❡✐s ❞❡ ❡①♣r❡ssã♦ ❞❡ ✉♠❛ ❣r❛♥❞❡ q✉❛♥t✐❞❛❞❡ ❞❡ ❣❡♥❡s ♦✉ ❢r❛❣♠❡♥t♦s ❞❡ ❣❡♥❡s s✐♠✉❧t❛♥❡❛♠❡♥t❡ ❡♠ s✐t✉✲ ❛çõ❡s ✈❛r✐❛❞❛s✳ ❈♦♠ ❡st❛ ❢❡rr❛♠❡♥t❛ é ♣♦ssí✈❡❧ ❞❡t❡r♠✐♥❛r ♣♦ssí✈❡✐s ❣❡♥❡s ❝❛✉s❛❞♦r❡s ❞❡ ❞♦❡♥ç❛s ❞❡ ♦r✐❣❡♠ ❣❡♥ét✐❝❛✳ ❯♠❛ ❛❜♦r❞❛❣❡♠ ❡st❛tíst✐❝❛ ❝♦♠✉♠❡♥t❡ ✉t✐❧✐③❛❞❛ ♣❛r❛ ❞❡t❡r♠✐♥❛r s❡ ✉♠ ❣❡♥❡g ❛♣r❡s❡♥t❛ ❡✈✐❞ê♥❝✐❛s ♣❛r❛ ♥í✈❡✐s ❞❡ ❡①♣r❡ssã♦ ❞✐❢❡r❡♥t❡s ❝♦♥s✐st❡
♥♦ t❡st❡t✱ q✉❡ ❡①✐❣❡ ❛ s✉♣♦s✐çã♦ ❞❡ ♥♦r♠❛❧✐❞❛❞❡ ❛♦s ❞❛❞♦s ✭❙❛r❛✐✈❛✱ ✷✵✵✻❀ ❇❛❧❞✐ ✫ ▲♦♥❣✱
✷✵✵✶✮✳ ◆♦ ❡♥t❛♥t♦✱ ❡st❛ s✉♣♦s✐çã♦ ♣♦❞❡ ♥ã♦ ❝♦♥❞✐③❡r ❝♦♠ ❛ ♥❛t✉r❡③❛ ❞♦s ❞❛❞♦s ❛♥❛❧✐s❛❞♦s✳ ◆❡st❡ tr❛❜❛❧❤♦✱ s❡rá ✉t✐❧✐③❛❞❛ ❛ ❞✐str✐❜✉✐çã♦ ♥♦r♠❛❧ ❛ss✐♠étr✐❝❛ ❞❡s❝r✐t❛ ❢♦r♠❛❧♠❡♥t❡ ♣♦r ❆③③❛❧✐♥✐ ✭✶✾✽✺✮✱ q✉❡ t❡♠ ❛ ❞✐str✐❜✉✐çã♦ ♥♦r♠❛❧ ❝♦♠♦ ❝❛s♦ ♣❛rt✐❝✉❧❛r✱ ❝♦♠ ♦ ✐♥t✉✐t♦ ❞❡ ✢❡①✐❜✐❧✐③❛r ❛ s✉♣♦s✐çã♦ ❞❡ ♥♦r♠❛❧✐❞❛❞❡✳ ❈♦♥s✐❞❡r❛♥❞♦ ❛ ❛❜♦r❞❛❣❡♠ ❝❧áss✐❝❛✱ é r❡❛❧✐③❛❞♦ ✉♠ ❡st✉❞♦ ❞❡ s✐♠✉❧❛çã♦ ♣❛r❛ ❞❡t❡❝t❛r ❞✐❢❡r❡♥ç❛s ❡♥tr❡ ♦s ♥í✈❡✐s ❞❡ ❡①♣r❡ssã♦ ❣ê♥✐❝❛ ❡♠ s✐t✉❛çõ❡s ❞❡ ❝♦♥tr♦❧❡ ❡ tr❛t❛♠❡♥t♦ ❛tr❛✈és ❞♦ t❡st❡ t✱ t❛♠❜é♠ é ❝♦♥s✐❞❡r❛❞♦ ✉♠ ❡st✉❞♦
❞❡ s✐♠✉❧❛çã♦ ♣❛r❛ ❛♥❛❧✐s❛r ♦ ♣♦❞❡r ❞♦ t❡st❡ t q✉❛♥❞♦ é ❛ss✉♠✐❞♦ ✉♠ ♠♦❞❡❧♦ ❛ss✐♠étr✐❝♦
♣❛r❛ ♦ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s✳ ❚❛♠❜é♠ é r❡❛❧✐③❛❞♦ ♦ t❡st❡ ❞❛ r❛③ã♦ ❞❡ ✈❡r♦ss✐♠✐❧❤❛♥ç❛✱ ♣❛r❛ ✈❡r✐✜❝❛r s❡ ♦ ❛❥✉st❡ ❞❡ ✉♠ ♠♦❞❡❧♦ ❛ss✐♠étr✐❝♦ ❛♦s ❞❛❞♦s é ❛❞❡q✉❛❞♦✳
P❛❧❛✈r❛s✲❝❤❛✈❡✿ ❉✐str✐❜✉✐çã♦ ◆♦r♠❛❧ ❆ss✐♠étr✐❝❛✱ ❚❡st❡ t✱ ❚❡st❡ ❞❛ ❘❛③ã♦ ❞❡
❱❡r♦ss✐♠✐❧❤❛♥ç❛✱ ▼✐❝r♦❛rr❛②✱ ❊①♣r❡ssã♦ ●ê♥✐❝❛✳
❆❜str❛❝t
▼✐❝r♦❛rr❛②s t❡❝❤♥♦❧♦❣✐❡s ❛r❡ ✉s❡❞ t♦ ♠❡❛s✉r❡ t❤❡ ❡①♣r❡ss✐♦♥ ❧❡✈❡❧s ♦❢ ❛ ❧❛r❣❡ ❛♠♦✉♥t ♦❢ ❣❡♥❡s ♦r ❢r❛❣♠❡♥ts ♦❢ ❣❡♥❡s s✐♠✉❧t❛♥❡♦✉s❧② ✐♥ ❞✐✛❡r❡♥t s✐t✉❛t✐♦♥s✳ ❚❤✐s t❡❝❤✲ ♥♦❧♦❣② ✐s ✉s❡❢✉❧ t♦ ❞❡t❡r♠✐♥❡ ❣❡♥❡s t❤❛t ❛r❡ r❡s♣♦♥s✐❜❧❡ ❢♦r ❣❡♥❡t✐❝ ❞✐s❡❛s❡s✳ ❆ ❝♦♠♠♦♥ st❛t✐st✐❝❛❧ ♠❡t❤♦❞♦❧♦❣② ✉s❡❞ t♦ ❞❡t❡r♠✐♥❡ ✇❤❡t❤❡r ❛ ❣❡♥❡ g ❤❛s ❡✈✐❞❡♥❝❡s t♦ ❞✐✛❡r❡♥t
❡①♣r❡ss✐♦♥ ❧❡✈❡❧s ✐s t❤❡ t✲t❡st ✇❤✐❝❤ r❡q✉✐r❡s t❤❡ ❛ss✉♠♣t✐♦♥ ♦❢ ♥♦r♠❛❧✐t② ❢♦r t❤❡ ❞❛t❛
✭❙❛r❛✐✈❛✱ ✷✵✵✻❀ ❇❛❧❞✐ ✫ ▲♦♥❣✱ ✷✵✵✶✮✳ ❍♦✇❡✈❡r t❤✐s ❛ss✉♠♣t✐♦♥ s♦♠❡t✐♠❡s ❞♦❡s ♥♦t ❛❣r❡❡ ✇✐t❤ t❤❡ ♥❛t✉r❡ ♦❢ t❤❡ ❛♥❛❧②③❡❞ ❞❛t❛✳ ■♥ t❤✐s ✇♦r❦ ✇❡ ✉s❡ t❤❡ s❦❡✇✲♥♦r♠❛❧ ❞✐str✐❜✉t✐♦♥ ❞❡s❝r✐❜❡❞ ❢♦r♠❛❧❧② ❜② ❆③③❛❧✐♥✐ ✭✶✾✽✺✮✱ ✇❤✐❝❤ ❤❛s t❤❡ ♥♦r♠❛❧ ❞✐str✐❜✉t✐♦♥ ❛s ❛ ♣❛rt✐❝✉❧❛r ❝❛s❡✱ ✐♥ ♦r❞❡r t♦ r❡❧❛① t❤❡ ❛ss✉♠♣t✐♦♥ ♦❢ ♥♦r♠❛❧✐t②✳ ❈♦♥s✐❞❡r✐♥❣ ❛ ❢r❡q✉❡♥t✐st ❛♣♣r♦❛❝❤ ✇❡ ♠❛❞❡ ❛ s✐♠✉❧❛t✐♦♥ st✉❞② t♦ ❞❡t❡❝t ❞✐✛❡r❡♥❝❡s ❜❡t✇❡❡♥ t❤❡ ❣❡♥❡ ❡①♣r❡ss✐♦♥ ❧❡✈❡❧s ✐♥ s✐t✉❛t✐♦♥s ♦❢ ❝♦♥tr♦❧ ❛♥❞ tr❡❛t♠❡♥t t❤r♦✉❣❤ t❤❡ t✲t❡st✳ ❆♥♦t❤❡r s✐♠✉❧❛t✐♦♥ ✇❛s ♠❛❞❡ t♦
❡①❛♠✐♥❡ t❤❡ ♣♦✇❡r ♦❢ t❤❡ t✲t❡st ✇❤❡♥ ✇❡ ❛ss✉♠❡ ❛♥ ❛s②♠♠❡tr✐❝❛❧ ♠♦❞❡❧ ❢♦r t❤❡ ❞❛t❛✳
❆❧s♦ ✇❡ ✉s❡❞ t❤❡ ❧✐❦❡❧✐❤♦♦❞ r❛t✐♦ t❡st t♦ ✈❡r✐❢② t❤❡ ❛❞❡q✉❛❜✐❧✐t② ♦❢ ❛♥ ❛s②♠♠❡tr✐❝❛❧ ♠♦❞❡❧ ❢♦r t❤❡ ❞❛t❛✳
❑❡②✇♦r❞s✿ ❙❦❡✇✲♥♦r♠❛❧ ❞✐str✐❜✉t✐♦♥✱ t✲t❡st✱ ❧✐❦❡❧✐❤♦♦❞ r❛t✐♦ t❡st✱ ♠✐❝r♦❛rr❛②✱ ❣❡♥✐❝ ❡①♣r❡ss✐♦♥✳
❙✉♠ár✐♦
❘❡s✉♠♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✐
❆❜str❛❝t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✐✐
▲✐st❛ ❞❡ ❋✐❣✉r❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✈
▲✐st❛ ❞❡ ❚❛❜❡❧❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✈✐✐
✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶
✷ ❊①♣r❡ssã♦ ●ê♥✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹
✷✳✶ ▼❡❞✐♥❞♦ ❊①♣r❡ssã♦ ●ê♥✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻
✷✳✶✳✶ ❊t❛♣❛s ❞❛ Pr❡♣❛r❛çã♦ ❞♦s ▼✐❝r♦❛rr❛②s ❞❡ ❝❉◆❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼
✷✳✶✳✷ ❚r❛♥s❢♦r♠❛çã♦ ❞♦s ❉❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾
✷✳✶✳✸ ❚é❝♥✐❝❛s ❊st❛tíst✐❝❛s P❛r❛ ❛ ❆♥á❧✐s❡ ❞❡ ❉❛❞♦s ❞❡ ❊①♣r❡ssã♦ ●ê♥✐❝❛ ✶✵
✷✳✷ ❈♦♥s✐❞❡r❛çõ❡s ❋✐♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶
✸ ❆ ❉✐str✐❜✉✐çã♦ ◆♦r♠❛❧ ❆ss✐♠étr✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷
✸✳✶ ❉❡✜♥✐çã♦ ❡ Pr♦♣r✐❡❞❛❞❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸
✸✳✷ ❉✐str✐❜✉✐çã♦ ◆♦r♠❛❧ ❆ss✐♠étr✐❝❛ ❝♦♠ ♣❛râ♠❡tr♦s ❞❡ ❧♦❝❛çã♦ ❡ ❡s❝❛❧❛ ✳ ✳ ✳ ✶✺
✸✳✸ ●❡r❛çã♦ ❞❡ ✉♠❛ ❉✐str✐❜✉✐çã♦ ◆♦r♠❛❧ ❆ss✐♠étr✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻
✸✳✹ ■♥❢❡rê♥❝✐❛ ❙♦❜r❡ ♦s P❛râ♠❡tr♦s ❞❛ ❉✐str✐❜✉✐çã♦ ◆♦r♠❛❧ ❆ss✐♠étr✐❝❛ ✳ ✳ ✳ ✳ ✶✻
✸✳✹✳✶ ▼ét♦❞♦ ❞♦s ▼♦♠❡♥t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼
✸✳✹✳✷ ▼ét♦❞♦ ❞❡ ▼á①✐♠❛ ❱❡r♦ss✐♠✐❧❤❛♥ç❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽
✸✳✺ ▼ét♦❞♦ ❞❡ ❙✐♠✉❧❛çã♦ ❇♦♦tstr❛♣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵
