❊①t❡♥sõ❡s ❡♠ ♠♦❞❡❧♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛
❝♦♠ ❢r❛çã♦ ❞❡ ❝✉r❛ ❡ ❡❢❡✐t♦s ❛❧❡❛tór✐♦s
❉✐❡❣♦ ■❣♥❛❝✐♦ ●❛❧❧❛r❞♦ ▼❛t❡❧✉♥❛
❚❡s❡ ❛♣r❡s❡♥t❛❞❛
❛♦
■♥st✐t✉t♦ ❞❡ ▼❛t❡♠át✐❝❛ ❡ ❊st❛tíst✐❝❛
❞❛
❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦
♣❛r❛
♦❜t❡♥çã♦ ❞♦ tít✉❧♦
❞❡
❉♦✉t♦r ❡♠ ❈✐ê♥❝✐❛s
Pr♦❣r❛♠❛✿ ❊st❛tíst✐❝❛
❖r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❉r✳ ❍❡❧❡♥♦ ❇♦❧❢❛r✐♥❡
❈♦♦r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❉r✳ ❆♥t♦♥✐♦ ❈❛r❧♦s P❡❞r♦s♦ ❞❡ ▲✐♠❛
❉✉r❛♥t❡ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡st❡ tr❛❜❛❧❤♦ ♦ ❛✉t♦r r❡❝❡❜❡✉ ❛✉①í❧✐♦ ✜♥❛♥❝❡✐r♦ ❞❡ ❈♦♥✐❝②t ✭❈♦♠✐s✐ó♥ ◆❛❝✐♦♥❛❧ ❞❡ ■♥✈❡st✐❣❛❝✐ó♥✱ ❈✐❡♥❝✐❛ ② ❚❡❝♥♦❧♦❣í❛ ✲ ❈❤✐❧❡✮
❊①t❡♥sõ❡s ❡♠ ♠♦❞❡❧♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛
❝♦♠ ❢r❛çã♦ ❞❡ ❝✉r❛ ❡ ❡❢❡✐t♦s ❛❧❡❛tór✐♦s
❊st❛ t❡s❡ ❝♦♥té♠ ❛s ❝♦rr❡çõ❡s ❡ ❛❧t❡r❛çõ❡s s✉❣❡r✐❞❛s ♣❡❧❛ ❈♦♠✐ssã♦ ❏✉❧❣❛❞♦r❛ ❞✉r❛♥t❡ ❛ ❞❡❢❡s❛ r❡❛❧✐③❛❞❛ ♣♦r ❉✐❡❣♦ ■❣♥❛❝✐♦ ●❛❧❧❛r❞♦ ▼❛t❡❧✉♥❛ ❡♠ ✵✸✴✵✷✴✷✵✶✹✳ ❖ ♦r✐❣✐♥❛❧ ❡♥❝♦♥tr❛✲s❡ ❞✐s♣♦♥í✈❡❧ ♥♦ ■♥st✐t✉t♦ ❞❡ ▼❛t❡♠át✐❝❛ ❡ ❊st❛tíst✐❝❛ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦✳
❈♦♠✐ssã♦ ❏✉❧❣❛❞♦r❛✿
❼ Pr♦❢✳ ❉r✳ ❍❡❧❡♥♦ ❇♦❧❢❛r✐♥❡ ✭♦r✐❡♥t❛❞♦r✮ ✲ ■▼❊✲❯❙P ❼ Pr♦❢✳ ❉r✳ ❆♥t♦♥✐♦ ❈❛r❧♦s P❡❞r♦s♦ ❞❡ ▲✐♠❛ ✲ ■▼❊✲❯❙P ❼ Pr♦❢✳ ❉r✳ ▼ár✐♦ ❞❡ ❈❛str♦ ❆♥❞r❛❞❡ ❋✐❧❤♦ ✲ ■❈▼❈✲❯❙P ❼ Pr♦❢✳ ❉r✳ ❋r❛♥❝✐s❝♦ ▲♦✉③❛❞❛ ◆❡t♦ ✲ ■❈▼❈✲❯❙P
❆❣r❛❞❡❝✐♠❡♥t♦s
❆ ❉❡✉s✱ ♣♦r ❢❛③❡r ♠❡✉ ❝❛♠✐♥❤♦ tã♦ ❡①♣❡❞✐t♦ ❡♠ t♦❞♦ ♠♦♠❡♥t♦✳ P♦r ❞❛r✲♠❡ s❛ú❞❡ ❡ ❛ ❢♦rç❛ ♥❡❝❡ssár✐❛ ❡♠ t♦❞♦s ❡st❡s ❛♥♦s ❞❡ ❉♦✉t♦r❛♠❡♥t♦✳
❆❣r❛❞❡ç♦ ❛♦s ♠❡✉s ♣❛✐s✱ q✉❡ ♠❡s♠♦ ♥ã♦ ❡♥t❡♥❞❡♥❞♦ ♠✉✐t♦ ❜❡♠ ♦ q✉❡ é ❊st❛tíst✐❝❛ ♥❡♠ ♦ q✉❡ é ✉♠ ❉♦✉t♦r❛❞♦✱ s❡♥t❡♠ ♦r❣✉❧❤♦ ❞♦ q✉❡ ❢❛ç♦✳ ❆❣r❛❞❡ç♦ ❡ss❡ ❛♠♦r ❡ ❛♣♦✐♦ ✐♥❝♦♥❞✐❝✐♦♥❛❧✱ ❡♠❜♦r❛ t✐✈❡r♠♦s ✉♠ ♣❛r ❞❡ ❦✐❧ó♠❡tr♦s ❞❡ ❞✐stâ♥❝✐❛ ❞✉r❛♥t❡ ♠❡✉ ❉♦✉t♦r❛❞♦✳ ✭❉✐❣❛♠♦s✱ ✉♥s ✷✳✻✵✵ ❦✐❧ó♠❡✲ tr♦s✮✳ ❚❛♠❜✐é♥ ❛❣r❛❞❡③❝♦ ❛ ❧❛ ❲❡❧②✱ ♣♦r s✉ ❝♦♥st❛♥t❡ ♣r❡♦❝✉♣❛❝✐ó♥ ♣♦r ♠í✳ ▲♦s ❛♠♦ ❛ t♦❞♦s✳
❆♦ ♣r♦❢❡ss♦r ❍❡❧❡♥♦✱ ♣♦r t❡r ❛❝❡✐t❛❞♦ ♦r✐❡♥t❛r✲♠❡ ❡ ♣❡❧❛s ✈❛❧✐♦s❛s s✉❣❡stõ❡s ❛♦ ❧♦♥❣♦ ❞❡st❡ tr❛✲ ❜❛❧❤♦✳ ❙❡♠ ❞ú✈✐❞❛✱ ❡st❡ tr❛❜❛❧❤♦ t❡✈❡ ✉♠❛ ❛❜♦r❞❛❣❡♠ ❞✐❢❡r❡♥t❡ ❝♦♠ s✉❛ ❝♦♥tr✐❜✉✐çã♦✳
❆❣r❛❞❡ç♦ ❛♦ ❆♥t♦♥✐♦ ❈❛r❧♦s ♣❡❧❛ ♣❛❝✐ê♥❝✐❛ ♥♦s ♠♦♠❡♥t♦s ♠❛✐s ❞✐❢í❝❡✐s ❞✉r❛♥t❡ ♦ ❞❡s❡♥✈♦❧✈✐✲ ♠❡♥t♦ ❞❡st❡ tr❛❜❛❧❤♦ ❡ ♣❡❧❛ ♠♦t✐✈❛çã♦ ❛ s❡❣✉✐r tr❛❜❛❧❤❛♥❞♦ ❝♦♥st❛♥t❡♠❡♥t❡✳ ❆❣r❛❞❡ç♦ t❛♠❜é♠ ❛s ❝♦♥tr✐❜✉✐çõ❡s ♠❡t♦❞♦❧ó❣✐❝❛s ❡ ♣♦r s❡♠♣r❡ s❡r ♠✉✐t♦ ❝rít✐❝♦ ❝♦♠✐❣♦✳
➪ ❜❛♥❝❛ ❥✉❧❣❛❞♦r❛✱ ♣♦r ❧❡r ❡ ❝♦rr❡❣✐r ❡st❛ ✈❡rsã♦ ❞❛ t❡s❡✳ ❈❡rt❛♠❡♥t❡ s✉❛s s✉❣❡stõ❡s ♠❡❧❤♦r❛r❛♠ ❛ ❛♣r❡s❡♥t❛çã♦ ❞❡st❡ tr❛❜❛❧❤♦✳
●✐s❡❧❛ t❛♠❜é♠ ♠❡r❡❝❡ ✉♠❛ ♠❡♥çã♦ ♥❡st❛ ♣á❣✐♥❛✱ ♣♦r t❡r✲♠❡ ❛❥✉❞❛❞♦ ❡♠ q✉❡stõ❡s ❜✉r♦❝rát✐❝❛s ♥❛ ♠✐♥❤❛ ❝❤❡❣❛❞❛ ❡♠ ❙ã♦ P❛✉❧♦ ❡ ♣❡❧❛ ♦r✐❡♥t❛çã♦ ❡♠ r❡❧❛çã♦ à ♠✉❞❛♥ç❛ ❞❡ ♦r✐❡♥t❛❞♦r✳ ❈❡rt❛♠❡♥t❡ ❛ s✉❣❡stã♦ ❞♦ ❆♥t♦♥✐♦ ❈❛r❧♦s ❢♦✐ ❛❝❡rt❛❞❛✳
❆ ♠✐ ♣♦❧♦❧❛ ② ❛♠✐❣❛ ❨♦❧❛♥❞❛✳ P♦r ♠❛♥t❡♥❡r ♠✐ ❝♦r❞✉r❛ ❡♥ ❛q✉❡❧❧♦s ♠♦♠❡♥t♦s ♠ás ❞✐❢í❝✐❧❡s✳ P♦r ❧❛ ♣❛❝✐❡♥❝✐❛✳ P♦r t✉ ❛♠♦r ② ❛♣♦②♦✳ ❙✐♥ ❞✉❞❛✱ ❧❛ ✜♥❛❧✐③❛❝✐ó♥ ❞❡ ❡st❡ tr❛❜❛❥♦ ❤✉❜✐❡s❡ s✐❞♦ ♠✉❝❤♦ ♠ás ❛❜✉rr✐❞❛ ② ❞✐❢í❝✐❧ s✐♥ t✉ ♣r❡s❡♥❝✐❛✳
➚ t✉r♠❛ ❞❡ ❛♠✐❣♦s ❝❤✐❧❡♥♦s ❛q✉✐ ❡♠ ❙ã♦ P❛✉❧♦✿ ❆❧✈❛r♦ ❈❡r❞❛✱ ▼ó♥✐❝❛ P❛✈❡③✱ ❈❛r❧♦s ▼♦♥✲ t❡♥❡❣r♦✱ ▼❛♥✉❡❧ ●♦♥③á❧❡③✱ ◆❛t❛❧✐❛ ▼✐❧❧❛✱ ❆♥❞rés ❉♦♥♦s♦✱ ❆❧❡❥❛♥❞r❛ ❚❛♣✐❛✱ P❡❞r♦ ❈♦rtés✱ ▼❛r❝♦ ❘✐q✉❡❧♠❡✱ ❈r✐st✐❛♥ ❱✐❧❧❡❣❛s✱ ◆✐❧t♦♥ ▲✐♥❝♦♣❛♥✱ ▼❛r✐t③❛ ❋❛rí❛s ❡ ▼✐❣✉❡❧ ▼✉rú❛✳ ❚❡r ✉♠❛ ♣❛rt❡ ❞♦ ♠❡✉ q✉❡r✐❞♦ ❈❍■▲❊ ❛q✉✐ ❡♠ ❙ã♦ P❛✉❧♦ ❛❥✉❞♦✉ ♥❛q✉❡❧❡s ♠♦♠❡♥t♦s ❞❡ s❛✉❞❛❞❡ ♠á①✐♠❛✳
❆❣r❛❞❡ç♦ t❛♠❜é♠ à t✉r♠❛ ❞❡ ❛♠✐❣♦s ❞♦ ■▼❊✿ ❚✐❛❣♦ ▼❛❣❛❧❤ã❡s✱ ❆❧❞♦ ▼❡❞✐♥❛✱ ❋r❛♥❝②❡❧❧❡ ▲✐♠❛✱ ❊❧✐s❛ ●♦♥③á❧❡③✱ ▲✐♥❛ ❚❤♦♠❛s✱ ❏♦r❣❡ ❚♦rr❡❥ó♥✱ ❊❧✐❛r❞♦ ●✉✐♠❛rã❡s✱ ♣❡❧♦s ❣r❛t♦s ♠♦♠❡♥t♦s ❝♦♠♣❛r✲ t✐❧❤❛❞♦s ❡ ♣❡❧❛s ❞✐s❝✉ssõ❡s ♥❛s ❞✐❢❡r❡♥t❡s ❞✐s❝✐♣❧✐♥❛s ❝✉rs❛❞❛s ❡♠ ❝♦♥❥✉♥t♦✳
◆ã♦ ♣♦ss♦ ❞❡✐①❛r ❞❡ ❛❣r❛❞❡❝❡r t❛♠❜é♠ ❛♦s ♠❡✉s ❛♠✐❣♦s q✉❡ ✜❝❛r❛♠ ♥♦ ❈❤✐❧❡✿ ❇❛st✐❛♥ P❛❧❛✲