✸✳✺✳✶ ■♥t❡r✈❛❧♦ ❞❡ ❈♦♥✜❛♥ç❛ ✈✐❛ ▼ét♦❞♦ ❇♦♦tstr❛♣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷
✸✳✺✳✷ ❆♣❧✐❝❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷
✸✳✻ ❈♦♥s✐❞❡r❛çõ❡s ❋✐♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹
✹ ❖ ❚❡st❡ t ♣❛r❛ ❉❛❞♦s ❞❡ ❊①♣r❡ssã♦ ●ê♥✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺
✹✳✶ ❊st✉❞♦ ❞❡ ❙✐♠✉❧❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼
✹✳✶✳✶ ❆✈❛❧✐❛çã♦ ❞♦ P♦❞❡r ❞♦ ❚❡st❡t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵
✹✳✷ ❊①❡♠♣❧♦ ❝♦♠ ❉❛❞♦s ❘❡❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸
✹✳✸ ❈♦♥s✐❞❡r❛çõ❡s ❋✐♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻
✺ ❚❡st❡ ❞❛ ❘❛③ã♦ ❞❡ ❱❡r♦ss✐♠✐❧❤❛♥ç❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼
✺✳✶ ❆♣❧✐❝❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾
✺✳✷ ❈♦♥s✐❞❡r❛çõ❡s ❋✐♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸
✻ ❈♦♥❝❧✉sõ❡s ❡ Pr♦♣♦st❛s ❋✉t✉r❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹
❘❡❢❡rê♥❝✐❛s ❇✐❜❧✐♦❣rá✜❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻
❆ ❋✐❣✉r❛s ❞♦ P♦❞❡r ❞♦ ❚❡st❡ t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾
❇ ❚❛❜❡❧❛s P♦❞❡r ❞♦ ❚❡st❡ t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✷✳✶ ❊①♣❡r✐♠❡♥t♦ ❝♦♠ ❛rr❛♥❥♦s ❞❡ ❉◆❆✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽
✸✳✶ ●rá✜❝♦ ❞❛ ❞❡♥s✐❞❛❞❡ ♥♦r♠❛❧ ❛ss✐♠étr✐❝❛ ♣❛❞rã♦ ♣❛r❛ ✈❛❧♦r❡s ❞✐❢❡r❡♥t❡s ❞❡λ✳ ✶✹
✹✳✶ ●rá✜❝♦ ❞♦ P♦❞❡r ❞♦ ❚❡st❡ t ✭σgt=σgc ❡n = 5✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶
✹✳✷ ●rá✜❝♦ ❞♦ P♦❞❡r ❞♦ ❚❡st❡ t ✭σgt =σgc ❡ n= 50✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷
✹✳✸ ●rá✜❝♦ ❞♦ P♦❞❡r ❞♦ ❚❡st❡ t ✭σgt= 4σgc ❡ n = 5✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷
✹✳✹ ●rá✜❝♦ ❞♦ P♦❞❡r ❞♦ ❚❡st❡ t ✭σgt = 4σgc ❡ n= 50✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸
✹✳✺ ❍✐st♦❣r❛♠❛ ❞♦ ❣r✉♣♦ ❝♦♥tr♦❧❡ ❡ tr❛t❛♠❡♥t♦ ♣❛r❛ ♦ ❣❡♥❡ ❍■P❑✸✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹
✹✳✻ ▼é❞✐❛s ❡ ✈❛r✐â♥❝✐❛s ❞♦ ❝♦♥tr♦❧❡ ❡ tr❛t❛♠❡♥t♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺
✺✳✶ ❚❛♠❛♥❤♦ ❞♦ t❡st❡ ✭♣r♦❝❡❞✐♠❡♥t♦ ♣❛❞rã♦✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵
✺✳✷ P♦❞❡r ❞♦ t❡st❡ ✭♣r♦❝❡❞✐♠❡♥t♦ ♣❛❞rã♦✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶
✺✳✸ ❚❛♠❛♥❤♦ ❞♦ t❡st❡ ✭❜♦♦tstr❛♣✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷
✺✳✹ P♦❞❡r ❞♦ t❡st❡ ✭❜♦♦tstr❛♣✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷
❆✳✶ ●rá✜❝♦ ❞♦ P♦❞❡r ❞♦ ❚❡st❡ t ✭σgt =σgc ❡ n= 10✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾
❆✳✷ ●rá✜❝♦ ❞♦ P♦❞❡r ❞♦ ❚❡st❡ t ✭σgt =σgc ❡ n= 30✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵
❆✳✸ ●rá✜❝♦ ❞♦ P♦❞❡r ❞♦ ❚❡st❡ t ✭σgt =σgc ❡ n= 100✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵
❆✳✹ ●rá✜❝♦ ❞♦ P♦❞❡r ❞♦ ❚❡st❡ t ✭σgt =σgc ❡ n= 300✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶
❆✳✺ ●rá✜❝♦ ❞♦ P♦❞❡r ❞♦ ❚❡st❡ t ✭σgt = 16σgc ❡n = 10✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶
❆✳✻ ●rá✜❝♦ ❞♦ P♦❞❡r ❞♦ ❚❡st❡ t ✭σgt = 16σgc ❡n = 30✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷
❆✳✼ ●rá✜❝♦ ❞♦ P♦❞❡r ❞♦ ❚❡st❡ t ✭σgt = 16σgc ❡n = 100✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✸✳✶ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ♠é❞✐❛s ❡ ❞❡s✈✐♦ ♣❛❞rã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸
✸✳✷ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ♠❡❞✐❛♥❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸
✸✳✸ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ✐♥t❡r✈❛❧♦s95%✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸
✹✳✶ ◆ú♠❡r♦ ❞❡ ❣❡♥❡s ❞✐❢❡r❡♥❝✐❛❧♠❡♥t❡ ❡①♣r❡ss♦s ♣❛r❛ λgt =−1✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽
✹✳✷ ◆ú♠❡r♦ ❞❡ ❣❡♥❡s ❞✐❢❡r❡♥❝✐❛❧♠❡♥t❡ ❡①♣r❡ss♦s ♣❛r❛ λgt =−0.5✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽
✹✳✸ ◆ú♠❡r♦ ❞❡ ❣❡♥❡s ❞✐❢❡r❡♥❝✐❛❧♠❡♥t❡ ❡①♣r❡ss♦s ♣❛r❛ λgt = 0✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽
✹✳✹ ◆ú♠❡r♦ ❞❡ ❣❡♥❡s ❞✐❢❡r❡♥❝✐❛❧♠❡♥t❡ ❡①♣r❡ss♦s ♣❛r❛ λgt = 0.5✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾
✹✳✺ ◆ú♠❡r♦ ❞❡ ❣❡♥❡s ❞✐❢❡r❡♥❝✐❛❧♠❡♥t❡ ❡①♣r❡ss♦s ♣❛r❛ λgt = 1✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾
✹✳✻ ●❡♥❡s ❞❡t❡❝t❛❞♦s ❝♦♠♦ ❞✐❢❡r❡♥❝✐❛❧♠❡♥t❡ ❡①♣r❡ss♦s ♣❡❧♦ t❡st❡ t✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺
✺✳✶ ❚❛♠❛♥❤♦ ❡ ♣♦❞❡r ❞♦ t❡st❡ ✭♣r♦❝❡❞✐♠❡♥t♦ ♣❛❞rã♦✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵
✺✳✷ ❚❛♠❛♥❤♦ ❡ ♣♦❞❡r ❞♦ t❡st❡ ✭❜♦♦tstr❛♣✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶
❇✳✶ P♦❞❡r ❞♦ t❡st❡ σgt =σgc ❡ n= 5 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹
❇✳✷ P♦❞❡r ❞♦ t❡st❡ σgt = 16σgc ❡ n = 5✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺
❇✳✸ P♦❞❡r ❞♦ t❡st❡ σgt =σgc ❡ n= 10 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺
❇✳✹ P♦❞❡r ❞♦ t❡st❡ σgt = 16σgc ❡ n = 10 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺
❇✳✺ P♦❞❡r ❞♦ t❡st❡ σgt =σgc ❡ n= 30 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻
❇✳✻ P♦❞❡r ❞♦ t❡st❡ σgt = 16σgc ❡ n = 30 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻
❇✳✼ P♦❞❡r ❞♦ t❡st❡ σgt =σgc ❡ n= 50 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻
✈✐✐✐
❇✳✽ P♦❞❡r ❞♦ t❡st❡ σgt = 16σgc ❡ n = 50 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼
❇✳✾ P♦❞❡r ❞♦ t❡st❡ σgt =σgc ❡ n= 100✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼
❇✳✶✵ P♦❞❡r ❞♦ t❡st❡ σgt = 16σgc ❡ n = 100 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼
❇✳✶✶ P♦❞❡r ❞♦ t❡st❡ σgt =σgc ❡ n= 300✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽
❇✳✶✷ P♦❞❡r ❞♦ t❡st❡ σgt = 16σgc ❡ n = 300 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽
❈✳✶ ◆ú♠❡r♦ ❞❡ ❣❡♥❡s ❞✐❢❡r❡♥❝✐❛❧♠❡♥t❡ ❡①♣r❡ss♦s ♣❛r❛ λgt =−1❡ n = 10✳ ✳ ✳ ✳ ✺✾
❈✳✷ ◆ú♠❡r♦ ❞❡ ❣❡♥❡s ❞✐❢❡r❡♥❝✐❛❧♠❡♥t❡ ❡①♣r❡ss♦s ♣❛r❛ λgt =−0.5 ❡ n= 10✳ ✳ ✳ ✻✵
❈✳✸ ◆ú♠❡r♦ ❞❡ ❣❡♥❡s ❞✐❢❡r❡♥❝✐❛❧♠❡♥t❡ ❡①♣r❡ss♦s ♣❛r❛ λgt = 0 ❡ n = 10✳ ✳ ✳ ✳ ✳ ✻✵
❈✳✹ ◆ú♠❡r♦ ❞❡ ❣❡♥❡s ❞✐❢❡r❡♥❝✐❛❧♠❡♥t❡ ❡①♣r❡ss♦s ♣❛r❛ λgt = 0.5 ❡ n= 10✳ ✳ ✳ ✳ ✻✵
❈✳✺ ◆ú♠❡r♦ ❞❡ ❣❡♥❡s ❞✐❢❡r❡♥❝✐❛❧♠❡♥t❡ ❡①♣r❡ss♦s ♣❛r❛ λgt = 1 ❡ n = 10✳ ✳ ✳ ✳ ✳ ✻✶
❈✳✻ ◆ú♠❡r♦ ❞❡ ❣❡♥❡s ❞✐❢❡r❡♥❝✐❛❧♠❡♥t❡ ❡①♣r❡ss♦s ♣❛r❛ λgt =−1❡ n = 30✳ ✳ ✳ ✳ ✻✶
❈✳✼ ◆ú♠❡r♦ ❞❡ ❣❡♥❡s ❞✐❢❡r❡♥❝✐❛❧♠❡♥t❡ ❡①♣r❡ss♦s ♣❛r❛ λgt =−0.5 ❡ n= 30✳ ✳ ✳ ✻✶
❈✳✽ ◆ú♠❡r♦ ❞❡ ❣❡♥❡s ❞✐❢❡r❡♥❝✐❛❧♠❡♥t❡ ❡①♣r❡ss♦s ♣❛r❛ λgt = 0 ❡ n = 30✳ ✳ ✳ ✳ ✳ ✻✷
❈✳✾ ◆ú♠❡r♦ ❞❡ ❣❡♥❡s ❞✐❢❡r❡♥❝✐❛❧♠❡♥t❡ ❡①♣r❡ss♦s ♣❛r❛ λgt = 0.5 ❡ n= 30✳ ✳ ✳ ✳ ✻✷
❈❛♣ít✉❧♦ ✶
■♥tr♦❞✉çã♦
◆♦s ú❧t✐♠♦s ❛♥♦s✱ ✉♠❛ ❡♥♦r♠❡ ♠❛ss❛ ❞❡ ❞❛❞♦s t❡♠ ✜❝❛❞♦ ❞✐s♣♦♥í✈❡❧ ♣❛r❛ q✉❡ ❜✐ó❧♦❣♦s ♠♦❧❡❝✉❧❛r❡s✱ ❜✐♦q✉í♠✐❝♦s ❡ ♦✉tr♦s ♣❡sq✉✐s❛❞♦r❡s ♣♦ss❛♠ ❛♥❛❧✐sá✲❧♦s✳ ❖ ❞❡s❡♥✲ ✈♦❧✈✐♠❡♥t♦ ❞❡ ❝♦♠♣✉t❛❞♦r❡s ❝❛♣❛③❡s ❞❡ ❛r♠❛③❡♥❛r ❡ ❣❡r❡♥❝✐❛r ✉♠ ❣r❛♥❞❡ ♥ú♠❡r♦ ❞❡ ✐♥❢♦r♠❛çõ❡s ❡✱ ❛s ❞❡s❝♦❜❡rt❛s ♥♦ ❝❛♠♣♦ ❞❛ ❜✐♦❧♦❣✐❛ ♠♦❧❡❝✉❧❛r t♦r♥❛r❛♠ ♣♦ssí✈❡❧ ❛ ❝r✐❛çã♦ ❞❡ ❜❛♥❝♦s ❞❡ ❞❛❞♦s ❣❡♥ét✐❝♦s ❡ ❛❧❣♦r✐t♠♦s ❞❡ ♠✐♥❡r❛çã♦ ❞❡ ❞❛❞♦s ♣❛r❛ ❛♥❛❧✐s❛r ♣r♦t❡í♥❛s✱ ❣❡♥❡s ❡ ❝♦❧❡çõ❡s ❝♦♠♣❧❡t❛s ❞❡ ❉◆❆ ✭á❝✐❞♦ ❞❡s♦①✐rr✐❜♦♥✉❝❧❡✐❝♦✮ ❡♠ ✉♠ ♥í✈❡❧ ❣❡♥ô♠✐❝♦✱ t❡♥❞♦ ❝♦♠♦ ♦❜❥❡t✐✈♦ ♣r✐♥❝✐♣❛❧ ❛ ♣r♦❞✉çã♦ ❞❡ ❝♦♥❤❡❝✐♠❡♥t♦s ♣❛r❛ ❛ ❝♦♠♣r❡❡♥sã♦ ❞♦ ❝ó❞✐❣♦ ❞❛ ✈✐❞❛ ✭❉◆❆✮✳
❖ rá♣✐❞♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ t❡❝♥♦❧♦❣✐❛s ❜✐♦❧ó❣✐❝❛s ♥❛ ú❧t✐♠❛ ❞é❝❛❞❛✱ ❢❡③ ❝♦♠ q✉❡ ♣❡sq✉✐s❛❞♦r❡s ❡ ❧❛❜♦r❛tór✐♦s tr❛❜❛❧❤❛ss❡♠ ❡♠ ❝♦♥❥✉♥t♦ ♥❛ ❞❡s❝♦❜❡rt❛ ❞♦ s❡q✉❡♥❝✐❛♠❡♥t♦ ❣❡♥ét✐❝♦ ❞❡ ❞✐✈❡rs♦s ♦r❣❛♥✐s♠♦s ✈✐✈♦s✱ ❛❧é♠ ❞❡ ❞✐s♣♦♥✐❜✐❧✐③❛r❡♠ ❡st❛s ✐♥❢♦r♠❛çõ❡s ❡♠ ❜❛♥❝♦s ❞❡ ❞❛❞♦s ♣ú❜❧✐❝♦s✱ ♣❡r♠✐t✐♥❞♦ ❛ss✐♠✱ ♦ ❡st✉❞♦ ❞❡ ♣r♦❝❡ss♦s ❜✐♦❧ó❣✐❝♦s r❡❧❛❝✐♦♥❛❞♦s ❛♦ ❣❡♥♦♠❛✳
❖ ❣❡♥♦♠❛ ❤✉♠❛♥♦ é ❛ ✐♠♣r❡ssã♦ ❞✐❣✐t❛❧ ❞❡ t♦❞❛s ❛s ❡str✉t✉r❛s ❡ ❛t✐✈✐❞❛❞❡s ❝❡❧✉❧❛r❡s ♥♦ ❝♦r♣♦ ❤✉♠❛♥♦✳ ❊❧❡ é ❝♦♠♣♦st♦ ♣♦r ✷✸ ♣❛r❡s ❞❡ ❝r♦♠♦ss♦♠♦s✱ ♥♦ q✉❛❧ ❝❛❞❛ ♣❛r ♣♦ss✉✐ ✉♠ ❝r♦♠♦ss♦♠♦ ♣r♦✈❡♥✐❡♥t❡ ❞❛ ♠ã❡ ❡ ♦✉tr♦ ❞♦ ♣❛✐✳ ❈❛❞❛ ❝r♦♠♦ss♦♠♦ é ❢♦r♠❛❞♦ ♣♦r ✉♠❛ ❧♦♥❣❛ ❝❛❞❡✐❛ ❞❡ ❞✉❛s ✜t❛s ❞❡ ❉◆❆ ❝❤❛♠❛❞❛ ❞❡ ❤é❧✐❝❡ ❞✉♣❧❛ ✭❙❝❤✇❡♥❞❡r ❡t ❛❧✳✱ ✷✵✵✻✮✳
❖s ❣❡♥❡s sã♦ s❡❣♠❡♥t♦s ❞❡ ❉◆❆ ❡ ❝❛rr❡❣❛♠ ❛ ✐♥❢♦r♠❛çã♦ ♥❡❝❡ssár✐❛ ♣❛r❛ ❛ sí♥t❡s❡ ❞❡ ♣r♦t❡í♥❛s✱ ❡ ❡st❛s✱ ❛t✉❛♠ ❞❡ ❢♦r♠❛ ✈✐t❛❧ ♥♦ s✐st❡♠❛ ❜✐♦❧ó❣✐❝♦ ❞❡ ✉♠ s❡r ✈✐✈♦✱ ♣♦r ✐ss♦
✶✳ ■♥tr♦❞✉çã♦ ✷
é ✐♠♣♦rt❛♥t❡ ❡♥t❡♥❞❡r ❝♦♠♦ ♦s ❣❡♥❡s sã♦ tr❛❞✉③✐❞♦s ❡♠ ♣r♦t❡í♥❛s✳
❆tr❛✈és ❞♦ ♣r♦❝❡ss♦ ❞❡ ♣❛r❡❛♠❡♥t♦ ❞❡ ❜❛s❡s ❝♦♠♣❧❡♠❡♥t❛r❡s✱ ♦ ❉◆❆ é tr❛♥s❝r✐t♦ ❡♠ ❘◆❆ ♠❡♥s❛❣❡✐r♦ ✭♠❘◆❆✮✳ ❖ ♠❘◆❆ ❞❡✐①❛ ♦ ♥ú❝❧❡♦ ❞❛ ❝é❧✉❧❛ ❡ é tr❛❞✉③✐❞♦ ❡♠ ♣r♦t❡í♥❛✳ ❖ ♣r♦❝❡ss♦ ❞❡ ❝♦♥✈❡rsã♦ ❞❡ ✉♠❛ s❡q✉ê♥❝✐❛ ❞❡ ❉◆❆ ❡♠ ♣r♦t❡í♥❛ é ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ ❡①♣r❡ssã♦ ❣ê♥✐❝❛ ✭❙❝❤✇❡♥❞❡r ❡t ❛❧✳✱ ✷✵✵✻❀ ▲❡❡✱ ✷✵✵✹✮✳ ❖ ❡st✉❞♦ ❞❛ ❡①♣r❡ssã♦ ❣ê♥✐❝❛ t♦r♥❛ ♣♦ssí✈❡❧ ❛ ❝♦♠♣r❡❡♥sã♦ ❞❡ ✉♠ ❡st❛❞♦ ❛❧t❡r❛❞♦ ❞♦ ❣❡♥❡ q✉❡ ♣♦❞❡ ❝❛✉s❛r ♣♦r ❡①❡♠♣❧♦✱ ❝â♥❝❡r ❡ ❞♦❡♥ç❛s ❣❡♥ét✐❝❛s✳