✐✐
❝✐♦s✱ ▼❛r✐❛ ❆♥❣é❧✐❝❛ ❋✉❡♥t❡s✱ ■r♠❛ ❈♦r♦♥❛❞♦✱ ◆❛t❛❧② ❖❧✐✈❛r❡s✱ ❈❛r♦❧✐♥❛ ❆❣✉✐❧❛r✱ ▼✐r❦♦ ❆r❛♥❞❛✱ ❏❛✐♠❡ ●ó♠❡③✱ ❍✉❣♦ P❡r❛❧t❛ ❡ ❘♦♥② P❛❧❛❝✐♦s✳ ❙✉❛s ♠❡♥s❛❣❡♥s ❞❡ ❛♣♦✐♦ ❡ ❧♦♥❣❛s ❝♦♥✈❡rs❛s s❡♠♣r❡ ❛❧❡❣r❛r❛♠ ♠❡✉s ❞✐❛s✳
❆♦ P❡♣❡✱ ♣♦r ❞❛r✲♠❡ ❡ss❛ ♠♦t✐✈❛çã♦ ✐♥✐❝✐❛❧ ♥❡❝❡ssár✐❛ ♣❛r❛ ❝✉rs❛r ♠❡✉s ❡st✉❞♦s ❞❡ ❉♦✉t♦r❛❞♦✳ ❊st❛r❡✐ ❛❣r❛❞❡❝✐❞♦ ♣♦r s❡♠♣r❡✳
❘❡s✉♠♦
◆❡st❡ tr❛❜❛❧❤♦ sã♦ ❛♣r❡s❡♥t❛❞❛s ❛❧❣✉♠❛s ❡①t❡♥sõ❡s ❞❡ ♠♦❞❡❧♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❝♦♠ ❢r❛çã♦ ❞❡ ❝✉r❛✱ ❛ss✉♠✐♥❞♦ ♦ ❝♦♥t❡①t♦ ❡♠ q✉❡ ❛s ♦❜s❡r✈❛çõ❡s ❡stã♦ ❛❣r✉♣❛❞❛s✳ ❉♦✐s ❡❢❡✐t♦s ❛❧❡❛tór✐♦s sã♦ ✐♥❝♦r♣♦r❛❞♦s ♣❛r❛ ❝❛❞❛ ❣r✉♣♦✿ ✉♠ ♣❛r❛ ❡①♣❧✐❝❛r ♦ ❡❢❡✐t♦ ♥♦ t❡♠♣♦ ❞❡ s♦❜r❡✈✐❞❛ ❞❛s ♦❜s❡r✈❛çõ❡s s✉s❝❡tí✈❡✐s ❡ ♦✉tr♦ ♣❛r❛ ❡①♣❧✐❝❛r ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ❝✉r❛✳ ❆♣r❡s❡♥t❛✲s❡ ✉♠❛ ❛❜♦r❞❛❣❡♠ ❝❧áss✐❝❛ ❛tr❛✈és ❞♦s ❡st✐♠❛❞♦r❡s ❘❊▼▲ ❡ ✉♠❛ ❛❜♦r❞❛❣❡♠ ❜❛②❡s✐❛♥❛ ❛tr❛✈és ❞♦ ✉s♦ ❞❡ ♣r♦❝❡ss♦s ❞❡ ❉✐r✐❝❤❧❡t✳ ❉✐s❝✉t❡✲s❡ ❛❧❣✉♥s ❡st✉❞♦s ❞❡ s✐♠✉❧❛çã♦ ❡♠ q✉❡ ❛✈❛❧✐❛✲s❡ ♦ ❞❡s❡♠♣❡♥❤♦ ❞♦s ❡st✐♠❛❞♦r❡s ♣r♦♣♦st♦s✱ ❛❧é♠ ❞❡ ❝♦♠♣❛r❛r ❛s ❞✉❛s ❛❜♦r❞❛❣❡♥s✳ ❋✐♥❛❧♠❡♥t❡✱ ✐❧✉str❛♠✲s❡ ♦s r❡s✉❧t❛❞♦s ❝♦♠ ❞❛❞♦s r❡❛✐s✳ P❛❧❛✈r❛s✲❝❤❛✈❡✿ ♠♦❞❡❧♦ ❞❡ t❡♠♣♦s ❞❡ ♣r♦♠♦çã♦✱ ♠♦❞❡❧♦s ❞❡str✉t✐✈♦s✱ ♠♦❞❡❧♦s ♠✐st♦s✱ ♣r♦❝❡ss♦s ❉✐r✐❝❤❧❡t✳
❆❜str❛❝t
■♥ t❤✐s ✇♦r❦ s♦♠❡ ❡①t❡♥s✐♦♥s ✐♥ s✉r✈✐✈❛❧ ♠♦❞❡❧s ✇✐t❤ ❝✉r❡ ❢r❛❝t✐♦♥ ❛r❡ ♣r❡s❡♥t❡❞✱ ❛ss✉♠✐♥❣ t❤❡ ❝♦♥t❡①t ✐♥ ✇❤✐❝❤ t❤❡ ♦❜s❡r✈❛t✐♦♥s ❛r❡ ❣r♦✉♣❡❞ ✐♥t♦ ❝❧✉st❡rs✳ ❚✇♦ r❛♥❞♦♠ ❡✛❡❝ts ❛r❡ ✐♥❝♦r♣♦r❛t❡❞ ❢♦r ❡❛❝❤ ❣r♦✉♣✿ ♦♥❡ t♦ ❡①♣❧❛✐♥ t❤❡ ❡✛❡❝t ♦♥ s✉r✈✐✈❛❧ t✐♠❡ ♦❢ s✉s❝❡♣t✐❜❧❡ ♦❜s❡r✈❛t✐♦♥s ❛♥❞ ❛♥♦t❤❡r t♦ ❡①♣❧❛✐♥ t❤❡ ♣r♦❜❛❜✐❧✐t② ♦❢ ❝✉r❡✳ ❆ ❝❧❛ss✐❝❛❧ ❛♣♣r♦❛❝❤ t❤r♦✉❣❤ t❤❡ ❘❊▼▲ ❡st✐♠❛t♦rs ✐s ♣r❡s❡♥t❡❞ ❛s ✇❡❧❧ ❛s ❛ ❜❛②❡s✐❛♥ ❛♣♣r♦❛❝❤ t❤r♦✉❣❤ ❉✐r✐❝❤❧❡t Pr♦❝❡ss✳ ❇❡s✐❞❡s ❝♦♠♣❛r✐♥❣ ❜♦t❤ ❛♣♣r♦❛❝❤❡s✱ s♦♠❡ s✐♠✉❧❛t✐♦♥ st✉❞✐❡s ✇❤✐❝❤ ❡✈❛❧✉❛t❡s t❤❡ ♣❡r❢♦r♠❛♥❝❡ ♦❢ t❤❡ ♣r♦♣♦s❡❞ ❡st✐♠❛t♦rs ❛r❡ ❞✐s❝✉ss❡❞✳ ❋✐♥❛❧❧②✱ t❤❡ r❡s✉❧ts ❛r❡ ✐❧❧✉str❛t❡❞ ✇✐t❤ ❛ r❡❛❧ ❞❛t❛❜❛s❡✳
❑❡②✇♦r❞s✿ ♣r♦♠♦t✐♦♥ t✐♠❡ ❝✉r❡ r❛t❡ ♠♦❞❡❧✱ ❞❡str✉❝t✐✈❡ ♠♦❞❡❧s✱ r❛♥❞♦♠ ❡✛❡❝t ♠♦❞❡❧s✱ ❉✐r✐❝❤❧❡t Pr♦❝❡ss✳
❙✉♠ár✐♦
▲✐st❛ ❞❡ ❆❜r❡✈✐❛t✉r❛s ✐①
▲✐st❛ ❞❡ ❋✐❣✉r❛s ①✐
▲✐st❛ ❞❡ ❚❛❜❡❧❛s ①✈
✶ ▼♦t✐✈❛çã♦ ✶
✶✳✶ ■♥tr♦❞✉çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶ ✶✳✷ ❉❡s❝r✐çã♦ ❞♦s ♦❜❥❡t✐✈♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸ ✶✳✸ ❖r❣❛♥✐③❛çã♦ ❞♦ tr❛❜❛❧❤♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸
✷ Pr❡❧✐♠✐♥❛r❡s ✺
✷✳✶ ❆❧❣✉♠❛s ❞✐str✐❜✉✐çõ❡s ❞❡ ✐♥t❡r❡ss❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺ ✷✳✶✳✶ ❉✐str✐❜✉✐çã♦ ❲❡✐❜✉❧❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺ ✷✳✶✳✷ ❉✐str✐❜✉✐çã♦ ❊①♣♦♥❡♥❝✐❛❧ ❙❡❣♠❡♥t❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽ ✷✳✶✳✸ ❉✐str✐❜✉✐çã♦ ❲✐s❤❛rt ❡ ❲✐s❤❛rt✲■♥✈❡rt✐❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵ ✷✳✷ ▼♦❞❡❧♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❝♦♠ ❢r❛çã♦ ❞❡ ❝✉r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✷✳✷✳✶ ▼♦❞❡❧♦ ❞❡ ♠✐st✉r❛ ♣❛❞rã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✷✳✷✳✷ ▼♦❞❡❧♦ ❞❡ t❡♠♣♦s ❞❡ ♣r♦♠♦çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸ ✷✳✷✳✸ ❊①t❡♥sõ❡s ❞♦ ♠♦❞❡❧♦ ❞❡ ❈❤❡♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✷✳✷✳✹ ▼♦❞❡❧♦s ❞❡str✉t✐✈♦s ❞❡ P♦✐ss♦♥ ♣♦♥❞❡r❛❞♦ ❝♦♠ ❢r❛çã♦ ❞❡ ❝✉r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽ ✷✳✷✳✺ ❖✉tr♦s ♠♦❞❡❧♦s ❞❡ ❝✉r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✷✳✷✳✻ ❈♦♠❡♥tár✐♦s ❛❞✐❝✐♦♥❛✐s s♦❜r❡ ♦s ♠♦❞❡❧♦s ❞❡ ❝✉r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✷✳✸ ❊st✐♠❛❞♦r❡s ❇▲❯P ❡ ❘❊▼▲ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✷✳✹ Pr♦❝❡ss♦s ❞❡ ❉✐r✐❝❤❧❡t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✷✳✹✳✶ ▼ét♦❞♦s ❞❡ ❛♠♦str❛❣❡♠ ♣❛r❛ ♣r♦❝❡ss♦s ❞❡ ❉✐r✐❝❤❧❡t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✷✳✹✳✷ Pr♦❝❡ss♦s ❞❡ ❉✐r✐❝❤❧❡t ❝❡♥tr❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾ ✸ ▼♦❞❡❧♦s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❝♦♠ ❢r❛çã♦ ❞❡ ❝✉r❛ ❡ ❡❢❡✐t♦s ❛❧❡❛tór✐♦s ✹✶ ✸✳✶ ▼♦❞❡❧♦ ❞❡ ♠✐st✉r❛ ❝♦♠ ❡❢❡✐t♦s ❛❧❡❛tór✐♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✸✳✷ ▼♦❞❡❧♦ ❞❡ ❈❤❡♥ ❝♦♠ ❡❢❡✐t♦s ❛❧❡❛tór✐♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✸✳✷✳✶ ❊st✉❞♦ ❞❡ s✐♠✉❧❛çã♦✿ ❘❡❝✉♣❡r❛çã♦ ❞❡ ♣❛râ♠❡tr♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✸✳✷✳✷ ❈♦♠♣❛r❛çã♦ ❞♦ ♠♦❞❡❧♦ ❞❡ ❈❤❡♥ ❝♦♠ ❡❢❡✐t♦s ❛❧❡❛tór✐♦s ♥♦r♠❛✐s ❞❡♣❡♥❞❡♥t❡s
✈❡rs✉s ✐♥❞❡♣❡♥❞❡♥t❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ✸✳✸ ▼♦❞❡❧♦ ❞❡ ♠✐st✉r❛ ❝♦♠ ♦✉tr❛s ❧✐❣❛çõ❡s ♥❛ ❝✉r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✽ ✸✳✸✳✶ ❊st✉❞♦ ❞❡ s✐♠✉❧❛çã♦✿ ❘❡❝✉♣❡r❛çã♦ ❞❡ ♣❛râ♠❡tr♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾ ✸✳✸✳✷ ❊st✐♠❛çã♦ ❞❛ ❢r❛çã♦ ❞❡ ❝✉r❛ ✉s❛♥❞♦ ❛s ❞✐❢❡r❡♥t❡s ❧✐❣❛çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸
✈✐✐✐ ❙❯▼➪❘■❖
✹ ▼♦❞❡❧♦s ❞❡str✉t✐✈♦s ❞❡ P♦✐ss♦♥ ♣♦♥❞❡r❛❞♦ ❝♦♠ ❢r❛çã♦ ❞❡ ❝✉r❛ ❡ ❡❢❡✐t♦s ❛❧❡❛tór✐♦s ✽✺ ✹✳✶ ❖ ♠♦❞❡❧♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺ ✹✳✷ ❆❜♦r❞❛❣❡♠ ❝❧áss✐❝❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✻ ✹✳✸ ❆❜♦r❞❛❣❡♠ ❜❛②❡s✐❛♥❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✽ ✹✳✹ ❊st✉❞♦ ❞❡ s✐♠✉❧❛çã♦✿ ❝♦♠♣❛r❛çã♦ ❞❛s ❛❜♦r❞❛❣❡♥s ❝❧áss✐❝❛ ❡ ❜❛②❡s✐❛♥❛ ♥♦s ▼❉PP❋❈
❝♦♠ ❡❢❡✐t♦s ❛❧❡❛tór✐♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✶
✺ ❆♣❧✐❝❛çã♦ ✶✵✺
✺✳✶ ❆♣r❡s❡♥t❛çã♦ ❞♦ ❜❛♥❝♦ ❞❡ ❞❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✺ ✺✳✷ ❆❥✉st❡ ❝❧áss✐❝♦ ❞♦s ♠♦❞❡❧♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✽ ✺✳✸ ❆❥✉st❡ ❜❛②❡s✐❛♥♦ ❞♦s ♠♦❞❡❧♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✷
✻ ❈♦♥❝❧✉sõ❡s ✶✷✾
✻✳✶ ❈♦♥s✐❞❡r❛çõ❡s ✜♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✾ ✻✳✷ ❙✉❣❡stõ❡s ♣❛r❛ ♣❡sq✉✐s❛s ❢✉t✉r❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✾
❆ ❆♣ê♥❞✐❝❡ ✶✸✶
❆✳✶ ❆❧❣✉♥s ❛s♣❡❝t♦s ❞♦s ♠♦❞❡❧♦s ❞❡str✉t✐✈♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✶ ❆✳✶✳✶ ❈á❧❝✉❧♦ ❞❡P(D=d|θ, p, φ) ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✶
❆✳✶✳✷ ❈❛❧❝✉❧❛♥❞♦ ❛ ❞✐str✐❜✉✐çã♦ ❞❡D, M ❡ D|M =m ❞❛❞❛ ❛ ✐♥❢♦r♠❛çã♦ ♦❜s❡r✈❛❞❛✶✸✷ ❆✳✶✳✸ Pr♦✈❛♥❞♦ q✉❡ ❛ ❢r❛çã♦ ❞❡ ❝✉r❛ ❞♦ ♠♦❞❡❧♦ ❉❇▲P ♥ã♦ é ✐❞❡♥t✐✜❝á✈❡❧ q✉❛♥❞♦
z1 ❡ z2 ✐♥❝❧✉❡♠ ✐♥t❡r❝❡♣t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✺
❆✳✷ ❉❡r✐✈❛❞❛s ♥❡❝❡ssár✐❛s ♥❛ ✐♠♣❧❡♠❡♥t❛çã♦ ❞♦ ❛❧❣♦r✐t♠♦ ❞❡ ◆❡✇t♦♥✲❘❛♣❤s♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✻ ❆✳✷✳✶ ▼♦❞❡❧♦ ❞❡ ❈❤❡♥ ❝♦♠ ❡❢❡✐t♦s ❛❧❡❛tór✐♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✻ ❆✳✷✳✷ ▼♦❞❡❧♦ ❞❡ ♠✐st✉r❛ ❝♦♠ ❡❢❡✐t♦s ❛❧❡❛tór✐♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✽ ❆✳✷✳✸ ▼♦❞❡❧♦s ❉❡str✉t✐✈♦s ❝♦♠ ❡❢❡✐t♦s ❛❧❡❛tór✐♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✵ ❆✳✸ Pr♦❣r❛♠❛s ❡♠ ❘ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✶
❆✳✸✳✶ ❊st✐♠❛çã♦ ❝❧áss✐❝❛ ❞♦s ♠♦❞❡❧♦s ❞❡ ❈❤❡♥ ❡ ❞♦s ♠♦❞❡❧♦s ❞❡str✉t✐✈♦s ❝♦♠ ❡❢❡✐t♦s ❛❧❡❛tór✐♦s ❜✐✈❛r✐❛❞♦s ◆♦r♠❛✐s✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✶
▲✐st❛ ❞❡ ❆❜r❡✈✐❛t✉r❛s
❇▲❯P ♠❡❧❤♦r ❡st✐♠❛❞♦r ❧✐♥❡❛r ♥ã♦ ✈✐❝✐❛❞♦ ✭❇❡st ▲✐♥❡❛r ❯♥❜✐❛s❡❞ Pr❡❞✐❝t♦r✮
❉▲❇P ♠♦❞❡❧♦ ❞❡str✉t✐✈♦ ❞❡ P♦✐ss♦♥ ❝♦♠ ✈✐és ❞❡ ❞✉r❛çã♦ ✭❉❡str✉❝t✐✈❡ ❧❡♥❣t❤✲❜✐❛s❡❞ P♦✐ss♦♥✮ ❡✳❛✳✭✬s✮ ❡❢❡✐t♦✭s✮ ❛❧❡❛tór✐♦✭s✮
❊✳◗✳▼✳ ❡rr♦ q✉❛❞rát✐❝♦ ♠é❞✐♦
❢✳❞✳❛✳ ❢✉♥çã♦ ❞❡ ❞✐str✐❜✉✐çã♦ ❛❝✉♠✉❧❛❞❛ ❢✳❞✳♣✳ ❢✉♥çã♦ ❞❡ ❞❡♥s✐❞❛❞❡ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡
✐✳✐✳❞✳ ✐♥❞❡♣❡♥❞❡♥t❡s ❡ ✐❞❡♥t✐❝❛♠❡♥t❡ ❞✐str✐❜✉í❞♦s✭❛s✮ ❑✲▼ ✭❡st✐♠❛❞♦r ❞❡✮ ❑❛♣❧❛♥✲▼❡✐❡r
▼❉PP❋❈ ♠♦❞❡❧♦ ❞❡str✉t✐✈♦ ❞❡ P♦✐ss♦♥ P♦♥❞❡r❛❞♦ ❝♦♠ ❢r❛çã♦ ❞❡ ❝✉r❛ ▼✳P✳ ♠❡❞✐❞❛ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡
P✳❉✳✭✬s✮ ♣r♦❝❡ss♦✭s✮ ❉✐r✐❝❤❧❡t
P✳❉✳❈✳✭✬s✮ ♣r♦❝❡ss♦✭s✮ ❉✐r✐❝❤❧❡t ❈❡♥tr❛❞♦✭s✮ q✳❝✳ q✉❛s❡ ❝❡rt❛♠❡♥t❡
❘❊▼▲ ♠á①✐♠❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ r❡s✐❞✉❛❧ ✭❘❡s✐❞✉❛❧ ▼❛①✐♠✉♠ ▲✐❦❡❧✐❤♦♦❞✮ ✈✳❛✳✭✬s✮ ✈❛r✐á✈❡❧✭✈❛r✐á✈❡✐s✮ ❛❧❡❛tór✐❛✭s✮
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✶✳✶ ❈✉r✈❛ ❞❡ ❑✲▼ ♣❛r❛ ♣❛❝✐❡♥t❡s ❝♦♠ ❝â♥❝❡r ❞❡ ❧í♥❣✉❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷ ✷✳✶ ❋✉♥çã♦ ❞❡ ❞❡♥s✐❞❛❞❡ ❞♦ ♠♦❞❡❧♦ ❲❡✐❜✉❧❧ ✭λ= 1✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻
✷✳✷ ❋✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❞♦ ♠♦❞❡❧♦ ❲❡✐❜✉❧❧ ✭λ= 1✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼
✷✳✸ ❋✉♥çã♦ ❞❡ r✐s❝♦ ❞♦ ♠♦❞❡❧♦ ❲❡✐❜✉❧❧ ✭λ= 1✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼
✷✳✹ ❋✉♥çã♦ ❞❡ ❞❡♥s✐❞❛❞❡ ❞♦ ♠♦❞❡❧♦ ❊①♣♦♥❡♥❝✐❛❧ ❙❡❣♠❡♥t❛❞♦ ❝♦♠ a= (2,5)✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾
✷✳✺ ❋✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❞♦ ♠♦❞❡❧♦ ❊①♣♦♥❡♥❝✐❛❧ ❙❡❣♠❡♥t❛❞♦ ❝♦♠ a= (2,5)✳✳ ✳ ✳ ✳ ✳ ✾
✷✳✻ ❋✉♥çã♦ ❞❡ r✐s❝♦ ❞♦ ♠♦❞❡❧♦ ❊①♣♦♥❡♥❝✐❛❧ ❙❡❣♠❡♥t❛❞♦ ❝♦♠ a= (2,5)✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵
✷✳✼ ●rá✜❝♦ ❞❛ ❢✳❞✳❛✳ ♣❛r❛ ✶✵✵ ❛♠♦str❛s ❞❡ t❛♠❛♥❤♦ ✶✵✵ ❞❡ P❉✭αG0✮✱ ❝♦♠ α= 1❡ G0 ❛
r❡s♣❡❝t✐✈❛ ♠❡❞✐❞❛ ❜❛s❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✷✳✽ ●rá✜❝♦ ❞❛ ❢✳❞✳❛✳ ♣❛r❛ ✶✵✵ ❛♠♦str❛s ❞❡ t❛♠❛♥❤♦ ✶✵✵ ❞❡ P❉✭αG0✮✱ ❝♦♠α = 10 ❡ G0
❛ r❡s♣❡❝t✐✈❛ ♠❡❞✐❞❛ ❜❛s❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✷✳✾ ●rá✜❝♦ ❞❛ ❢✳❞✳❛✳ ♣❛r❛ ✶✵✵ ❛♠♦str❛s ❞❡ t❛♠❛♥❤♦ ✶✵✵ ❞❡ P❉✭αG0✮✱ ❝♦♠ α= 100❡ G0
❛ r❡s♣❡❝t✐✈❛ ♠❡❞✐❞❛ ❜❛s❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✷✳✶✵ ●rá✜❝♦ ❞❛ ❢✳❞✳❛✳ ♣❛r❛ ✶✵✵ ❛♠♦str❛s ❞❡ t❛♠❛♥❤♦ ✶✵✵ ❞❡ P❉✭αG0✮✱ ❝♦♠ α = 1000 ❡
G0 ❛ r❡s♣❡❝t✐✈❛ ♠❡❞✐❞❛ ❜❛s❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹
✸✳✶ ❍✐st♦❣r❛♠❛s ❞❛s ❡st✐♠❛t✐✈❛s ❞♦s ♣❛râ♠❡tr♦s ♣❛r❛ ♦ ♠♦❞❡❧♦ ❞❡ ❈❤❡♥ ❝♦♠ ❡❢❡✐t♦s ❛❧❡❛tór✐♦s ❞❡♣❡♥❞❡♥t❡s ❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❜❛s❛❧ ❲❡✐❜✉❧❧✿ ●r✉♣♦ ■ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✸✳✷ ❍✐st♦❣r❛♠❛s ❞❛s ❡st✐♠❛t✐✈❛s ❞♦s ♣❛râ♠❡tr♦s ♣❛r❛ ♦ ♠♦❞❡❧♦ ❞❡ ❈❤❡♥ ❝♦♠ ❡❢❡✐t♦s
❛❧❡❛tór✐♦s ❞❡♣❡♥❞❡♥t❡s ❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❜❛s❛❧ ❲❡✐❜✉❧❧✿ ●r✉♣♦ ■■ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺ ✸✳✸ ❍✐st♦❣r❛♠❛s ❞❛s ❡st✐♠❛t✐✈❛s ❞♦s ♣❛râ♠❡tr♦s ♣❛r❛ ♦ ♠♦❞❡❧♦ ❞❡ ❈❤❡♥ ❝♦♠ ❡❢❡✐t♦s
❛❧❡❛tór✐♦s ❞❡♣❡♥❞❡♥t❡s ❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❜❛s❛❧ ❲❡✐❜✉❧❧✿ ●r✉♣♦ ■■■ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ✸✳✹ ❍✐st♦❣r❛♠❛s ❞❛s ❡st✐♠❛t✐✈❛s ❞♦s ♣❛râ♠❡tr♦s ♣❛r❛ ♦ ♠♦❞❡❧♦ ❞❡ ❈❤❡♥ ❝♦♠ ❡❢❡✐t♦s
❛❧❡❛tór✐♦s ❞❡♣❡♥❞❡♥t❡s ❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❜❛s❛❧ ❲❡✐❜✉❧❧✿ ●r✉♣♦ ■❱ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼ ✸✳✺ ❍✐st♦❣r❛♠❛s ❞❛s ❡st✐♠❛t✐✈❛s ❞♦s ♣❛râ♠❡tr♦s ♣❛r❛ ♦ ♠♦❞❡❧♦ ❞❡ ❈❤❡♥ ❝♦♠ ❡❢❡✐t♦s ❛❧❡✲
❛tór✐♦s ❞❡♣❡♥❞❡♥t❡s ❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❜❛s❛❧ ❊①♣♦♥❡♥❝✐❛❧ ❙❡❣♠❡♥t❛❞❛ ✭L= 3✮✿ ●r✉♣♦
■ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ✸✳✻ ❍✐st♦❣r❛♠❛s ❞❛s ❡st✐♠❛t✐✈❛s ❞♦s ♣❛râ♠❡tr♦s ♣❛r❛ ♦ ♠♦❞❡❧♦ ❞❡ ❈❤❡♥ ❝♦♠ ❡❢❡✐t♦s ❛❧❡✲
❛tór✐♦s ❞❡♣❡♥❞❡♥t❡s ❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❜❛s❛❧ ❊①♣♦♥❡♥❝✐❛❧ ❙❡❣♠❡♥t❛❞❛ ✭L= 3✮✿ ●r✉♣♦
■■ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ✸✳✼ ❍✐st♦❣r❛♠❛s ❞❛s ❡st✐♠❛t✐✈❛s ❞♦s ♣❛râ♠❡tr♦s ♣❛r❛ ♦ ♠♦❞❡❧♦ ❞❡ ❈❤❡♥ ❝♦♠ ❡❢❡✐t♦s ❛❧❡✲