❯♠❛ ❞❛s ♣r✐♥❝✐♣❛✐s ❢❡rr❛♠❡♥t❛s ♣❛r❛ ♦ ❡st✉❞♦ ❞❛ ❡①♣r❡ssã♦ ❣ê♥✐❝❛ sã♦ ♦s ❛rr❛♥❥♦s ❞❡ ❉◆❆✱ ♦✉ s✐♠♣❧❡s♠❡♥t❡✱ ♠✐❝r♦❛rr❛②s✳ ❆ t❡❝♥♦❧♦❣✐❛ ❞♦s ♠✐❝r♦❛rr❛②s ♣❡r♠✐t❡ ❛ ✐❞❡♥✲ t✐✜❝❛çã♦ ❡ q✉❛♥t✐✜❝❛çã♦ ❞❛ ❡①♣r❡ssã♦ ❣ê♥✐❝❛✱ s✐♠✉❧t❛♥❡❛♠❡♥t❡✱ ♣❛r❛ t♦❞♦s ♦s ❣❡♥❡s ♥♦ ♦r❣❛♥✐s♠♦ ❛♥❛❧✐s❛❞♦✳ ❖ ♦❜❥❡t✐✈♦ ♣r✐♥❝✐♣❛❧ ❞❡st❛ té❝♥✐❝❛ é ♠❡❞✐r ❛ ❝♦♥❝❡♥tr❛çã♦ ❞❡ ♠❘◆❆ ❡♠ ❝é❧✉❧❛s ♦✉ t❡❝✐❞♦s ❞❡ ✐♥t❡r❡ss❡✳
❖ ♣r✐♥❝í♣✐♦ ❞♦s ❛rr❛♥❥♦s ❞❡ ❉◆❆ ❝♦♠❡ç♦✉ ❛ s❡r ❛❜♦r❞❛❞♦ ❡♠ ♠❡❛❞♦s ✶✾✾✶✱ s❡♥❞♦ ▲❡♥♥♦♥ ❡ ▲❡❤r❛❝❤ ❛❧❣✉♥s ❞♦s ♣✐♦♥❡✐r♦s ✭▲❡♥♥♦♥ ✫ ▲❡❤r❛❝❤✱ ✶✾✾✶✮✳ P♦ré♠✱ ❡st❛ té❝♥✐❝❛ ♣❛ss❛ ❛ s❡r ❞✐ss❡♠✐♥❛❞❛ ❛♥♦s à ❢r❡♥t❡✱ ❡♠ tr❛❜❛❧❤♦s ❝♦♠♦ ♦s ❞❡ ◆❣✉②❡♥ ✫ ❙♠❛rt ❏r ✭✶✾✾✺✮ ❡ ❩❤❛♦ ✭✶✾✾✺✮✳
❖s ♠✐❝r♦❛rr❛②s sã♦ ♠❛tr✐③❡s ❝♦♠♣♦st❛s ♣♦r ♣❡q✉❡♥❛s ♣❧❛❝❛s ❞❡ ✈✐❞r♦ ♦✉ ♥②❧♦♥✱ ♥❛s q✉❛✐s s❡✉s ❡❧❡♠❡♥t♦s ✭s♣♦ts✮ sã♦ ♠♦❧é❝✉❧❛s ❞❡ ❉◆❆✳ ❖ ♠✐❝r♦❛rr❛② t❡♠ ❝♦♠♦ ❢✉♥çã♦ ❡①♣❧♦r❛r ❛ ❤❛❜✐❧✐❞❛❞❡ q✉❡ ✉♠❛ ❞❛❞❛ ♠♦❧é❝✉❧❛ ❞❡ ❝❉◆❆ ✭✈❡rsã♦ tr❛♥s❝r✐t❛ ❞♦ ♠❘◆❆✮ t❡♠ ❞❡ s❡ ❤✐❜r✐❞✐③❛r ❛ ✉♠❛ s❡q✉ê♥❝✐❛ ❝♦♠♣❧❡♠❡♥t❛r ♥♦ ❛rr❛②✳ ❆tr❛✈és ❞♦ ✉s♦ ❞♦s ♠✐❝r♦❛rr❛②s ♦s ❝✐❡♥t✐st❛s ♣♦❞❡♠ ♠❡❞✐r✱ ❡♠ ✉♠ ú♥✐❝♦ ❡①♣❡r✐♠❡♥t♦✱ ♦s ♥í✈❡✐s ❞❡ ❡①♣r❡ssã♦ ❞❡ ❝❡♥t❡♥❛s ♦✉ ♠✐❧❤❛r❡s ❞❡ ❣❡♥❡s ❞❡♥tr♦ ❞❡ ✉♠❛ ❝é❧✉❧❛✱ t❡❝✐❞♦ ♦✉ ♦r❣❛♥✐s♠♦✱ ♠❡❞✐♥❞♦ ❛ q✉❛♥t✐❞❛❞❡ ❞❡ ❝❉◆❆ q✉❡ s❡ ❤✐❜r✐❞✐③♦✉ ❛ ❝❛❞❛ s♣♦t ❞♦ ❛rr❛② ✭❈❛✉st♦♥ ❡t ❛❧✳✱ ✷✵✵✸✮✳
❖s ❞❛❞♦s ♥✉♠ér✐❝♦s ✭r❡❧❛❝✐♦♥❛❞♦s às ♠❡❞✐❞❛s ❞♦s ♥í✈❡✐s ❞❡ ❡①♣r❡ssã♦ ❞♦s ❣❡♥❡s✮ ♦❜t✐❞♦s sã♦ ♣♦s✐t✐✈♦s ❡ ♣♦ss✉❡♠ ❣r❛♥❞❡ ✈❛r✐❛❜✐❧✐❞❛❞❡✳ P❛r❛ q✉❡ ❛ ❛♥á❧✐s❡ ❡ ✐♥tr❡♣r❡t❛çã♦ ❞♦s ❞❛❞♦s s❡❥❛ ❢❡✐t❛ é ♥❡❝❡ssár✐♦ ♦ ✉s♦ ❞❡ ♠ét♦❞♦s ❡st❛tíst✐❝♦s✳ ❖s ♣r✐♠❡✐r♦s ♠ét♦❞♦s ❡st❛tíst✐❝♦s ❞❡s❝r✐t♦s ♣❛r❛ ❛ ❛♥á❧✐s❡ ❞❡ ❞❛❞♦s ❞❡ ❡①♣r❡ssã♦ ❣ê♥✐❝❛ ❢♦r❛♠ ❞✐s❝✉t✐❞♦s ♣♦r ❙❝❤❡♥❛ ❡t ❛❧✳ ✭✶✾✾✺✮✱ ❙❝❤❡♥❛ ❡t ❛❧✳ ✭✶✾✾✻✮ ❡ ❉❡❘✐s✐ ❡t ❛❧✳ ✭✶✾✾✻✮✳
✶✳ ■♥tr♦❞✉çã♦ ✸
❝♦♠ ❛ ✉t✐❧✐③❛çã♦ ❞♦ t❡st❡ t ❡ ✉♠❛ ❛❜♦r❞❛❣❡♠ ❜❛②❡s✐❛♥❛ ❡ ❊❢r♦♥ ❡t ❛❧✳ ✭✷✵✵✶✮ ❛tr❛✈és
❞❡ ✉♠❛ ❛❜♦r❞❛❣❡♠ ❜❛②❡s✐❛♥❛ ❡♠♣ír✐❝❛✳ ❊st❡s tr❛❜❛❧❤♦s ♣♦ss✉❡♠ ✉♠❛ ❝❛r❛❝t❡ríst✐❝❛ ❡♠ ❝♦♠✉♠✱ q✉❡ é ❛ s✉♣♦s✐çã♦ ❞❡ ♥♦r♠❛❧✐❞❛❞❡ ❛♦s ❞❛❞♦s tr❛♥s❢♦r♠❛❞♦s✳
❖ ♦❜❥❡t✐✈♦ ❞❡st❡ tr❛❜❛❧❤♦ é ✢❡①✐❜✐❧✐③❛r ❡ss❛ s✉♣♦s✐çã♦ ✉t✐❧✐③❛♥❞♦ ❛ ❞✐str✐❜✉✐çã♦ ♥♦r♠❛❧ ❛ss✐♠étr✐❝❛ ✭❆③③❛❧✐♥✐✱ ✶✾✽✺✮✱ q✉❡ ♣♦ss✉✐ ❝♦♠♦ ❝❛s♦ ♣❛rt✐❝✉❧❛r ❛ ❞✐str✐❜✉✐çã♦ ♥♦r✲ ♠❛❧✳
P❛r❛ ❛♥á❧✐s❡ ❞❛ ❡①♣r❡ssã♦ ❣ê♥✐❝❛✱ s❡rã♦ ❝♦♥s✐❞❡r❛❞♦s ❛s s✐t✉❛çõ❡s ❝♦♥tr♦❧❡ ✭♣♦r ❡①❡♠♣❧♦✱ ♠❡❞✐❞❛s ❞❡ ♥í✈❡✐s ❞❡ ❡①♣r❡ssã♦ ❞❛s s♦♥❞❛s ❞❡ ❝❉◆❆✬s ♣r♦✈❡♥✐❡♥t❡s ❞❡ ❝é❧✉❧❛s ♥♦r♠❛✐s✮ ❡ tr❛t❛♠❡♥t♦ ✭♠❡❞✐❞❛s ❞❡ ♥í✈❡✐s ❞❡ ❡①♣r❡ssã♦ ❞❛s s♦♥❞❛s ❞❡ ❝❉◆❆✬s ❡♠ q✉❛❧q✉❡r s✐t✉❛çã♦ ❞✐❢❡r❡♥t❡ ❞♦ ❝♦♥tr♦❧❡✮✳ P♦ré♠✱ ♥❛ ❧✐t❡r❛t✉r❛ é ♣♦ss✐✈❡❧ ❡♥❝♦♥tr❛r ❛ ❛♥á❧✐s❡ ❞❡ ❞❛❞♦s ❞❡ ❡①♣r❡ssã♦ ❣ê♥✐❝❛ ♣❛r❛ ♠❛✐s ❞❡ ❞♦✐s ❣r✉♣♦s✱ ✈❡r ♣♦r ❡①❡♠♣❧♦ ❑❡rr ✫ ❈❤✉r❝❤✐❧❧ ✭✷✵✵✶✮✳
❊st❡ tr❛❜❛❧❤♦ ❡stá ♦r❣❛♥✐③❛❞♦ ❞❛ s❡❣✉✐♥t❡ ❢♦r♠❛✿ ♥♦ ❈❛♣ít✉❧♦ ✷ s❡rá ❞❡t❛❧❤❛❞♦ ♦ ♣r♦❝❡ss♦ ♣❛r❛ ♦❜t❡♥çã♦ ❞❛ ❡①♣r❡ssã♦ ❣ê♥✐❝❛ ❞❡ ✉♠ ❞❡t❡r♠✐♥❛❞♦ ❣❡♥❡❀ ♦ ❈❛♣ít✉❧♦ ✸ ❛♣r❡✲ s❡♥t❛ ❛ ❞✐str✐❜✉✐çã♦ ♥♦r♠❛❧ ❛ss✐♠étr✐❝❛ ❡ ❛❧❣✉♠❛s ❞❡ s✉❛s ♣r♦♣r✐❡❞❛❞❡s ♣r♦❜❛❜✐❧íst✐❝❛s❀ ♥♦ ❈❛♣ít✉❧♦ ✹✱ é r❡❛❧✐③❛❞♦ ✉♠ ❡st✉❞♦ ❞❡ s✐♠✉❧❛çã♦ ✉t✐❧✐③❛♥❞♦ ♦ t❡st❡t♣❛r❛ ❞❡t❡❝t❛r ❞✐❢❡r❡♥ç❛s
❡♥tr❡ ♦s ♥í✈❡✐s ❞❡ ❡①♣r❡ssã♦ ❣ê♥✐❝❛ ❡♠ s✐t✉❛çõ❡s ❞❡ ❝♦♥tr♦❧❡ ❡ tr❛t❛♠❡♥t♦✱ q✉❛♥❞♦ s❡ s✉♣õ❡ q✉❡ ✉♠ ❞♦s ♠❡s♠♦s s❡❣✉❡ ✉♠❛ ❞✐str✐❜✉✐çã♦ ♥♦r♠❛❧ ❛ss✐♠étr✐❝❛✳ ◆❡st❡ ❝❛♣ít✉❧♦ t❛♠❜é♠ é ✈❡r✐✜❝❛❞♦ ♦ ♣♦❞❡r ❞♦ t❡st❡ t✱ ❡ é r❡❛❧✐③❛❞♦ ♦ t❡st❡ t ❝♦♠ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s r❡❛✐s✳
❈❛♣ít✉❧♦ ✷
❊①♣r❡ssã♦ ●ê♥✐❝❛
❆ ❝é❧✉❧❛ é ❛ ♠❡♥♦r ✉♥✐❞❛❞❡ ❞❡ ✈✐❞❛ ♣r❡s❡♥t❡ ❡♠ ✉♠ ♦r❣❛♥✐s♠♦ ❡✱ ❡①✐st❡ ✉♠ ❣r❛♥❞❡ ♥ú♠❡r♦ ❞❡ tr❛♥s❢♦r♠❛çõ❡s q✉í♠✐❝❛s ❡s♣❡❝í✜❝❛s✱ q✉❡ ♥ã♦ ❛♣❡♥❛s ❢♦r♥❡❝❡♠ ❛ ❡♥❡r❣✐❛ ♥❡❝❡ssár✐❛ à ❝é❧✉❧❛ ♠❛s t❛♠❜é♠✱ ❝♦♦r❞❡♥❛ t♦❞♦s ♦s ❡✈❡♥t♦s ❡ ❛t✐✈✐❞❛❞❡s ❞❡♥tr♦ ❞❡❧❛✳ ❖ ♣r♦❝❡ss♦ ❞❛ ✈✐❞❛ ❡♥✈♦❧✈❡ ✉♠❛ ❝♦❧❡çã♦ ❞❡ ♠♦❧é❝✉❧❛s ❞❡s❞❡ ❛ á❣✉❛ à ❝♦♠♣♦st♦s ♦r❣â♥✐❝♦s ✭♣♦r ❡①❡♠♣❧♦✱ ❣♦r❞✉r❛s ❡ ❛çú❝❛r❡s✮✱ ❡ ♠❛❝r♦♠♦❧é❝✉❧❛s ✭❉◆❆ ✲ á❝✐❞♦ ❞❡s♦①✐rr✐❜♦♥✉❝❧❡✐❝♦✱ ♣r♦t❡í♥❛s✱ ❡ ♣♦❧✐s❛❝❛rí❞❡♦s✮ q✉❡ ❞❡✜♥❡♠ ❛ ❡str✉t✉r❛ ❞❛s ❝é❧✉❧❛s✳ ❆s ♠❛❝r♦♠♦❧é❝✉❧❛s ❝♦♥tr♦❧❛♠ ❡ ❣♦✈❡r♥❛♠ ❛ ♠❛✐♦r✐❛ ❞❛s ❛t✐✈✐❞❛❞❡s ♣r❡s❡♥t❡s ❡♠ ✉♠ s❡r ✈✐✈♦✳ ❆s ♠♦❧é❝✉❧❛s ❞❡ ❉◆❆ ❛r♠❛③❡♥❛♠ ✐♥❢♦r♠❛çõ❡s s♦❜r❡ ❛ ❡str✉t✉r❛ ❞❛s ♠❛❝r♦♠♦❧é❝✉❧❛s✱ ♣❡r♠✐t✐♥❞♦ q✉❡ ❡❧❛s s❡❥❛♠ ❢❡✐t❛s✱ ♣r❡❝✐s❛♠❡♥t❡✱ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛s ❡s♣❡❝✐✜❝❛çõ❡s ❡ ♥❡❝❡ss✐❞❛❞❡s ❞❛ ❝é❧✉❧❛ ✭▲❡❡✱ ✷✵✵✹❀ ●r✐✣t❤s ❡t ❛❧✳✱ ✷✵✵✹✮✳
❆s ❝é❧✉❧❛s s♦♠át✐❝❛s ✭r❡s♣♦♥sá✈❡✐s ♣❡❧❛ ❢♦r♠❛çã♦ ❞♦ ❝♦r♣♦ ❞❡ ✉♠ ♦r❣❛♥✐s♠♦✮ ❞❡ q✉❛s❡ t♦❞❛s ❛s ♣❧❛♥t❛s ❡ ❛♥✐♠❛✐s ❝♦♥tê♠ ❞✉❛s ❝ó♣✐❛s ❞❡ s❡✉s r❡s♣❡❝t✐✈♦s ❣❡♥♦♠❛ ❡✱ ♦s ♦r❣❛♥✐s♠♦s ❝♦♠ ❡ss❛ ❝❛r❛❝t❡ríst✐❝❛ sã♦ ❝♦♥❤❡❝✐❞♦s ❝♦♠♦ ❞✐♣❧ó✐❞❡s✳ ❖ ❣❡♥♦♠❛ é ❢♦r♠❛❞♦ ♣♦r ✉♠❛ ♦✉ ♠❛✐s ♠♦❧é❝✉❧❛s ❞❡ ❉◆❆ ❡①tr❡♠❛♠❡♥t❡ ❧♦♥❣❛s✱ q✉❡ sã♦ ♦r❣❛♥✐③❛❞❛s ❡♠ ❝r♦♠♦ss♦♠♦s✳ ■st♦ é✱ ❝❛❞❛ ❝r♦♠♦ss♦♠♦ é ❝♦♠♣♦st♦ ♣♦r ❞✉❛s ❧♦♥❣❛s ✜t❛s ❞❡ ❉◆❆ ❢♦r♠❛♥❞♦ ✉♠❛ ❤é❧✐❝❡ ❞✉♣❧❛✳ ❊♠ ♦r❣❛♥✐s♠♦s ❞✐♣❧ó✐❞❡s✱ ❝❛❞❛ ❝r♦♠♦ss♦♠♦ ❡stá ♣r❡s❡♥t❡ ❡♠ ❞♦❜r♦✳ P♦r ❡①❡♠♣❧♦✱ ❛s ❝é❧✉❧❛s s♦♠át✐❝❛s ❤✉♠❛♥❛s ❝♦♥tê♠ ❞♦✐s ❝♦♥❥✉♥t♦s ❝♦♠♣♦st♦s ♣♦r ✷✸ ❝r♦♠♦ss♦♠♦s✱ r❡s✉❧t❛♥❞♦ ♥✉♠ t♦t❛❧ ❞❡ ✹✻ ❝r♦♠♦ss♦♠♦s✳ ❉♦✐s ❝r♦♠♦ss♦♠♦s ❝♦♠ ❛ ♠❡s♠❛ ❝♦❧❡çã♦ ❞❡ ❣❡♥❡s sã♦ ❝❤❛♠❛❞♦s ❞❡ ❤♦♠ó❧♦❣♦s✳
❆s ✜t❛s ❞❡ ❉◆❆ sã♦ ❝♦♠♣♦st❛s ♣♦r s❡q✉ê♥❝✐❛s ❞❡ ♥✉❝❧❡♦tí❞❡♦s✱ ♦♥❞❡ ❝❛❞❛ ♥✉✲
✷✳ ❊①♣r❡ssã♦ ●ê♥✐❝❛ ✺
❝❧❡♦tí❞❡♦ é ❝♦♠♣♦st♦ ♣♦r ✉♠ ❣r✉♣♦ ❢♦s❢❛t♦✱ ❛çú❝❛r❡s ❡ ✉♠❛ ❞❛s q✉❛tr♦ ❜❛s❡s ♥✐tr♦❣❡♥❛❞❛s ✲ ❛❞❡♥✐♥❛ ✭❆✮✱ t✐♠✐♥❛ ✭❚✮✱ ❝✐t♦s✐♥❛ ✭❈✮ ❡ ❣✉❛♥✐♥❛ ✭●✮✳ P❛r❛ ❞❡s❝r❡✈❡r ♦ ❉◆❆✱ ❜❛st❛ s❛❜❡r ❛ s❡q✉ê♥❝✐❛ ❞❡ ✉♠ ❞❛s ✜t❛s✱ ❛ r❛③ã♦ ♣❛r❛ ❡st❡ ❢❛t♦ é ♦ ♣❛r❡❛♠❡♥t♦ ❞❡ ❜❛s❡s ❝♦♠♣❧❡♠❡♥t❛r❡s✿ ❛ ❜❛s❡ ❆ ❡♠ ✉♠❛ ✜t❛ ❡stá s❡♠♣r❡ ❧✐❣❛❞❛ ✭✈✐❛ ❧✐❣❛çõ❡s ❞❡ ❤✐❞r♦❣ê♥✐♦✮ à ❜❛s❡ ❚ ♥❛ ✜t❛ ♦♣♦st❛✱ ❡♥q✉❛♥t♦ ❈ ❡stá s❡♠♣r❡ ❧✐❣❛❞❛ à ●✳
❆s ♠♦❧é❝✉❧❛s ❞❡ ❉◆❆ sã♦ r❡s♣♦♥sá✈❡✐s ♣❡❧❛ ❝♦♥✈❡rsã♦ ❞❛ ✐♥❢♦r♠❛çã♦ ♥❡❝❡ssár✐❛ ♣❛r❛ ❛ ♣r♦❞✉çã♦ ❞❡ ♣r♦t❡í♥❛s ♦✉ ♠♦❧é❝✉❧❛s ❞❡ ❘◆❆ ✭á❝✐❞♦ r✐❜♦♥✉❝❧❡✐❝♦✮ ❡♥❝♦♥tr❛❞❛s ❡♠ ✉♠ ♦r❣❛♥✐s♠♦✳ ❊ss❡ ♣r♦❝❡ss♦✱ ♣♦❞❡ s❡r ❞❡s❝r✐t♦ ♥♦s ♣❛ss♦s ❛ s❡❣✉✐r ✭❈r✐❝❦✱ ✶✾✼✵✮✿
• ❘❡♣❧✐❝❛çã♦✿ ❛ ✐♥❢♦r♠❛çã♦ ❝♦♥t✐❞❛ ♥♦ ❉◆❆ é ❞✉♣❧✐❝❛❞❛✱ ❝♦♥s❡r✈❛♥❞♦ ❛ ✐♥❢♦r♠❛çã♦
❣❡♥ét✐❝❛✳
• ❚r❛♥s❝r✐çã♦✿ ♣❡r♠✐t❡ ❛ ♣❛ss❛❣❡♠ ❞❛ ✐♥❢♦r♠❛çã♦ ❝♦♥t✐❞❛ ♥♦ ❉◆❆ ♣❛r❛ ♦ ❘◆❆
♠❡♥ss❛❣❡✐r♦ ✭♠❘◆❆✮✱ ❛tr❛✈és ❞♦ ❡♠♣❛r❡❧❤❛♠❡♥t♦ ❞❡ ❜❛s❡s ❝♦♠♣❧❡♠❡♥t❛r❡s✱ ❝♦♠ ❡①❝❡çã♦ ❞❡ ✉♠❛ ❜❛s❡ ♣♦✐s✱ ♥♦ ❘◆❆ ❛ ❜❛s❡ t✐♠✐♥❛ ✭❚✮ é s✉❜st✐t✉í❞❛ ♣❡❧❛ ❜❛s❡ ✉r❛❝✐❧❛ ✭❯✮✳
• ❚r❛❞✉çã♦✿ ♣♦ss✐❜✐❧✐t❛ ❛ sí♥t❡s❡ ❞❡ ♣r♦t❡í♥❛s ♠❡❞✐❛♥t❡ ❛ ✐♥❢♦r♠❛çã♦ ❝♦♥t✐❞❛ ♥♦
♠❘◆❆✳
❆s ♣r♦t❡í♥❛s✱ ♣♦r s✉❛ ✈❡③✱ ❛t✉❛♠ ❞❡ ❢♦r♠❛ ✈✐t❛❧ ♣❛r❛ ♦ ❢✉♥❝✐♦♥❛♠❡♥t♦ ❞❛s ❝é❧✉❧❛s✳ P♦ré♠✱ ♥♦ ♣r♦❝❡ss♦ ❞❡ tr❛❞✉çã♦✱ ❛♣❡♥❛s ❛❧❣✉♠❛s ♣❛rt❡s ❞♦s ❣❡♥❡s ✲ ♦s ❡①♦♥s ✲ sã♦ ♥❡❝❡ssár✐❛s✳ ➱ ♣♦r ✐ss♦✱ q✉❡ ♥♦ ♣r♦❝❡ss♦ ❞❡ tr❛♥s❝r✐çã♦✱ ♦s ✐♥tr♦♥s ✲ ♣❛rt❡s ♥ã♦ ❝♦❞✐✜❝❛♥t❡s ❞♦s ❣❡♥❡s ✲ sã♦ r❡♠♦✈✐❞♦s ❛tr❛✈és ❞♦ ❘◆❆✲s♣❧✐❝✐♥❣ ✭❥✉♥çã♦ ❞♦ ❘◆❆✮✳ ◆♦ ❡♥t❛♥t♦✱ ♦s ♠❡s♠♦s ❡①♦♥s ♥❡♠ s❡♠♣r❡ sã♦ ❝♦♥s❡r✈❛❞♦s✳ ❊♥tã♦✱ ❞✐❢❡r❡♥t❡s ❝♦♠❜✐♥❛çõ❡s ❞♦s ❡①♦♥s ❞❡ ✉♠ ❣❡♥❡✱ ♣♦❞❡♠ s❡r ✉♥✐❞❛s ♣❛r❛ ♣r♦❞✉③✐r ❞✐❢❡r❡♥t❡s ♠❘◆❆s✱ q✉❡ ♣♦❞❡♠ ❧❡✈❛r ❛ sí♥t❡s❡ ❞❡ ❞✐❢❡r❡♥t❡s ♣r♦t❡í♥❛s✳ ❆❝r❡❞✐t❛✲s❡ q✉❡ ❝❡r❝❛ ❞❡ ✻✵ ✪ ❞♦s ❣❡♥❡s sã♦ ❛❢❡t❛❞♦s ♣♦r ❡ss❛ ✉♥✐ã♦ ❞♦ ❘◆❆ ✭♣❛r❛ ♠❛✐s ❞❡t❛❧❤❡s ✈❡r✱ ❙❝❤✇❡♥❞❡r ❡t ❛❧✳✱ ✷✵✵✻❀ ●r✐✣t❤s ❡t ❛❧✳✱ ✷✵✵✹❀ ❩❤❛♥❣✱ ✷✵✵✻✮✳
✷✳ ❊①♣r❡ssã♦ ●ê♥✐❝❛ ✻
♣❛rt✐r ❞✐ss♦✱ é ♣♦ssí✈❡❧ ❡st✉❞❛r ♦ q✉❡ ❛❝♦♥t❡❝❡ ❡♠ ✉♠ ❡st❛❞♦ ❛❧t❡r❛❞♦ ❞♦ ❣❡♥❡✱ ❝♦♠♦ ♣♦r ❡①❡♠♣❧♦✱ ❝â♥❝❡r✳
✷✳✶ ▼❡❞✐♥❞♦ ❊①♣r❡ssã♦ ●ê♥✐❝❛
❯♠❛ ❞❛s ♣r✐♥❝✐♣❛✐s ❢❡rr❛♠❡♥t❛s ♣❛r❛ ♦ ❡st✉❞♦ ❞❛ ❡①♣r❡ssã♦ ❣ê♥✐❝❛ sã♦ ♦s ❛rr❛♥❥♦s ❞❡ ❉◆❆ ✭❉◆❆ ❛rr❛②✮ ♦✉ ♠✐❝r♦❛rr❛②s ✭♠✐❝r♦❛rr❛♥❥♦s✮✳ ❖s ♠✐❝r♦❛rr❛②s t♦r♥❛♠ ♣♦ssí✈❡❧ ❛ q✉❛♥t✐✜❝❛çã♦ ❞❛ ❡①♣r❡ssã♦ ❣ê♥✐❝❛✱ ♠❡❞✐♥❞♦ ❛ ❤✐❜r✐❞✐③❛çã♦ ♦✉ ❝♦♠❜✐♥❛çã♦ ❞♦ ❉◆❆ ✜①❛❞♦ ❡♠ ✉♠❛ ♣❡q✉❡♥❛ ❧â♠✐♥❛ ❞❡ ✈✐❞r♦✱ ♣❧ást✐❝♦ ♦✉ ♠❡❜r❛♥❞❛ ❞❡ ♥②❧♦♥✱ ❛♦ ♠❘◆❆ r❡❢❡r❡♥t❡ ❛ ❛♠♦str❛ s♦❜ ❡st✉❞♦✳ ❉❡ss❛ ❢♦r♠❛✱ ❛ t❡❝♥♦❧♦❣✐❛ ❞❡ ♠✐❝r♦❛rr❛② ♣❡r♠✐t❡ q✉❡ ♦ ♥í✈❡❧ ❞❡ ❡①♣r❡ssã♦ ❞❡ ♠✐❧❤❛r❡s ❞❡ ❣❡♥❡s ❝♦♥t✐❞♦s ♥♦ ❣❡♥♦♠❛ ♣♦ss❛ s❡r ♠❡❞✐❞♦ s✐♠✉❧t❛♥❡❛♠❡♥t❡ ✭▼ü❧❧❡r ✫ ◆✐❝♦❧❛✉✱ ✷✵✵✹❀ ▲❡❡✱ ✷✵✵✹✮✳ ❚❛❧ ❤❛❜✐❧✐❞❛❞❡ ♣❛r❛ ♠❡❞✐r s✐♠✉❧t❛♥❡❛♠❡♥t❡ ❣r❛♥❞❡s ♣r♦♣♦rçõ❡s ❞❡ ❣❡♥❡s ♥♦ ❣❡♥♦♠❛✱ ❛❜r❡ ❛s ♣♦rt❛s ♣❛r❛ ❛ ✐♥✈❡st✐❣❛çã♦ ❞❡ ✐t❡r❛çõ❡s ❡♥tr❡ ♦s ❣❡♥❡s ♥✉♠❛ ❣r❛♥❞❡ ❡s❝❛❧❛✱ ♣❡r♠✐t✐♥❞♦ ❛ ❞❡s❝♦❜❡rt❛ ❞♦ ♣❛♣❡❧ ❞❡s❡♠♣❡♥❤❛❞♦ ♣❡❧♦s ❣❡♥❡s ❝✉❥❛s ❢✉♥çõ❡s ❛✐♥❞❛ sã♦ ❞❡s❝♦♥❤❡❝✐❞❛s✳
❊①✐st❡♠ ❞✐❢❡r❡♥t❡s t❡❝♥♦❧♦❣✐❛s ❞❡ ♠✐❝r♦❛rr❛②s✱ ❡♥tr❡ ❡❧❛s ❡stã♦ ♦s ❛rr❛♥❥♦s ❞❡ ❝❉◆❆ ❡ ♦s ❛rr❛♥❥♦s ❞❡ ♦❧✐❣♦♥✉❝❧❡♦tí❞❡♦s✳ ❊♠❜♦r❛ ♦ ♦❜❥❡t✐✈♦ ❞❡ ❛♠❜❛s ❛s t❡❝♥♦❧♦❣✐❛s s❡❥❛ ❛ ❤✐❜r✐❞✐③❛çã♦✱ ❡❧❛s ❞✐❢❡r❡♠ ♥♦ ♠♦❞♦ ❡♠ q✉❡ ❛s s❡q✉ê♥❝✐❛s ❞❡ ❉◆❆ sã♦ ❝♦❧♦❝❛❞❛s ♥♦ ❛rr❛② ❡ ♥♦ t❛♠❛♥❤♦ ❞❡ss❛s s❡q✉ê♥❝✐❛s✳ ❙♦❜❡❦ ❡t ❛❧✳ ✭✷✵✵✻✮ ❡ ❍♦❤❡✐s❡❧ ✭✷✵✵✻✮ ❞❡s❝r❡✈❡♠ ❡♠ ❞❡t❛❧❤❡s ❛s ❛t✉❛✐s t❡❝♥♦❧♦❣✐❛s ❞❡ ♠✐❝r♦❛rr❛②s ❡ s✉❛s ❞✐❢❡r❡♥t❡s ❛♣❧✐❝❛çõ❡s ♥♦s ❞✐❛s ❛t✉❛✐s✳