❛tór✐♦s ❞❡♣❡♥❞❡♥t❡s ❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❜❛s❛❧ ❊①♣♦♥❡♥❝✐❛❧ ❙❡❣♠❡♥t❛❞❛ ✭L= 3✮✿ ●r✉♣♦
■■■ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹
①✐✐ ▲■❙❚❆ ❉❊ ❋■●❯❘❆❙
✸✳✽ ❍✐st♦❣r❛♠❛s ❞❛s ❡st✐♠❛t✐✈❛s ❞♦s ♣❛râ♠❡tr♦s ♣❛r❛ ♦ ♠♦❞❡❧♦ ❞❡ ❈❤❡♥ ❝♦♠ ❡❢❡✐t♦s ❛❧❡✲ ❛tór✐♦s ❞❡♣❡♥❞❡♥t❡s ❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❜❛s❛❧ ❊①♣♦♥❡♥❝✐❛❧ ❙❡❣♠❡♥t❛❞❛ ✭L= 3✮✿ ●r✉♣♦
■❱ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺ ✸✳✾ ❍✐st♦❣r❛♠❛s ❞❛s ❡st✐♠❛t✐✈❛s ❞♦s ♣❛râ♠❡tr♦s ♥❛ ❝♦♠♣❛r❛çã♦ ❞♦s ♠♦❞❡❧♦s ❞❡ ❈❤❡♥
❝♦♠ ❡❢❡✐t♦s ❛❧❡❛tór✐♦s ✐♥❞❡♣❡♥❞❡♥t❡s ❡ ❞❡♣❡♥❞❡♥t❡s ❝♦♠ s♦❜r❡✈✐✈ê♥❝✐❛ ❜❛s❛❧ ❲❡✐❜✉❧❧✿ ●r✉♣♦ ■ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✸✳✶✵ ❍✐st♦❣r❛♠❛s ❞❛s ❡st✐♠❛t✐✈❛s ❞♦s ♣❛râ♠❡tr♦s ♥❛ ❝♦♠♣❛r❛çã♦ ❞♦s ♠♦❞❡❧♦s ❞❡ ❈❤❡♥
❝♦♠ ❡❢❡✐t♦s ❛❧❡❛tór✐♦s ✐♥❞❡♣❡♥❞❡♥t❡s ❡ ❞❡♣❡♥❞❡♥t❡s ❝♦♠ s♦❜r❡✈✐✈ê♥❝✐❛ ❜❛s❛❧ ❲❡✐❜✉❧❧✿ ●r✉♣♦ ■■ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶ ✸✳✶✶ ❍✐st♦❣r❛♠❛s ❞❛s ❡st✐♠❛t✐✈❛s ❞♦s ♣❛râ♠❡tr♦s ♥❛ ❝♦♠♣❛r❛çã♦ ❞♦s ♠♦❞❡❧♦s ❞❡ ❈❤❡♥
❝♦♠ ❡❢❡✐t♦s ❛❧❡❛tór✐♦s ✐♥❞❡♣❡♥❞❡♥t❡s ❡ ❞❡♣❡♥❞❡♥t❡s ❝♦♠ s♦❜r❡✈✐✈ê♥❝✐❛ ❜❛s❛❧ ❲❡✐❜✉❧❧✿ ●r✉♣♦ ■■■ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷ ✸✳✶✷ ❍✐st♦❣r❛♠❛s ❞❛s ❡st✐♠❛t✐✈❛s ❞♦s ♣❛râ♠❡tr♦s ♥❛ ❝♦♠♣❛r❛çã♦ ❞♦s ♠♦❞❡❧♦s ❞❡ ❈❤❡♥
❝♦♠ ❡❢❡✐t♦s ❛❧❡❛tór✐♦s ✐♥❞❡♣❡♥❞❡♥t❡s ❡ ❞❡♣❡♥❞❡♥t❡s ❝♦♠ s♦❜r❡✈✐✈ê♥❝✐❛ ❜❛s❛❧ ❊①♣♦✲ ♥❡♥❝✐❛❧ ❙❡❣♠❡♥t❛❞❛ ✭L= 3✮✿ ●r✉♣♦ ■ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺
✸✳✶✸ ❍✐st♦❣r❛♠❛s ❞❛s ❡st✐♠❛t✐✈❛s ❞♦s ♣❛râ♠❡tr♦s ♥❛ ❝♦♠♣❛r❛çã♦ ❞♦s ♠♦❞❡❧♦s ❞❡ ❈❤❡♥ ❝♦♠ ❡❢❡✐t♦s ❛❧❡❛tór✐♦s ✐♥❞❡♣❡♥❞❡♥t❡s ❡ ❞❡♣❡♥❞❡♥t❡s ❝♦♠ s♦❜r❡✈✐✈ê♥❝✐❛ ❜❛s❛❧ ❊①♣♦✲ ♥❡♥❝✐❛❧ ❙❡❣♠❡♥t❛❞❛ ✭L= 3✮✿ ●r✉♣♦ ■■ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻
✸✳✶✹ ❍✐st♦❣r❛♠❛s ❞❛s ❡st✐♠❛t✐✈❛s ❞♦s ♣❛râ♠❡tr♦s ♥❛ ❝♦♠♣❛r❛çã♦ ❞♦s ♠♦❞❡❧♦s ❞❡ ❈❤❡♥ ❝♦♠ ❡❢❡✐t♦s ❛❧❡❛tór✐♦s ✐♥❞❡♣❡♥❞❡♥t❡s ❡ ❞❡♣❡♥❞❡♥t❡s ❝♦♠ s♦❜r❡✈✐✈ê♥❝✐❛ ❜❛s❛❧ ❊①♣♦✲ ♥❡♥❝✐❛❧ ❙❡❣♠❡♥t❛❞❛ ✭L= 3✮✿ ●r✉♣♦ ■■■ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✼
✸✳✶✺ ❍✐st♦❣r❛♠❛ ❞♦s ♣❛râ♠❡tr♦s ❡st✐♠❛❞♦s ♥♦ ♠♦❞❡❧♦ ❞❡ ♠✐st✉r❛ ❝♦♠ ❡❢❡✐t♦s ❛❧❡❛tór✐♦s ✉s❛♥❞♦ ❧✐❣❛çã♦ ❝♦♠♣❧❡♠❡♥t❛r ❧♦❣✲❧♦❣ ♣❛r❛ ❛ ❝✉r❛ ❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❜❛s❛❧ ❲❡✐❜✉❧❧ ✳ ✳ ✳ ✽✷ ✹✳✶ ❋✉♥çõ❡s ❞❡ ❞❡♥s✐❞❛❞❡ ✭♠❛r❣✐♥❛✐s✮ ❞❛s ❞✐str✐❜✉✐çõ❡s s❡❧❡❝❝✐♦♥❛❞❛s ♣❛r❛ ♦s ❡✳❛✳✬s✳ ✳ ✳ ✳ ✾✸ ✺✳✶ ❈✉r✈❛ ❞❡ ❑✲▼ ♣❛r❛ ❛s s❡✐s ❝❧í♥✐❝❛s q✉❡ ♣❛rt✐❝✐♣❛✈❛♠ ♥♦ ❡st✉❞♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✻ ✺✳✷ ❈✉r✈❛ ❞❡ ❑✲▼ ♣❛r❛ ❛ ❝♦✈❛r✐á✈❡❧ r❡❝❛t❡❣♦r✐③❛❞❛ T✲st❛❣❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✼ ✺✳✸ ❈✉r✈❛ ❞❡ ❑✲▼ ♣❛r❛ ❛ ✈❛r✐á✈❡❧ ■❞❛❞❡ ✭❝❛t❡❣♦r✐③❛❞❛✮✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✼ ✺✳✹ ❋✉♥çã♦ ❞❡ r✐s❝♦ ❛❝✉♠✉❧❛❞❛ ❡st✐♠❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✽ ✺✳✺ ❋r❛çã♦ ❞❡ ❝✉r❛ ❡st✐♠❛❞❛ ♣❛r❛ ♣❛❝✐❡♥t❡s ❞❛ ❝❧í♥✐❝❛ ✷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✵ ✺✳✻ ❋✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❡st✐♠❛❞❛ ✈✐❛ ❑✲▼ ❡ ♣❡❧♦ ♠♦❞❡❧♦ ❡s❝♦❧❤✐❞♦ ♣❛r❛ ❛ ❝❧í♥✐❝❛ ✷ ✳ ✶✶✵ ✺✳✼ ❈✉r✈❛ ❞❡ ❑✲▼ ♣❛r❛ ♦s r❡sí❞✉♦s ❞❡ ❈♦①✲❙♥❡❧❧ ❞♦ ♠♦❞❡❧♦ ❡s❝♦❧❤✐❞♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✶ ✺✳✽ ❋✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❡st✐♠❛❞❛ ❡♠ ❝❛❞❛ ❝❧í♥✐❝❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✶ ✺✳✾ ❈r✐tér✐♦s ❝❆■❈ ❡ ❝❇■❈ ♣❛r❛ ♦ ♠♦❞❡❧♦ ❉❇◆ ✭❝❛s♦ ✶✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✷ ✺✳✶✵ ❋✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ♣♦♣✉❧❛❝✐♦♥❛❧ ❡st✐♠❛❞❛ ♥❛ ❝❧í♥✐❝❛ ✷ ♣❛r❛ ❞✐❢❡r❡♥t❡s ♠♦❞❡❧♦s
❞❡ ❝✉r❛ ❡ ❞✐❢❡r❡♥t❡s ♣❡r✜s ❞❡ ♣❛❝✐❡♥t❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✺ ✺✳✶✶ ❋✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❡st✐♠❛❞❛ ♣❛r❛ ♦s ✐♥❞✐✈í❞✉♦s s✉s❝❡tí✈❡✐s ❞❛ ❝❧í♥✐❝❛ ✷ ♣❛r❛