◆♦s ♠✐❝r♦❛rr❛②s ❞❡ ❝❉◆❆✱ ♦ ♠❘◆❆ ❞❡ ❞✉❛s ❛♠♦str❛s ❜✐♦❧ó❣✐❝❛s ❞✐❢❡r❡♥t❡s ✭♣♦r ❡①❡♠♣❧♦✱ ❝♦♥tr♦❧❡ ❡ tr❛t❛♠❡♥t♦✮ é tr❛♥s❝r✐t♦ ❞❡ ♠♦❞♦ r❡✈❡rs♦ ❡♠ ❝❉◆❆✱ ♠❛r❝❛❞♦ ❝♦♠ ❞✐❢❡r❡♥t❡s ✢✉♦r❡s❝ê♥❝✐❛s ✭♥❡st❡ ❝❛s♦✱ ✈❡r❞❡ ❡ ✈❡r♠❡❧❤♦✮ ❡ ❡♥tã♦✱ ❝♦❧♦❝❛❞♦ ♥❛ ❧â♠✐♥❛ ❞❡ ✈✐❞r♦ ♦♥❞❡ é ❤✐❜r✐❞✐③❛❞♦ ❛s s❡q✉ê♥❝✐❛s ❞❡ ❉◆❆ ♣r❡s❡♥t❡s ♥❛ ♠❡s♠❛✳ ❆♣ós ❛ ❤✐❜r✐❞✐③❛çã♦✱ ❛ ❧â♠✐♥❛ é ❡s❝❛♥❡❛❞❛ ♠❡❞✐♥❞♦ ❛ ✐♥t❡♥s✐❞❛❞❡ ❞❛ ✢✉♦r❡s❝ê♥❝✐❛ ❞❡ ❝❛❞❛ ❝♦r✱ ✉♠❛ ♠❛✐♦r ✢✉♦r❡s❝ê♥❝✐❛ ✐♥❞✐❝❛ ✉♠❛ q✉❛♥t✐❞❛❞❡ ♠❛✐♦r ❞❡ ❝❉◆❆ ❤✐❜r✐❞✐③❛❞♦✱ ♦✉ s❡❥❛✱ ✐♥❞✐❝❛ ✉♠❛ ❡①♣r❡ssã♦ ❣ê♥✐❝❛ ♠❛✐♦r ♥❛ ❛♠♦str❛✳ ❯♠❛ ❞❡s❝r✐çã♦ ♠❛✐s ❞❡t❛❧❤❛❞❛ s♦❜r❡ ♦s ♠✐❝r♦❛rr❛②s ❞❡ ❝❉◆❆ ♣♦❞❡ s❡r ❡♥❝♦♥tr❛❞❛ ❡♠ ❙❝❤❡♥❛ ❡t ❛❧✳ ✭✶✾✾✺✮ ❡ ❉❡❘✐s✐ ❡t ❛❧✳ ✭✶✾✾✻✮✳
✷✳ ❊①♣r❡ssã♦ ●ê♥✐❝❛ ✼
té❝♥✐❝❛s ❡st❛tíst✐❝❛s ♥❛ ❛♥á❧✐s❡ ❞♦s ♠❡s♠♦s✳
✷✳✶✳✶ ❊t❛♣❛s ❞❛ Pr❡♣❛r❛çã♦ ❞♦s ▼✐❝r♦❛rr❛②s ❞❡ ❝❉◆❆
❖ ♣r♦❝❡ss♦ ♣❛r❛ ❛ ❢❛❜r✐❝❛çã♦ ❞♦ ♠✐❝r♦❛rr❛② ❞❡ ❝❉◆❆ ❡ ❛ ♦❜t❡♥çã♦ ❞♦s ❞❛❞♦s ♣❛r❛ ❛ ❛♥á❧✐s❡ ♣♦❞❡ s❡r ❞❡s❝r✐t♦ ♣♦r✿
✶✳ ❋❛❜r✐❝❛çã♦ ❞♦ ❛rr❛♥❥♦✿ r♦❜♦t✐❝❛♠❡♥t❡ é ❢❡✐t❛ ❛ ❞❡♣♦s✐çã♦ ❞❡ s❡q✉ê♥❝✐❛s ❞❡ ❝❉◆❆ ❝♦♥❤❡❝✐❞❛s ❡♠ ♣♦s✐çõ❡s ❡s♣❡❝í✜❝❛s ❞❡ ✉♠❛ ❧â♠✐♥❛ ❞❡ ✈✐❞r♦❀
✷✳ Pr❡♣❛r❛çã♦ ❞❛s ❛♠♦str❛s ❜✐♦❧ó❣✐❝❛s ❛ s❡r❡♠ ❡st✉❞❛❞❛s✱ ✉♠❛ ❝♦rr❡s♣♦♥❞❡♥t❡ à s✐t✉✲ ❛çã♦ ♣❛❞rã♦ ♦✉ ❝♦♥tr♦❧❡ ❡ ❛ ♦✉tr❛ ❝♦rr❡s♣♦♥❞❡♥t❡ à s✐t✉❛çã♦ q✉❡ s❡ ❞❡s❡❥❛ ❡st✉❞❛r ✭tr❛t❛♠❡♥t♦✮✳
✸✳ ❊①tr❛çã♦ ❞♦ ♠❘◆❆ ❞❡ ❝❛❞❛ ❛♠♦str❛✳
✹✳ ▼❛r❝❛çã♦ ❞♦ ♠❘◆❆✿ ❛tr❛✈és ❞❡ tr❛♥s❝r✐çã♦ r❡✈❡rs❛ ❛ ❛♠♦str❛ ❝♦♥tr♦❧❡ é ♠❛r❝❛❞❛ ❝♦♠ ❝✐❛♥✐♥❛ ✸ ✭❈②✸✮ ✲ ✈❡r❞❡ ✲ ✢✉♦r❡s❝❡♥t❡ ❡ ❛ ❛♠♦str❛ ❞♦ tr❛t❛♠❡♥t♦ é ♠❛r❝❛❞❛ ❝♦♠ ❝✐❛♥✐♥❛ ✺ ✭❈②✺✮ ✲ ✈❡r♠❡❧❤♦ ✲ ✢✉♦r❡s❝❡♥t❡❀
✺✳ ❆♠❜❛s ❛s ❛♠♦str❛s sã♦ ❝♦❧♦❝❛❞❛s ♥♦ ♠✐❝r♦❛rr❛②✱ r❡s✉❧t❛♥❞♦ ♥❛ ❤✐❜r✐❞✐③❛çã♦ ❞❛s ♠❡s♠❛s ❝♦♠ ❛s s❡q✉ê♥❝✐❛s ❞❡ ❝❉◆❆ ❝♦♥t✐❞❛s ♥♦ ❛rr❛♥❥♦✳
✻✳ ➱ ❢❡✐t♦ ♦ ❡s❝❛♥❡❛♠❡♥t♦ ❞♦ ♠✐❝r♦❛rr❛② ❤✐❜r✐❞✐③❛❞♦✳
✷✳ ❊①♣r❡ssã♦ ●ê♥✐❝❛ ✽
❋■●❯❘❆ ✷✳✶✿ ❊①♣❡r✐♠❡♥t♦ ❝♦♠ ❛rr❛♥❥♦s ❞❡ ❉◆❆✳
❖s ❞❛❞♦s ♦❜t✐❞♦s ❛tr❛✈és ❞❡ ❡①♣❡r✐♠❡♥t♦s ❞❡ ♠✐❝r♦❛rr❛② ♣♦ss✉❡♠ ❞✉❛s ❝❛r❛❝✲ t❡ríst✐❝❛s ❜ás✐❝❛s✱ ♦ s✐❣♥✐✜❝❛❞♦ ❜✐♦❧ó❣✐❝♦ ❡ ♦ s✐❣♥✐✜❝❛❞♦ ❡st❛tíst✐❝♦✳ ❖ s✐❣♥✐✜❝❛❞♦ ❜✐♦❧ó❣✐❝♦ é ♦ q✉❡ ✐♥t❡r❡ss❛ ❛♦s ♣❡sq✉✐s❛❞♦r❡s ❡ ♠♦str❛ ♦ q✉❛♥t♦ ❛ ❡①♣r❡ssã♦ ❞❡ ✉♠ ❣❡♥❡ é ✐♥✢✉✲ ❡♥❝✐❛❞❛ ♣❡❧❛ ❝♦♥❞✐çã♦ s♦❜ ❡st✉❞♦✳ ❏á ♦ s✐❣♥✐✜❝❛❞♦ ❡st❛tíst✐❝♦ ♠♦str❛ ♦ q✉ã♦ ❝♦♥✜á✈❡❧ é ♦ s✐❣♥✐✜❝❛❞♦ ❜✐♦❧ó❣✐❝♦✳ ❉❡✈✐❞♦ ❛s ❣r❛♥❞❡s ❢♦♥t❡s ❞❡ ✈❛r✐❛çã♦ ♥♦s ❡①♣❡r✐♠❡♥t♦s ❞❡ ♠✐❝r♦❛rr❛② ✭❑❡rr ✫ ❈❤✉r❝❤✐❧❧✱ ✷✵✵✶❀ ❩❤❛♥❣✱ ✷✵✵✻✮✱ ❛ ❛♥á❧✐s❡ ❡st❛tíst✐❝❛ é ❝r✉❝✐❛❧ ♣❛r❛ ♦ s✉❝❡ss♦ ♥❛ ✐♥t❡r♣r❡t❛çã♦ ❞♦ ❢❡♥ô♠❡♥♦ ❜✐♦❧ó❣✐❝♦ s♦❜ ❡st✉❞♦✳ P♦r ❡ss❛ r❛③ã♦✱ é ♥❡❝❡ssár✐❛ ❛ ❝♦♠♣r❡❡♥sã♦ ❞♦ ❢♦r♠❛t♦ ❞♦s ❞❛❞♦s ❞❡ ♠✐❝r♦❛rr❛②✱ ♦✉ s❡❥❛✱ s❛❜❡r ✐♥t❡r♣r❡tá✲❧♦s ♣❛r❛ q✉❡ ✉♠❛ ❛♥á❧✐s❡ ❡st❛tíst✐❝❛ s✐❣♥✐✜❝❛t✐✈❛ s❡❥❛ ❢❡✐t❛✳
❖ ❡st✉❞♦ ❞❡ ❞❛❞♦s ❞❡ ❡①♣r❡ssã♦ ❣ê♥✐❝❛ ♣♦❞❡♠ ❡♥✈♦❧✈❡r ❛s s❡❣✉✐♥t❡s ❡t❛♣❛s✿
• ❆ ✐❞❡♥t✐✜❝❛çã♦ ❞❡ ❣❡♥❡s ❞✐❢❡r❡♥❝✐❛❧♠❡♥t❡ ❡①♣r❡ss♦s✱ ✐st♦ é✱ ❣❡♥❡s ❝✉❥♦ ♦ ♥í✈❡❧ ❞❡
❡①♣r❡ssã♦ ❞✐❢❡r❡ ❢♦rt❡♠❡♥t❡ ❡♥tr❡ ❣r✉♣♦s ✭♣♦r ❡①❡♠♣❧♦✱ ❝â♥❝❡r ✈❡rs✉s ♥ã♦ ❝â♥❝❡r✮✳
• ❊♥❝♦♥tr❛r ❣❡♥❡s ❝✉❥♦s ♥í✈❡✐s ❞❡ ❡①♣r❡ssã♦ ✈❛r✐❛♠ ❥✉♥t♦s ✭❣r✉♣♦s ❞❡ ❣❡♥❡s ✲ ❝❧✉st❡r✐♥❣
❣❡♥❡s✮✳
• ❈♦♥str✉✐r ✉♠❛ r❡❣r❛ ❞❡ ❝❧❛ss✐✜❝❛çã♦ ❜❛s❡❛❞❛ ♥♦s ❞❛❞♦s ❞❡ ❡①♣r❡ssã♦ ❣ê♥✐❝❛✱ ♣❛r❛
✷✳ ❊①♣r❡ssã♦ ●ê♥✐❝❛ ✾
❆♥t❡s ❞❡ ✐♥✐❝✐❛r q✉❛❧q✉❡r ✉♠❛ ❞❡ss❛s ❛♥á❧✐s❡s é ♥❡❝❡ssár✐♦ ♣r♦❝❡ss❛r ♦s ❞❛❞♦s ❣❡r❛❞♦s ♥♦ ❡①♣❡r✐♠❡♥t♦ ❞❡ ♠✐❝r♦❛rr❛②✳ ❖s ❞❛❞♦s ❞❡ ❡①♣r❡ssã♦ ❣ê♥✐❝❛ ♦❜t✐❞♦s ♣♦r ❛rr❛♥❥♦s ❞❡ ❝❉◆❆ ♦✉ ❛rr❛♥❥♦s ❞❡ ♦❧✐❣♦♥✉❝❧❡♦tí❞❡♦s sã♦ s✐♠✐❧❛r❡s ❡♠ ❢♦r♠❛t♦✳ ❊①✐st❡♠ ❞✐✈❡rs♦s s♦❢t✇❛r❡s ✭❝♦♠❡r❝✐❛✐s ❡ ❧✐✈r❡s✮ q✉❡ tê♠ ❞✐s♣♦♥í✈❡❧ ♣❛❝♦t❡s ♣❛r❛ ❛ ❛♥á❧✐s❡ ❞❛s ✐♠❛❣❡♥s ❡ q✉❛♥t✐✜❝❛çã♦ ❞♦s ♥í✈❡✐s ❞❡ ❡①♣r❡ssã♦✳ ❉❡ ♠♦❞♦ ❣❡r❛❧✱ ♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s sã♦ ❝♦♠♣♦st♦s ♣♦r ♠❛tr✐③❡s q✉❡ ✐♥❝❧✉❡♠ ❛ ❧♦❝❛❧✐③❛çã♦ ❞♦s s♣♦ts ✭♣♦♥t♦s✮ ♥♦ ♠✐❝r♦❛rr❛②✱ ✐❞❡♥t✐❞❛❞❡ ❞♦s ❣❡♥❡s✱ ♠é❞✐❛ ❡ ♠❡❞✐❛♥❛ ❞❛ ✐♥t❡♥s✐❞❛❞❡ ❞♦s ♣✐①❡❧s ❞❡♥tr♦ ❞❡ ❝❛❞❛ s♣♦t ❡ ✐♥t❡♥s✐❞❛❞❡s ❧♦❝❛✐s ❞♦s ❜❛❝❦❣r♦✉♥❞s ✭r❡❣✐õ❡s ❡♥tr❡ ♣♦♥t♦s✮✳
❆ ❤✐❜r✐❞✐③❛çã♦ s✐♠✉❧tâ♥❡❛ ❞❡ ❞✉❛s ❛♠♦str❛s ❞✐❢❡r❡♥t❡s r♦t✉❧❛❞❛s ❝♦♠ ♠❛r❝❛❞♦r❡s ❈②✸ ✭✈❡r❞❡✮ ❡ ❈②✺ ✭✈❡r♠❡❧❤♦✮ r❡q✉❡r ✉♠❛ ❛♥á❧✐s❡ ❡s♣❡❝✐❛❧✳ ❖s ❞♦✐s ♠❛r❝❛❞♦r❡s tê♠ ❞✐❢❡r❡♥t❡s ♣r♦♣r✐❡❞❛❞❡s ❡ s❡♥s✐✈✐❞❛❞❡s à ❧✉③✳ ❆ ❡♠✐ssã♦ ❞❡ ✢✉♦r❡s❝ê♥❝✐❛ ❞♦ ♠❛r❝❛❞♦r ❈②✺ t❡♠ ♠❡♥♦r ✐♥t❡♥s✐❞❛❞❡✱ ♣♦r ✐ss♦ ♦s s✐♥❛✐s ❞❡ ✢✉♦r❡s❝ê♥❝✐❛ ❞♦s ❞♦✐s ♠❛r❝❛❞♦r❡s tê♠ q✉❡ s❡r ✏♥♦r♠❛❧✐③❛❞♦s✑ ✭❈❛✉st♦♥ ❡t ❛❧✳✱ ✷✵✵✸❀ ▲❡❡✱ ✷✵✵✹✮✳
❖ ♣r♦♣ós✐t♦ ❞❛ ♥♦r♠❛❧✐③❛çã♦✱ é ♠✐♥✐♠✐③❛r ❛ ✈❛r✐❛çã♦ ♥❛s ♠❡❞✐❞❛s ❞♦s ♥í✈❡✐s ❞❡ ❡①♣r❡ssã♦ ❞❛s ❛♠♦str❛s ❞❡ ♠❘◆❆ ❤✐❜r✐❞✐③❛❞❛s✱ ❞❡ t❛❧ ♠♦❞♦ q✉❡✱ ❛s ❞✐❢❡r❡♥ç❛s ❜✐♦❧ó❣✐❝❛s ✭❞✐❢❡r❡♥ç❛s ♥❛ ❡①♣r❡ssã♦ ❣ê♥✐❝❛✮ ♣♦ss❛♠ s❡r ♠❡❧❤♦r ❞✐st✐♥❣✉✐❞❛s✳ P❛r❛ ♠❛✐♦r❡s ❞❡t❛❧❤❡s s♦❜r❡ ♦ ♣r♦❝❡ss♦ ❞❡ ♥♦r♠❛❧✐③❛çã♦ ❞♦s ❞❛❞♦s ❞❡ ❡①♣r❡ssã♦ ❣ê♥✐❝❛ ✈❡r✱ ▲❡❡ ✭✷✵✵✹✮❀ ❩❤❛♥❣ ✭✷✵✵✻✮❀ ❈❛✉st♦♥ ❡t ❛❧✳ ✭✷✵✵✸✮ ❡ ❑❡rr ✫ ❈❤✉r❝❤✐❧❧ ✭✷✵✵✶✮✳