❞✐❢❡r❡♥t❡s ♠♦❞❡❧♦s ❞❡ ❝✉r❛ ❡ ❞✐❢❡r❡♥t❡s ♣❡r✜s ❞❡ ♣❛❝✐❡♥t❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✻ ✺✳✶✷ ❋r❛çã♦ ❞❡ ❝✉r❛ ❡st✐♠❛❞❛ ♥❛ ❝❧í♥✐❝❛ ✷ ♣❛r❛ ♦s ❞✐❢❡r❡♥t❡s ♠♦❞❡❧♦s ❛❥✉st❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✼ ✺✳✶✸ ❊st✐♠❛❞♦r ❞❡ ❑✲▼ ♣❛r❛ ♦s r❡sí❞✉♦s ❞❡ ❈♦①✲❙♥❡❧❧ ♣❛r❛ ♦s ♠♦❞❡❧♦s ❝♦♠ ❡✳❛✳✬s ❛❥✉st❛❞♦s✶✶✽ ✺✳✶✹ ❉✐❢❡r❡♥t❡s ❝♦♠♣♦♥❡♥t❡s ❡st✐♠❛❞❛s ♣❛r❛ ♦s ♠♦❞❡❧♦s ❞❡ ❈❤❡♥✱ ❉▲❇P ❡ ❉❊❲P▼ ❝♦♠
▲■❙❚❆ ❉❊ ❋■●❯❘❆❙ ①✐✐✐
✺✳✶✺ ❉✐❢❡r❡♥t❡s ❝♦♠♣♦♥❡♥t❡s ❡st✐♠❛❞❛s ♣❛r❛ ♦s ♠♦❞❡❧♦s ❉▲❇P ❡ ❉❊❲P▼ ❝♦♠ ❡✳❛✳✬s ❡♠ t♦❞♦s ♦s ♣❛❝✐❡♥t❡s ❞♦ ❡st✉❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✵ ✺✳✶✻ ❋✉♥çã♦ ❞❡ ❧♦❣✲✈❡r♦ss✐♠✐❧❤❛♥ç❛ ♣❡r✜❧❛❞❛ ♣❛r❛✿ ✭❛✮β11 ♥♦ ♠♦❞❡❧♦ ❉▲❇P ❝♦♠ ❡✳❛✳✬s✱
✭❜✮β11 ♥♦ ♠♦❞❡❧♦ ❉❊❲P▼ ❝♦♠ ❡✳❛✳✬s✱ ✭❝✮ V1 ♥♦ ♠♦❞❡❧♦ ❉▲❇P ❝♦♠ ❡✳❛✳✬s ✭❞✮ ❡ ♥♦
♠♦❞❡❧♦ ❉❊❲P▼ ❝♦♠ ❡✳❛✳✬s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✶ ✺✳✶✼ ❋✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ♣♦♣✉❧❛❝✐♦♥❛❧ ❞❛ ❝❧í♥✐❝❛ ✷ ♣❛r❛ ♦s ♠♦❞❡❧♦s ❉▲❇P ❡ ❉❊❲P▼
❝♦♠ ❡✳❛✳✬s ❡ ❞✐❢❡r❡♥t❡s ♣❡r✜s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✺ ✺✳✶✽ ❋r❛çã♦ ❞❡ ❝✉r❛ ❡st✐♠❛❞❛ ♥❛ ❝❧í♥✐❝❛ ✷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✻ ✺✳✶✾ ■♥t❡r✈❛❧♦s ❞❡ ❝r❡❞✐❜✐❧✐❞❛❞❡ ❛♦ ✾✺✪ ♣❛r❛ ♦ ♥ú♠❡r♦ ✐♥✐❝✐❛❧ ❞❡ ❝é❧✉❧❛s✱ ♥ú♠❡r♦ ❞❡ ❝é❧✉❧❛s
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✶✳✶ ❘❡❧❛çã♦ ❡♥tr❡ ❛s ❢✉♥çõ❡s ❞❡ ✐♥t❡r❡ss❡ ♥❛ ❛♥á❧✐s❡ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷ ✸✳✶ ❱í❝✐♦ ❡st✐♠❛❞♦ ❞♦s ❡st✐♠❛❞♦r❡s ❘❊▼▲ ♥♦ ♠♦❞❡❧♦ ❞❡ ❈❤❡♥ ❝♦♠ ❡❢❡✐t♦s ❛❧❡❛tór✐♦s
❞❡♣❡♥❞❡♥t❡s✿ ❝❛s♦ s♦❜r❡✈✐✈ê♥❝✐❛ ❜❛s❛❧ ❲❡✐❜✉❧❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ✸✳✷ ❱í❝✐♦ ❡st✐♠❛❞♦ ❞♦s ❡st✐♠❛❞♦r❡s ❘❊▼▲ ♥♦ ♠♦❞❡❧♦ ❞❡ ❈❤❡♥ ❝♦♠ ❡❢❡✐t♦s ❛❧❡❛tór✐♦s
❞❡♣❡♥❞❡♥t❡s✿ ❝❛s♦ s♦❜r❡✈✐✈ê♥❝✐❛ ❊①♣♦♥❡♥❝✐❛❧ ❙❡❣♠❡♥t❛❞❛ ✭L= 3✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾
✸✳✸ ❱í❝✐♦ ❡ ❉❡s✈✐♦ P❛❞rã♦ ❡st✐♠❛❞♦ ❞♦s ❡st✐♠❛❞♦r❡s ❘❊▼▲ ♥♦ ♠♦❞❡❧♦ ❞❡ ❈❤❡♥ ❝♦♠ ❡❢❡✐t♦s ❛❧❡❛tór✐♦s ✐♥❞❡♣❡♥❞❡♥t❡s ❡ ❞❡♣❡♥❞❡♥t❡s✿ ❝❛s♦ s♦❜r❡✈✐✈ê♥❝✐❛ ❲❡✐❜✉❧❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽ ✸✳✹ ❱í❝✐♦ ❡ ❉❡s✈✐♦ P❛❞rã♦ ❡st✐♠❛❞♦ ❞♦s ❡st✐♠❛❞♦r❡s ❘❊▼▲ ♥♦ ♠♦❞❡❧♦ ❞❡ ❈❤❡♥ ❝♦♠
❡❢❡✐t♦s ❛❧❡❛tór✐♦s ✐♥❞❡♣❡♥❞❡♥t❡s ❡ ❞❡♣❡♥❞❡♥t❡s✿ ❝❛s♦ s♦❜r❡✈✐✈ê♥❝✐❛ ❊①♣♦♥❡♥❝✐❛❧ ❙❡❣✲ ♠❡♥t❛❞❛ ✭L= 3✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸
✸✳✺ ▲✐❣❛çõ❡s ♣❛r❛ ♠♦❞❡❧❛r ❛ ♣r♦♣♦rçã♦ ❞❡ ♥ã♦ ❝✉r❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✽ ✸✳✻ ❱í❝✐♦ ❡st✐♠❛❞♦ ♣❛r❛ ♦s ❡st✐♠❛❞♦r❡s ❘❊▼▲ ❜❛s❡❛❞♦s ❡♠ ✺✵✵ ré♣❧✐❝❛s ✭❋✉♥çã♦ ❞❡
s♦❜r❡✈✐✈ê♥❝✐❛ ❞♦s ♥ã♦ ❝✉r❛❞♦s ❝♦♥s✐❞❡r❛❞❛ ❞♦ ♠♦❞❡❧♦ ❲❡✐❜✉❧❧✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶ ✸✳✼ ❱í❝✐♦ ❡st✐♠❛❞♦ ❡ ✈í❝✐♦ ♠á①✐♠♦ ❡st✐♠❛❞♦ ♣❛r❛ ❛ ❢r❛çã♦ ❞❡ ❝✉r❛ ✉s❛♥❞♦ ❛s ✸ ❧✐❣❛çõ❡s
♣r♦♣♦st❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹ ✹✳✶ ❋✉♥çõ❡s ❞❡ ♣❡s♦ ♣❛r❛ ❝❛❞❛ ♠♦❞❡❧♦ ❉❡str✉t✐✈♦✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺ ✹✳✷ ❋✉♥çõ❡s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❡ r✐s❝♦ ♣❛r❛ ♦s ♠♦❞❡❧♦s ❉▲❇P✱ ❊❲P▼ ❡ ❉❇◆✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✼ ✹✳✸ ❈♦♠♣❛r❛çã♦ ❞❛s ❡st✐♠❛t✐✈❛s ❞♦s ❡❢❡✐t♦s ✜①♦s ♥♦s ▼❉PP❋❈ ❡ ❡❢❡✐t♦s ❛❧❡❛tór✐♦s ✉s❛♥❞♦
❛❜♦r❞❛❣❡♠ ❈❧áss✐❝❛ ❡ ❜❛②❡s✐❛♥❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✺ ✹✳✹ ❆♥á❧✐s❡ ❝♦♠♣❛r❛t✐✈❛ ♣❛r❛ ♦s ❡❢❡✐t♦s ✜①♦s ❡♥tr❡ ❛s ❛❜♦r❞❛❣❡♥s ❈❧áss✐❝❛ ❡ ❜❛②❡s✐❛♥❛
♥♦ ▼❉PP❋❈ ❡ ❡❢❡✐t♦s ❛❧❡❛tór✐♦s ✭❉❡t❛❧❤❡ ♣♦r ❝❛s♦✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✶ ✹✳✺ ❆♥á❧✐s❡ ❝♦♠♣❛r❛t✐✈❛ ♣❛r❛ ♦s ❡❢❡✐t♦s ✜①♦s ❡♥tr❡ ❛s ❛❜♦r❞❛❣❡♥s ❈❧áss✐❝❛ ❡ ❜❛②❡s✐❛♥❛
♥♦ ▼❉PP❋❈ ❡ ❡❢❡✐t♦s ❛❧❡❛tór✐♦s ✭❉❡t❛❧❤❡ ♣♦r ♣❛râ♠❡tr♦✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✶ ✹✳✻ ❆♥á❧✐s❡ ❝♦♠♣❛r❛t✐✈❛ ♣❛r❛ ♦s ❡❢❡✐t♦s ✜①♦s ❡♥tr❡ ❛s ❛❜♦r❞❛❣❡♥s ❈❧áss✐❝❛ ❡ ❜❛②❡s✐❛♥❛
♥♦ ▼❉PP❋❈ ❡ ❡❢❡✐t♦s ❛❧❡❛tór✐♦s ✭❉❡t❛❧❤❡ ♣♦r ❝♦♠❜✐♥❛çã♦ ❞❡ ♥ú♠❡r♦ ❞❡ ❝❧í♥✐❝❛s ❡ ♣❛❝✐❡♥t❡s ❡♠ ❝❛❞❛✮✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✶ ✹✳✼ ❆♥á❧✐s❡ ❝♦♠♣❛r❛t✐✈❛ ♣❛r❛ ♦s ❡❢❡✐t♦s ❛❧❡❛tór✐♦s ❡♥tr❡ ❛s ❛❜♦r❞❛❣❡♥s ❈❧áss✐❝❛ ❡ ❜❛②❡s✐✲
❛♥❛ ♥♦ ▼❉PP❋❈ ❡ ❡❢❡✐t♦s ❛❧❡❛tór✐♦s ✭❉❡t❛❧❤❡ ♣♦r ❝❛s♦✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✸ ✹✳✽ ❆♥á❧✐s❡ ❝♦♠♣❛r❛t✐✈❛ ♣❛r❛ ♦s ❡❢❡✐t♦s ❛❧❡❛tór✐♦s ❡♥tr❡ ❛s ❛❜♦r❞❛❣❡♥s ❈❧áss✐❝❛ ❡ ❜❛②❡s✐✲
❛♥❛ ♥♦ ▼❉PP❋❈ ❡ ❡❢❡✐t♦s ❛❧❡❛tór✐♦s ✭❉❡t❛❧❤❡ ♣♦r ❝♦♠❜✐♥❛çã♦ ❞❡ ♥ú♠❡r♦ ❞❡ ❝❧í♥✐❝❛s ❡ ♣❛❝✐❡♥t❡s ❡♠ ❝❛❞❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✸ ✺✳✶ ❉✐str✐❜✉✐çã♦ ❞❡ ❝❧í♥✐❝❛ ❡ ❞❛ ✈❛r✐á✈❡❧ T✲st❛❣❡ ❝❛t❡❣♦r✐③❛❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✻ ✺✳✷ ❈r✐tér✐♦s ❞❡ s❡❧❡çã♦ ♣❛r❛ ❞✐❢❡r❡♥t❡s ❧✐❣❛çõ❡s ♥♦ ♠♦❞❡❧♦ ❞❡ ♠✐st✉r❛ ❝♦♠ ❡✳❛✳✬s ✳ ✳ ✳ ✳ ✳ ✶✵✾
①✈✐ ▲■❙❚❆ ❉❊ ❚❆❇❊▲❆❙
✺✳✸ ❊st✐♠❛t✐✈❛s ♣❛r❛ ♦ ♠♦❞❡❧♦ ❞❡ ♠✐st✉r❛ ❝♦♠ ❡✳❛✳✬s ❞❡♣❡♥❞❡♥t❡s ✉s❛♥❞♦ ❧✐❣❛çã♦ ❝❧♦❣❧♦❣ ♥❛ ❝✉r❛ ❡ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❜❛s❛❧ ❲❡✐❜✉❧❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✾ ✺✳✹ ❈♦♠❜✐♥❛çõ❡s ❞❡ ❝♦✈❛r✐á✈❡✐s ❡ ❡✳❛✳✬s ♥❛ ❝✉r❛ ❝♦♥s✐❞❡r❛❞❛s ♣❛r❛ ♦s ♠♦❞❡❧♦s ❉❡str✉t✐✈♦s✳✶✶✷ ✺✳✺ ❈r✐tér✐♦s ❝❆■❈ ❡ ❝❇■❈ ♣❛r❛ ♦s ♠♦❞❡❧♦s ❞❡ ❈❤❡♥ ❡ ❉❡str✉t✐✈♦s ❛❥✉st❛❞♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✸ ✺✳✻ ❊st✐♠❛t✐✈❛s ♦❜t✐❞❛s ♣❛r❛ ♦s ♠♦❞❡❧♦s ❡s❝♦❧❤✐❞♦s ✉s❛♥❞♦ ♦ ❝r✐tér✐♦ ❝❆■❈ ❡ ❝❇■❈✳ ✳ ✳ ✳ ✶✶✹ ✺✳✼ ❉✐str✐❜✉✐çõ❡s ❛ ♣r✐♦r✐ ❝♦♥s✐❞❡r❛❞❛s ♣❛r❛α✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✷ ✺✳✽ ❱❛❧♦r❡s ❞❡ pRb ♥♦s ♠♦❞❡❧♦s ❛❥✉st❛❞♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✸
✺✳✾ ❋❛t♦r ❞❡ ❇❛②❡s ♣❛r❛ ♦s ♠♦❞❡❧♦s ❛❥✉st❛❞♦s✳ ◆❛ ❞✐❛❣♦♥❛❧✱ ♦s ✈❛❧♦r❡s ❞❛ ❢✉♥çã♦ ❞❡ ❧♦❣✲✈❡r♦ss✐♠✐❧❤❛♥ç❛ ♠❛r❣✐♥❛✐s ♣❛r❛ ❝❛❞❛ ♠♦❞❡❧♦✳ ◆❛ ♣❛rt❡ ❛❜❛✐①♦ ❞❛ ❞✐❛❣♦♥❛❧✱ ♦ ❧♦❣❛r✐t♠♦ ❞♦ ❢❛t♦r ❞❡ ❇❛②❡s ❞♦ ♠♦❞❡❧♦ ❞❛ r❡s♣❡❝t✐✈❛ ❧✐♥❤❛ ✈❡rs✉s ♦ ♠♦❞❡❧♦ ❞❛ r❡s✲ ♣❡❝t✐✈❛ ❝♦❧✉♥❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✸ ✺✳✶✵ ❊st✐♠❛t✐✈❛s ♦❜t✐❞❛s ♣❛r❛ ♦ ♠♦❞❡❧♦ ❉▲❇P ❡ ❉❊❲P▼ ❝♦♠ ❡✳❛✳✬s ♥♦r♠❛✐s ✉s❛♥❞♦ ❛
❛❜♦r❞❛❣❡♠ ❜❛②❡s✐❛♥❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✹ ✺✳✶✶ ❈r✐t❡r✐♦ ❉■❈ ♣❛r❛ ♦ ♠♦❞❡❧♦s ❉▲❇P ❡ ❉❊❲P▼ ❝♦♠ ❡✳❛✳✬s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✼ ❆✳✶ ❋✳❞✳❛✳ ❞❛s ❞✐str✐❜✉✐çõ❡s ▲♦❣íst✐❝❛✱ ◆♦r♠❛❧ ❡ ❞❡ ●✉♠❜❡❧ ❡ s✉❛s ❞❡r✐✈❛❞❛s ❞❡ ♣r✐♠❡✐r♦
❈❛♣ít✉❧♦ ✶
▼♦t✐✈❛çã♦
✶✳✶ ■♥tr♦❞✉çã♦
❆ ❛♥á❧✐s❡ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ é ✉t✐❧✐③❛❞❛ ❡♠ ❡st✉❞♦s ❡♠ q✉❡ ❛ ✈❛r✐á✈❡❧ ❡♠ ❡st✉❞♦ é ♦ t❡♠♣♦ ❛té ❛ ♦❝♦rrê♥❝✐❛ ❞❡ ❛❧❣✉♠ ❡✈❡♥t♦ ❞❡ ✐♥t❡r❡ss❡ ✭q✉❡ s❡rá ❞❡♥♦t❛❞♦ ♣♦r T✮✳ ❉❡st❛ ❢♦r♠❛✱ ❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛S(·) ❛✈❛❧✐❛❞❛ ❡♠t ❞❡✜♥❡✲s❡ ❝♦♠♦
S(t) =P(T > t) =
Z ∞
t
f(u)du= 1−F(t),
❡♠ q✉❡f(·)❡F(·)❞❡♥♦t❛♠ ❛ ❢✉♥çã♦ ❞❡ ❞❡♥s✐❞❛❞❡ ❡ ❛ ❢✳❞✳❛✳ ❞❡T r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ❯♠❛ ♣r♦♣r✐❡❞❛❞❡ ❜ás✐❝❛ ❞❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ✭♣❡❧♦ ♠❡♥♦s ♥❛ ❛♥á❧✐s❡ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ✉s✉❛❧✮ é ♦ ❢❛t♦ q✉❡ ❡❧❛ é ♣ró♣r✐❛✱ ✐✳❡✳✱
lim
t→∞S(t) = 0. ✭✶✳✶✮
❊♠ t❡r♠♦s ♣rát✐❝♦s✱ ❛ ❡q✉❛çã♦ ✭✶✳✶✮ ✐♥❞✐❝❛ q✉❡ s❡ ♦ t❡♠♣♦ ❞❡ s❡❣✉✐♠❡♥t♦ ❞♦ ❡st✉❞♦ ❢♦r s✉✜❝✐❡♥t❡✲ ♠❡♥t❡ ❧♦♥❣♦✱ ❡♥tã♦ ❡s♣❡r❛✲s❡ ♦❜s❡r✈❛r ♦ ❡✈❡♥t♦ ❞❡ ✐♥t❡r❡ss❡ ❡♠ t♦❞♦s ♦s ✐♥❞✐✈í❞✉♦s ❞❛ ♣♦♣✉❧❛çã♦✳
❯♠❛ ♦✉tr❛ ❢✉♥çã♦ ❞❡ ✐♥t❡r❡ss❡ ♥♦ ❝♦♥t❡①t♦ ❞❡ ❛♥á❧✐s❡ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ é ❛ ❢✉♥çã♦ ❞❡ r✐s❝♦✱ ❝♦♥❤❡❝✐❞❛ ♥❛ ❧✐t❡r❛t✉r❛ t❛♠❜é♠ ❝♦♠♦ t❛①❛ ❞❡ ❢❛❧❤❛ ❡ q✉❡ s❡rá ❞❡♥♦t❛❞❛ ♣♦r h(·)✱ ❛ q✉❛❧ é ❞❡✜♥✐❞❛ ♣♦r
h(t) = lim
△t→0
P(t < T ≤t+△t|T > t)
△t .