✷✳✶✳✷ ❚r❛♥s❢♦r♠❛çã♦ ❞♦s ❉❛❞♦s
▼❡s♠♦ ❛♣ós ❛ ♥♦r♠❛❧✐③❛çã♦✱ ❛s ♠❡❞✐❞❛s ❞♦s ♥í✈❡✐s ❞❡ ❡①♣r❡ssã♦ ♥ã♦ ♣♦ss✉❡♠ ♥❡✲ ❝❡ss❛r✐❛♠❡♥t❡ ♣r♦♣r✐❡❞❛❞❡s ❡st❛tíst✐❝❛s ❞❡s❡❥❛❞❛s✱ ❝♦♠♦ ♣♦r ❡①❡♠♣❧♦✱ ✈❛r✐â♥❝✐❛ ❝♦♥st❛♥t❡ ❡ ♥♦r♠❛❧✐❞❛❞❡✳ P♦r ❡ss❛ r❛③ã♦✱ ❛ tr❛♥❢♦r♠❛çã♦ ❞♦s ❞❛❞♦s é ✐♠♣♦rt❛♥t❡✳ ◆❡st❛ s✉❜s❡çã♦✱ s❡rã♦ ❛❜♦r❞❛❞❛s ❛❧❣✉♠❛s tr❛♥s❢♦r♠❛çõ❡s q✉❡ tê♠ s❡ ♠♦str❛❞♦ út❡✐s ♥❛ ❛♥á❧✐s❡ ❞❡ ❞❛❞♦s ❞❡ ♠✐❝r♦❛rr❛② ✭♣❛r❛ ♠❛✐s ❞❡t❛❧❤❡s✱ ▲❡❡✱ ✷✵✵✹✮✳
❆❧❣✉♥s ▼ét♦❞♦s ❞❡ ❚r❛♥s❢♦r♠❛çã♦ ❞♦s ❉❛❞♦s
• ❚r❛♥s❢♦r♠❛çã♦ ❧♦❣❛rít♠✐❝❛✿
➱ ❛ tr❛♥s❢♦r♠❛çã♦ ♠❛✐s ❝♦♠✉♠ ❛♣❧✐❝❛❞❛ ❛♦s ❞❛❞♦s ❞❡ ❡①♣r❡ssã♦ ❣ê♥✐❝❛✱
✷✳ ❊①♣r❡ssã♦ ●ê♥✐❝❛ ✶✵
♦♥❞❡ i= 1,2, . . . , G é r❡❢❡r❡♥t❡ ❛♦ ❣❡♥❡ ❡♠ q✉❡stã♦ ❡ j = 1,2, . . . , n é ♦ ♥ú♠❡r♦ ❞❡
♦❜s❡r✈❛çõ❡s ♣❛r❛ ❝❛❞❛ ❣❡♥❡✳ ❖ ❧♦❣❛r✐t♠♦ ✉t✐❧✐③❛❞♦ ♣♦❞❡ s❡r ♥❛ ❜❛s❡ ✷✱ ✶✵ ♦✉ ♥❛ ❜❛s❡ e ✭❧♦❣❛r✐t♠♦ ♥❛t✉r❛❧✮✳
• ❚r❛♥s❢♦r♠❛çã♦ ❞❛ r❛✐③ q✉❛❞r❛❞❛✿
◆♦r♠❛❧♠❡♥t❡ é ✉t✐❧✐③❛❞❛ ♣❛r❛ ❡st❛❜✐❧✐③❛r ❛ ✈❛r✐â♥❝✐❛ ❞♦s ❞❛❞♦s✱ ✐st♦ é✱ ❛ ✈❛r✐â♥❝✐❛ t❡♥❞❡rá ❛ s❡r ✉♠❛ ❝♦♥st❛♥t❡
yij =√xij,
♦♥❞❡ i= 1,2, . . . , G é r❡❢❡r❡♥t❡ ❛♦ ❣❡♥❡ ❡♠ q✉❡stã♦ ❡ j = 1,2, . . . , n é ♦ ♥ú♠❡r♦ ❞❡
♦❜s❡r✈❛çõ❡s ♣❛r❛ ❝❛❞❛ ❣❡♥❡✳
• ❚r❛♥s❢♦r♠❛çã♦ ❞❡ ❇♦①✲❈♦①✿
❆s tr❛♥s❢♦r♠❛çõ❡s ❛♥t❡r✐♦r❡s sã♦ ❞♦✐s ♠❡♠❜r♦s ❞❛ ❢❛♠í❧✐❛ ❞❡ tr❛♥s❢♦r♠❛çõ❡s ❇♦①✲ ❈♦①✱ q✉❡ é ❞❡✜♥✐❞❛ ♣♦r✿
yij =
xd ij −1
d ,
♦♥❞❡ i = 1,2, . . . , G é r❡❢❡r❡♥t❡ ❛♦ ❣❡♥❡ ❡♠ q✉❡stã♦✱ j = 1,2, . . . , n é ♦ ♥ú♠❡r♦
❞❡ ♦❜s❡r✈❛çõ❡s ♣❛r❛ ❝❛❞❛ ❣❡♥❡ ❡ d = 1
2✱ ❝♦rr❡s♣♦♥❞❡♥❞♦ ❛ tr❛♥s❢♦r♠❛çã♦ ❞❛ r❛✐③
q✉❛❞r❛❞❛✳ ❖ ❧✐♠✐t❡ ❞❛ ❢✉♥çã♦ yij✱ q✉❛♥❞♦ d → 0 ❝♦rr❡s♣♦♥❞❡ ❛ tr❛♥s❢♦r♠❛çã♦
❧♦❣❛rít♠✐❝❛✳ ◗✉❛♥❞♦ d = 1✱ ♥❡♥❤✉♠❛ tr❛♥s❢♦r♠❛çã♦ é ❛❞♦t❛❞❛✱ ❡①❝❡t♦ ♣♦r ✉♠ ♣❡q✉❡♥♦ ❞❡s❧♦❝❛♠❡♥t♦✳
✷✳✶✳✸ ❚é❝♥✐❝❛s ❊st❛tíst✐❝❛s P❛r❛ ❛ ❆♥á❧✐s❡ ❞❡ ❉❛❞♦s ❞❡ ❊①♣r❡ssã♦
●ê♥✐❝❛
❆t✉❛❧♠❡♥t❡✱ é ♣♦ssí✈❡❧ ❡♥❝♦♥tr❛r ❞✐✈❡rs♦s ❛rt✐❣♦s q✉❡ ✉t✐❧✐③❛♠ ❞✐❢❡r❡♥t❡s ♠ét♦❞♦s ❡st❛tíst✐❝♦s ♣❛r❛ ❛ ❛♥á❧✐s❡ ❞❡ ❞❛❞♦s ❞❡ ❡①♣r❡ssã♦ ❣ê♥✐❝❛✱ ❡♥tr❡ ❡❧❡s✿
• ❚❡st❡ t✿ ✉t✐❧✐③❛✲s❡ ♦ t❡st❡ t ♣❛r❛ ✈❡r✐✜❝❛r s❡ ❛s ♠é❞✐❛s ❞♦s ✈❛❧♦r❡s ❞❡ ✐♥t❡♥s✐❞❛❞❡
♦❜t✐❞♦s ♣❛r❛ ♦ ❝♦♥tr♦❧❡ ❡ ♣❛r❛ ♦ tr❛t❛♠❡♥t♦ ❞❡ ✉♠ ❞❡t❡r♠✐♥❛❞♦ ❣❡♥❡g sã♦ ✐❣✉❛✐s✱
✐st♦ é ♣❛r❛ ✈❡r✐✜❝❛r s❡ ❤á ❞✐❢❡r❡♥ç❛ ♥♦ ♥í✈❡❧ ❞❡ ❡①♣r❡ssã♦ ♦❜t✐❞♦ ♣❛r❛ ♦ ❝♦♥tr♦❧❡ ❡ ♦ tr❛t❛♠❡♥t♦ ♣❛r❛ ❝❛❞❛ ❣❡♥❡✳ ❆rt✐❣♦s ❝♦♠♦ ♦s ❞❡ ❇❛❧❞✐ ✫ ▲♦♥❣ ✭✷✵✵✶✮ ❡ ❞❡ ▼❡♥❡③❡s ❡t ❛❧✳ ✭✷✵✵✹✮ ✉t✐❧✐③❛♠ ♦ t❡st❡ t ❡✴♦✉ ✈❛r✐❛çõ❡s ❞♦ ♠❡s♠♦✱ ♣❛r❛ ✈❡r✐✜❝❛r s❡ ❡①✐st❡
✷✳ ❊①♣r❡ssã♦ ●ê♥✐❝❛ ✶✶
• ❆❜♦r❞❛❣❡♠ ❇❛②❡s✐❛♥❛✿ ✉♠❛ ❛❧t❡r♥❛t✐✈❛ ❛♦s ♠ét♦❞♦s ❝❧áss✐❝♦s✱ é ♣♦ssí✈❡❧ ❡♥❝♦♥✲
tr❛r ♥❛ ❧✐t❡r❛t✉r❛ ❞✐✈❡rs♦s ❛rt✐❣♦s q✉❡ ✉t✐❧✐③❛♠ ❛❜♦r❞❛❣❡♠ ❇❛②❡s✐❛♥❛ ♣❛r❛ ❛♥❛❧✐✲ s❛r ❞❛❞♦s ❞❡ ❡①♣r❡ssõ❡s ❣ê♥✐❝❛✱ ❝♦♠♦ ❊❢r♦♥ ❡t ❛❧✳ ✭✷✵✵✶✮✱ q✉❡ tr❛❜❛❧❤❛ ❝♦♠ ✉♠❛ ❛❜♦r❞❛❣❡♠ ❜❛②❡s✐❛♥❛ ❡♠♣ír✐❝❛✱ ❡ ❙❛r❛✐✈❛ ✭✷✵✵✻✮✱ q✉❡ ❡♠ s❡✉ tr❛❜❛❧❤♦ ✉t✐❧✐③❛ ❞✐✲ ✈❡rs♦s ♠ét♦❞♦s ❡st❛tíst✐❝♦s✱ ❡♥tr❡ ❡❧❡s ✉♠❛ ❛❜♦r❞❛❣❡♠ ❜❛②❡s✐❛♥❛ ♣❛r❛♠étr✐❝❛ ❡ ♥ã♦ ♣❛r❛♠étr✐❝❛✳
• ❆♥á❧✐s❡ ❞❡ ❈❧✉st❡r✿ té❝♥✐❝❛ ❞❡ ❝❧❛ss✐✜❝❛çã♦ ❞❡ ♦❜❥❡t♦s ♦✉ ✐♥❞✐✈í❞✉♦s ❡♠ ❞✐❢❡r❡♥t❡s
❣r✉♣♦s✳ ▼❛✐s ♣r❡❝✐s❛♠❡♥t❡✱ é ✉♠❛ té❝♥✐❝❛ q✉❡ ♣❛rt✐❝✐♦♥❛ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s ❡♠ s✉❜❝♦♥❥✉♥t♦s ♦✉ ❣r✉♣♦s✱ ❞❡ t❛❧ ❢♦r♠❛ q✉❡ ♦s ❡❧❡♠❡♥t♦s ❡♠ ❝❛❞❛ ❝❧✉st❡r t❡♥❤❛♠ ✉♠❛ ♦✉ ♠❛✐s ❝❛r❛❝t❡ríst✐❝❛s ❡♠ ❝♦♠✉♠✱ q✉❡ ❡st❡❥❛♠ ♣ró①✐♠♦s s❡❣✉♥❞♦ ✉♠❛ ♠❡❞✐❞❛ ❞❡ ❞✐stâ♥❝✐❛ ❞❡✜♥✐❞❛✳ ❊ss❛ té❝♥✐❝❛ ❛♣❧✐❝❛❞❛ ❛ ❞❛❞♦s ❞❡ ❡①♣r❡ssã♦ ❣ê♥✐❝❛ ♣♦❞❡ s❡r ✈✐st❛ ❡♠ ❑✉r✐❛❦♦s❡ ❡t ❛❧✳ ✭✷✵✵✹✮✳
❖✉tr❛s té❝♥✐❝❛s ❡♥✈♦❧✈❡♠ ❛♥á❧✐s❡ ❞❡ ❝♦♠♣♦♥❡♥t❡s ♣r✐♥❝✐♣❛✐s ❡ ❛♥á❧✐s❡ ❢❛t♦r✐❛❧✳
✷✳✷ ❈♦♥s✐❞❡r❛çõ❡s ❋✐♥❛✐s
❈❛♣ít✉❧♦ ✸
❆ ❉✐str✐❜✉✐çã♦ ◆♦r♠❛❧ ❆ss✐♠étr✐❝❛
❆ ❛♥á❧✐s❡ ❡st❛tíst✐❝❛ ♣❛r❛ ♦ ❡st✉❞♦ ❞❡ ❞❛❞♦s ❝♦♥tí♥✉♦s t❡♠ s✐❞♦ ❞❡s❡♥✈♦❧✈✐❞❛✱ ❡♠ ❣r❛♥❞❡ ♣❛rt❡✱ ❝♦♠ ❜❛s❡ ♥♦ ♠♦❞❡❧♦ ♥♦r♠❛❧✳ ◆♦ ❡♥t❛♥t♦✱ ❛ s✉♣♦s✐çã♦ ❞❡ s✐♠❡tr✐❛ ♣❛r❛ ♦s ❞❛❞♦s ♣♦❞❡ ❢❛③❡r ❝♦♠ q✉❡ s❡❥❛♠ ❢❡✐t❛s ✐♥❢❡rê♥❝✐❛s ♣♦✉❝♦ ❛♣r♦♣r✐❛❞❛s s♦❜r❡ ♦s ♣❛râ♠❡tr♦s ❞❡ ✐♥t❡r❡ss❡✳ ❯♠❛ ❛❧t❡r♥❛t✐✈❛ ♣❛r❛ ❡ss❛ s✐t✉❛çã♦ s❡r✐❛ ✢❡①✐❜✐❧✐③❛r ❛ s✉♣♦s✐çã♦ ❞❡ ♥♦r♠❛❧✐❞❛❞❡✱ ❝♦♥s✐❞❡r❛♥❞♦ ✉♠❛ ❝❧❛ss❡ ❞❡ ❞✐str✐❜✉✐çõ❡s ❛ss✐♠étr✐❝❛s q✉❡ ♣♦ss✉✐ ❝♦♠♦ ❝❛s♦ ♣❛rt✐❝✉❧❛r ❛ ❞✐str✐❜✉✐çã♦ ♥♦r♠❛❧✳
❊♠❜♦r❛ ❛ ❞✐str✐❜✉✐çã♦ ♥♦r♠❛❧ s❡❥❛ ♦ ♠♦❞❡❧♦ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ♠❛✐s ✉t✐❧✐③❛❞♦ ❡♠ ❡st❛tíst✐❝❛✱ ❡①✐st❡♠ ♠✉✐t♦s ❢❡♥ô♠❡♥♦s q✉❡ ♥ã♦ ♣♦❞❡♠ s❡r ❞❡s❝r✐t♦s ♣❡❧❛ ❞✐str✐❜✉✐çã♦ ♥♦r♠❛❧ ❡ ♥❡♠ ♣♦r ❞✐str✐❜✉✐çõ❡s s✐♠étr✐❝❛s✳ ❆♣❧✐❝❛çõ❡s ❞❡ ❞✐str✐❜✉✐çõ❡s ❛ss✐♠étr✐❝❛s sã♦ ❝♦♠✉♠❡♥t❡ ❡♥❝♦♥tr❛❞❛s ❡♠ ❞✐✈❡rs❛s ár❡❛s✱ t❛✐s ❝♦♠♦✿ ❝✐ê♥❝✐❛s ❛t✉ár✐❛s✱ ❞❡♠♦❣r❛✜❛✱ ❡❝♦♥♦♠✐❛✱ ❡♥❣❡♥❤❛r✐❛✱ ❝✐ê♥❝✐❛ ❛♠❜✐❡♥t❛❧✱ ✜♥❛♥ç❛s ❡ ❝✐ê♥❝✐❛s ♠é❞✐❝❛s ✭✈❡r✱ ❏♦❤♥s♦♥ ❡t ❛❧✳✱ ✶✾✾✹✱ ✶✾✾✺❀ ❙❡s❤❛❞r✐✱ ✶✾✾✾✮✳
❆ ❞✐str✐❜✉✐çã♦ ♥♦r♠❛❧ ❛ss✐♠étr✐❝❛ ✭s❦❡✇✲♥♦r♠❛❧✮ ❢♦✐ ❢♦r♠❛❧♠❡♥t❡ ✐♥tr♦❞✉③✐❞❛ ♣♦r ❆③③❛❧✐♥✐ ✭✶✾✽✺✮✳ ❆ ♣❛rt✐r ❞❡ ❡♥tã♦✱ ❛s ♣r♦♣r✐❡❞❛❞❡s ♣r♦❜❛❜✐❧íst✐❝❛s ❞❡ss❛ ❞✐str✐❜✉✐çã♦ ❢♦r❛♠ ❛♠♣❧❛♠❡♥t❡ ❡st✉❞❛❞❛s✳ ❊♠ ❆r❡❧❧❛♥♦✲❱❛❧❧❡ ✫ ❆③③❛❧✐♥✐ ✭✷✵✵✻✮ é ❛♣r❡s❡♥t❛❞❛ ❛ ♣❛r❛♠❡tr✐③❛çã♦ ❝❡♥tr❛❞❛ ❞❡ss❛ ❞✐str✐❜✉✐çã♦✱ ❝♦rr✐❣✐♥❞♦ ♦ ♣r♦❜❧❡♠❛ ❞❡ s✐♥❣✉❧❛r✐❞❛❞❡ ❞❛ ♠❛tr✐③ ❞❡ ✐♥❢♦r♠❛çã♦ ❞❡ ❋✐s❤❡r q✉❛♥❞♦ ♦ ♣❛râ♠❡tr♦ ❞❡ ❛ss✐♠❡tr✐❛ é ♥✉❧♦✳ ❖ ❛rt✐❣♦ ❞❡ ❆r❡❧❧❛♥♦✲❱❛❧❧❡ ✫ ❆③③❛❧✐♥✐ ✭✷✵✵✻✮ ♠♦str❛ ❛ ❝♦rr❡❧❛çã♦ ✭✉♥✐✜❝❛çã♦✮ ❞❛s ❞✐✈❡rs❛s ♣r♦♣♦st❛s ♦r✐❣✐♥❛❞❛s ♥♦ ❞❡❝♦rr❡r ❞♦s ❛♥♦s✱ ♣❛r❛ ♦ ❝❛s♦ ♠✉❧t✐✈❛r✐❛❞♦ ❞❛ ❞✐str✐❜✉✐çã♦ ♥♦r♠❛❧ ❛s✲ s✐♠étr✐❝❛✳
✸✳ ❆ ❉✐str✐❜✉✐çã♦ ◆♦r♠❛❧ ❆ss✐♠étr✐❝❛ ✶✸
❉❡✈✐❞♦ à s✉❛ ❝♦♥tí♥✉❛ ✈❛r✐❛çã♦ ❞❡ ♥♦r♠❛❧✐❞❛❞❡ ♣❛r❛ ♥ã♦ ♥♦r♠❛❧✐❞❛❞❡✱ ❡ ♣♦r s❡r ♠❛t❡♠❛t✐❝❛♠❡♥t❡ tr❛tá✈❡❧✱ ❡st❛ ❞✐str✐❜✉✐çã♦ t❡♠ s✐❞♦ ❛♣❧✐❝❛❞❛ ❛ ❞✐✈❡rs❛s ár❡❛s ✭✈❡r ♣♦r ❡①❡♠♣❧♦✱ P♦✉r❛❤♠❛❞✐✱ ✷✵✵✼❀ ●❤♦s❤ ❡t ❛❧✳✱ ✷✵✵✻✮✳
◆❡st❡ ❝❛♣ít✉❧♦✱ é ❛♣r❡s❡♥t❛❞❛ ✉♠❛ r❡✈✐sã♦ ❞❛ ❞✐str✐❜✉✐çã♦ ♥♦r♠❛❧ ❛ss✐♠étr✐❝❛ ❝♦♥s✐❞❡r❛♥❞♦ ❞✉❛s r❡♣r❡s❡♥t❛çõ❡s✱ ✉♠❛ ❢♦r♠❛❧♠❡♥t❡ ✐♥tr♦❞✉③✐❞❛ ♣♦r ❆③③❛❧✐♥✐ ✭✶✾✽✺✮ ❡ ♦✉tr❛ ♣♦r ❍❡♥③❡ ✭✶✾✽✻✮✱ ♦ q✉❛❧ ♦❜té♠ ❛ ❞❡♥s✐❞❛❞❡ ♣r♦♣♦st❛ ♣♦r ❆③③❛❧✐♥✐ ❛tr❛✈és ❞❡ tr❛♥s❢♦♠❛çã♦ ❞❡ ✈❛r✐á✈❡✐s✱ ♦♥❞❡ ❛ ✈❛r✐á✈❡❧ ❡♠ q✉❡stã♦ é ♦❜t✐❞❛ ❝♦♠♦ ❝♦♠❜✐♥❛çã♦ ❧✐♥❡❛r ❞❡ ✈❛r✐á✈❡✐s ❛❧❡❛tór✐❛s ✐♥❞❡♣❡♥❞❡♥t❡s✳ ❙❡rã♦ ❛♣r❡s❡♥t❛❞❛s t❛♠❜é♠ ❛❧❣✉♠❛s ♣r♦♣r✐❡❞❛❞❡s ❡ ♠ét♦❞♦s ❞❡ ✐♥❢❡rê♥❝✐❛ ♣❛r❛ ♦s ♣❛râ♠❡tr♦s ❞❡ss❛ ❞✐str✐❜✉✐çã♦✳
✸✳✶ ❉❡✜♥✐çã♦ ❡ Pr♦♣r✐❡❞❛❞❡s
◆❡st❛ ❙❡çã♦ s❡rã♦ ❞❡s❝r✐t❛s ❛ ❞✐str✐❜✉✐çã♦ ♥♦r♠❛❧ ❛ss✐♠étr✐❝❛ ❡ s✉❛s ♣r♦♣r✐❡❞❛❞❡s✳
❉❡✜♥✐çã♦✿ ❯♠❛ ✈❛r✐á✈❡❧ ❛❧❡❛tór✐❛Z t❡♠ ❞✐str✐❜✉✐çã♦ ♥♦r♠❛❧ ❛ss✐♠étr✐❝❛ ♣❛❞rã♦
❝♦♠ ♣❛râ♠❡tr♦ ❞❡ ❛ss✐♠❡tr✐❛λ✱ ❞❡♥♦t❛❞❛ ♣♦r SN(λ)✱ s❡ s✉❛ ❞❡♥s✐❞❛❞❡ é ❞❛❞❛ ♣♦r
f(z) = 2φ(z)Φ(λz), z∈ ℜ, ✭✸✳✶✮
♦♥❞❡ λ é ✉♠ ✈❛❧♦r ❞❡✜♥✐❞♦ ❡♠ ℜ✱ ❡ φ(.) ❡ Φ(.) ❞❡♥♦t❛♠ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ❛ ❢✉♥çã♦ ❞❡♥s✐❞❛❞❡ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❡ ❛ ❢✉♥çã♦ ❞❡ ❞✐str✐❜✉✐çã♦ ❛❝✉♠✉❧❛❞❛ ❞❛ ❞✐str✐❜✉✐çã♦ ♥♦r♠❛❧ ♣❛❞rã♦✳
❆ ❋✐❣✉r❛ ✸✳✶ ♠♦str❛ ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❡ f(z) ♣❛r❛ ❞✐❢❡r❡♥t❡s ✈❛❧♦r❡s ❞❡ λ✱ ❡ é
❢á❝✐❧ ♥♦t❛r q✉❡ ❛ ❞✐str✐❜✉✐çã♦ ♥♦r♠❛❧ ♣❛❞rã♦ ❡stá ✐♥❝❧✉í❞❛ ❝♦♠♦ ❝❛s♦ ♣❛rt✐❝✉❧❛r ❞❛ ♥♦r♠❛❧ ❛ss✐♠étr✐❝❛ ♣❛❞rã♦ q✉❛♥❞♦λ= 0✳
❆ ❢✉♥çã♦ ❞❡ ❞✐str✐❜✉✐çã♦ ❛❝✉♠✉❧❛❞❛ ✭❢❞❛✮ ❞❛ ♥♦r♠❛❧ ❛ss✐♠étr✐❝❛ ♣❛❞rã♦ ❞❡♥♦t❛❞❛ ♣♦r F(z;λ) é ❞❛❞❛ ♣♦r
F(z;λ) = 2
Z z
−∞
Z λt
−∞
φ(t)Φ(u)dudt. ✭✸✳✷✮
✸✳ ❆ ❉✐str✐❜✉✐çã♦ ◆♦r♠❛❧ ❆ss✐♠étr✐❝❛ ✶✹
❋■●❯❘❆ ✸✳✶✿ ●rá✜❝♦ ❞❛ ❞❡♥s✐❞❛❞❡ ♥♦r♠❛❧ ❛ss✐♠étr✐❝❛ ♣❛❞rã♦ ♣❛r❛ ✈❛❧♦r❡s ❞✐❢❡r❡♥t❡s ❞❡
λ✳
Pr♦♣r✐❡❞❛❞❡s
✶✳ SN(0) é ✐❣✉❛❧ à N(0,1)✳
✷✳ ❙❡ Z ∼SN(λ)❡♥tã♦ Y =|Z| ∼HN(0,1)✱ ♦♥❞❡HN(0,1)r❡♣r❡s❡♥t❛ ❛ ❞✐str✐❜✉✐çã♦ ❞❡♥♦♠✐♥❛❞❛ ❤❛❧❢✲♥♦r♠❛❧ ❝♦♠ ❞❡♥s✐❞❛❞❡ ❞❛❞❛ ♣♦r f(y) = 2φ(y)I[y>0](y)✳
✸✳ ❙❡ Z ∼SN(λ) ❡♥tã♦ q✉❛♥❞♦ λ→∞✱ Z →D HN(0,1)✳
✹✳ ❙❡ Z ∼SN(λ) ❡♥tã♦ −Z ∼SN(−λ)✳
✺✳ ❙❡ Z ∼SN(λ) ❡♥tã♦ ❛ ❢❞♣ ❞❡ ❩ é ✉♥✐♠♦❞❛❧ ❡logf(z)é ✉♠❛ ❢✉♥çã♦ ❝ô♥❝❛✈❛✳
✸✳ ❆ ❉✐str✐❜✉✐çã♦ ◆♦r♠❛❧ ❆ss✐♠étr✐❝❛ ✶✺
✼✳ F(z,1) ={Φ(z)}2✳
✽✳ ❙❡ Z ∼SN(λ) ❡♥tã♦ Z2 ∼χ2 1✳
✸✳✷ ❉✐str✐❜✉✐çã♦ ◆♦r♠❛❧ ❆ss✐♠étr✐❝❛ ❝♦♠ ♣❛râ♠❡tr♦s
❞❡ ❧♦❝❛çã♦ ❡ ❡s❝❛❧❛
❉❡✜♥✐çã♦✿ ❯♠❛ ✈❛r✐á✈❡❧ ❛❧❡❛tór✐❛ Y t❡♠ ❞✐str✐❜✉✐çã♦ ♥♦r♠❛❧ ❛ss✐♠étr✐❝❛ ✭Y ∼ SN(µ, σ, λ)✮ ❝♦♠ ♣❛râ♠❡tr♦ ❞❡ ❛ss✐♠❡tr✐❛ λ✱ ♣❛râ♠❡tr♦ ❞❡ ❧♦❝❛çã♦ µ ❡ ♣❛râ♠❡tr♦ ❞❡
❡s❝❛❧❛ σ ✭σ >0✮ s❡ s✉❛ ❞❡♥s✐❞❛❞❡ é ❞❛❞❛ ♣♦r
f(y) = 21
σφ
y−µ σ Φ λ
y−µ σ
, y ∈ ℜ ✭✸✳✸✮
♦♥❞❡φ(.)❡Φ(.)❞❡♥♦t❛♠ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ❛ ❢✉♥çã♦ ❞❡♥s✐❞❛❞❡ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❡ ❛ ❢✉♥çã♦ ❞❡ ❞✐str✐❜✉✐çã♦ ❛❝✉♠✉❧❛❞❛ ❞❛ ❞✐str✐❜✉✐çã♦ ♥♦r♠❛❧ ♣❛❞rã♦✳
◆♦t❡ q✉❡ s❡ Z ∼ SN(λ) ❡ Y = µ+ σZ✱ ❡♥tã♦ Y ∼ SN(µ, σ, λ)✳ ❖✉ s❡❥❛✱
q✉❛❧q✉❡r ❝♦♠❜✐♥❛çã♦ ❧✐♥❡❛r ❞❡ ✉♠❛ ✈❛r✐á✈❡❧ ❛❧❡❛tór✐❛ ♥♦r♠❛❧ ❛ss✐♠étr✐❝❛ ♣❛❞rã♦ t❛♠❜é♠ t❡rá ❞✐str✐❜✉✐çã♦ ♥♦r♠❛❧ ❛ss✐♠étr✐❝❛✳
Pr♦♣r✐❡❞❛❞❡s
✾✳ ❙❡ Y ∼SN(µ, σ, λ) ❡♥tã♦ X =a+bY ∼SN(a+bµ, bσ, λ)✱a, b∈ ℜ✳
✶✵✳ ❆ ❢✉♥çã♦ ❣❡r❛❞♦r❛ ❞❡ ♠♦♠❡♥t♦s ❞❡ Y é ❞❛❞❛ ♣♦r
My(t) = 2 exp
(t−µ)2
2σ2
Φ
δ
y−µ σ
, ✭✸✳✹✮
♦♥❞❡ δ= √λ
1+λ2✳
✶✶✳ ❆ ♠é❞✐❛ ❞❡ Y é ❞❛❞❛ ♣♦r
E(Y) = µ+σδ
r
2
π ✭✸✳✺✮
✶✷✳ ❆ ✈❛r✐â♥❝✐❛ ❞❡ Y é ❞❛❞❛ ♣♦r
V ar(Y) =σ2
1− 2
πδ
2