❆ ❢✉♥çã♦ ❞❡ r✐s❝♦ ♣♦❞❡ s❡r ✐♥t❡r♣r❡t❛❞❛ ❝♦♠♦ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❛♣r♦①✐♠❛❞❛ ❞♦ ❡✈❡♥t♦ ❞❡ ✐♥t❡r❡ss❡ ♦❝♦rr❡r ♥♦ ✐♥st❛♥t❡ ✐♠❡❞✐❛t❛♠❡♥t❡ ♣♦st❡r✐♦r ❛t❞❛❞♦ q✉❡ ♦ ✐♥❞✐✈í❞✉♦ s♦❜r❡✈✐✈❡✉ ❛té t✳
❋✐♥❛❧♠❡♥t❡✱ ❛ ❢✉♥çã♦ ❞❡ r✐s❝♦ ❛❝✉♠✉❧❛❞♦ H(·) é ❞❡✜♥✐❞❛ ♣♦r
H(t) =
Z t
0
h(u)du.
❆ ❢✉♥çã♦ ❞❡ r✐s❝♦ ❛❝✉♠✉❧❛❞♦ ♣♦❞❡ s❡r ✐♥t❡r♣r❡t❛❞❛ ❝♦♠♦ ♦ r✐s❝♦ ❞❡ ♦❝♦rrê♥❝✐❛ ❞♦ ❡✈❡♥t♦ ❞❡ ✐♥t❡r❡ss❡ ❛té ♦ ✐♥st❛♥t❡t✱ ❞❛❞♦ q✉❡ ♦ ❡✈❡♥t♦ ♥ã♦ ❛❝♦♥t❡❝❡✉ ❛té ✐♥st❛♥t❡t✳
❍á ✉♠❛ r❡❧❛çã♦ ✉♠ ❛ ✉♠ ❡♥tr❡ ❛s ❢✉♥çõ❡sf(·)✱S(·)✱h(·)❡H(·)❞✐s❝✉t✐❞❛s ❛♥t❡r✐♦r♠❡♥t❡✳ ❉❡st❛ ❢♦r♠❛✱ ❞❛❞❛ ✉♠❛ ❞❡❧❛s ♣♦❞❡✲s❡ ❡♥❝♦♥tr❛r t♦❞❛s ❛s ♦✉tr❛s✳ ❊st❡ ❢❛t♦ t❛♠❜é♠ ✐♠♣❧✐❝❛ q✉❡ ♣♦❞❡✲s❡ ❢❛③❡r ❛ ♠♦❞❡❧❛❣❡♠ ❞❡ q✉❛❧q✉❡r ✉♠❛ ❞❡❧❛s✱ ❞❡✜♥✐♥❞♦ ✉♠ ♠♦❞❡❧♦ ú♥✐❝♦✳ ❆ ❚❛❜❡❧❛ ✶✳✶ ❛♣r❡s❡♥t❛ ❛ r❡❧❛çã♦ ❡♥tr❡ ❛s ❢✉♥çõ❡s ♠❡♥❝✐♦♥❛❞❛s ❛♥t❡r✐♦r♠❡♥t❡✳
❖s ♠♦❞❡❧♦s ❝♦♠ ❢r❛çã♦ ❞❡ ❝✉r❛ sã♦ ♠♦❞❡❧♦s ❛❞ ❤♦❝ ❡♠ ❡st✉❞♦s ❡♠ q✉❡ ♦ ❡✈❡♥t♦ ❞❡ ✐♥t❡r❡ss❡ ♥ã♦ ♥❡❝❡ss❛r✐❛♠❡♥t❡ ♠❛♥✐❢❡st❛✲s❡ ❡♠ t♦❞♦s ♦s ✐♥❞✐✈í❞✉♦s ❞❛ ♣♦♣✉❧❛çã♦✳ ❊st❛ s✐t✉❛çã♦ ✐♠♣❧✐❝❛ q✉❡
✷ ▼❖❚■❱❆➬➹❖ ✶✳✶
❋✉♥çã♦ r❡q✉❡r✐❞❛
❋✉♥çã♦ ♦❜t✐❞❛ f(t) S(t) h(t) H(t)
f(t) ✲ Rt∞f(u)du R∞f(t)
t f(u)du
−log Rt∞f(u)du
S(t) −dSdt(t) ✲ −[dSS(t()t/dt) ] −logS(t)
h(t) h(t) expn−R0th(u)duo expn−R0th(u)duo ✲ R0th(u)du
H(t) dHdt(t)exp{−H(t)} exp{−H(t)} dHdt(t) ✲
❚❛❜❡❧❛ ✶✳✶✿ ❘❡❧❛çã♦ ❡♥tr❡ ❛s ❢✉♥çõ❡s ❞❡ ✐♥t❡r❡ss❡ ♥❛ ❛♥á❧✐s❡ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛✳
❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❞❛ ♣♦♣✉❧❛çã♦ ♥ã♦ ♥❡❝❡ss❛r✐❛♠❡♥t❡ s❛t✐s❢❛ç❛ ❛ ❡q✉❛çã♦ ❡♠ ✭✶✳✶✮✳ P♦r ❡①❡♠♣❧♦✱ ♠✉✐t♦s t✐♣♦s ❞❡ ❝â♥❝❡r ♣♦❞❡♠ s❡r ❡♥❝❛✐①❛❞♦s ♥❡st❛s ❝✐r❝✉♥stâ♥❝✐❛s✳❑❛❧❜✢❡✐s❝❤ ❡ Pr❡♥t✐❝❡
❬✷✵✵✷❪ ❛♣r❡s❡♥t❛♠ ✉♠ ❜❛♥❝♦ ❞❡ ❞❛❞♦s r❡❢❡r❡♥t❡ ❛ ❝â♥❝❡r ❞❡ ❧í♥❣✉❛ ❧♦❝❛❧✐③❛❞♦ ❡♠ três ③♦♥❛s ❞✐❢❡r❡♥t❡s ❞❡❧❛✳ ❈♦♥s✐❞❡r❛♥❞♦ só ♦s ♣❛❝✐❡♥t❡s ❝♦♠ ❝â♥❝❡r ❞❡ ❧í♥❣✉❛ ♥❛ ♣❛rt❡ ♣♦st❡r✐♦r ❞❡❧❛✱ ❝♦♥str✉✐✉✲s❡ ❛ ❝✉r✈❛ ❞❡ ❑❛♣❧❛♥✲▼❡✐❡r ❞❛ ❋✐❣✉r❛✶✳✶✳
0 500 1000 1500
0.0 0.2 0.4 0.6 0.8 1.0
Tempo (Dias)
Probabilidade de Sobre
viv
ência
❋✐❣✉r❛ ✶✳✶✿ ❈✉r✈❛ ❞❡ ❑✲▼ ♣❛r❛ ♣❛❝✐❡♥t❡s ❝♦♠ ❝â♥❝❡r ❞❡ ❧í♥❣✉❛✳
◆♦t❡ q✉❡ ♦ ❡st✐♠❛❞♦r ❞❡ ❑✲▼ ❡st❛❜✐❧✐③❛✲s❡ ❡♠ ✉♠ ✈❛❧♦r ♣♦s✐t✐✈♦ ✭♣ró①✐♠♦ ❞❡ ✵✳✷✮✱ s✉❣❡r✐♥❞♦ q✉❡ ❛ ❢✉♥çã♦ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❞❡st❛ ♣♦♣✉❧❛çã♦ ✭♣❡❧♦ ♠❡♥♦s ♦❧❤❛❞❛ s❡♠ ❝♦♥s✐❞❡r❛r ❡✈❡♥t✉❛✐s ❝♦✈❛r✐á✈❡✐s✮ ♥ã♦ s❛t✐s❢❛③ ❛ ❝♦♥❞✐çã♦ ❞❡ s❡r ♣ró♣r✐❛ ❝♦♠♦ ♥❛ ❡q✉❛çã♦ ✭✶✳✶✮✳
✶✳✸ ❉❊❙❈❘■➬➹❖ ❉❖❙ ❖❇❏❊❚■❱❖❙ ✸
P♦ré♠✱ ❡①✐st❡♠ ♦✉tr♦s ♠♦❞❡❧♦s q✉❡ ♣♦❞❡♠ ❢♦r♥❡❝❡r ❛✐♥❞❛ ♠❛✐s ✐♥❢♦r♠❛çã♦ ❞❛ ♠❡♥❝✐♦♥❛❞❛ ❛♥✲ t❡r✐♦r♠❡♥t❡✳ P♦r ❡①❡♠♣❧♦✱ ♥♦ ❝♦♥t❡①t♦ ❞❡ ❡st✉❞♦s ❞❡ ❝â♥❝❡r✱ ♦ ♠♦❞❡❧♦ ❞❡ t❡♠♣♦s ❞❡ ♣r♦♠♦çã♦✱ ❞✐s❝✉t✐❞♦ ❡♠❨❛❦♦❧❡✈ ❡ ❚s♦❞✐❦♦✈ ❬✶✾✾✻❪ ❡❈❤❡♥ ❡t ❛❧✳ ❬✶✾✾✾❛❪✱ ♣❡r♠✐t❡ t❛♠❜é♠ ❢❛③❡r ✐♥❢❡rê♥❝✐❛ ❡♠ r❡❧❛çã♦ à ❞✐str✐❜✉✐çã♦ ❞❛s ❝é❧✉❧❛s q✉❡ ♣r♦❞✉③❡♠ ♦ ❝â♥❝❡r✳ ❏á ♥♦ ❝❛s♦ ❞♦s ♠♦❞❡❧♦s ❞❡str✉t✐✈♦s ✭❘♦❞r✐❣✉❡s ❡t ❛❧✳❬✷✵✶✶❪✮✱ ✐♥tr♦❞✉③✲s❡ ♥♦ ♠♦❞❡❧♦ ❛ s✉♣♦s✐çã♦ ❞❡ ❡①✐stê♥❝✐❛ ❞❡ ❝é❧✉❧❛s q✉❡ ♣♦❞❡♠ ♦✉ ♥ã♦ ♣r♦❞✉③✐r ❝â♥❝❡r ✭❛❧❣✉♠❛s ❞❡❧❛s ♣♦❞❡♠ s❡r ❞❡str✉í❞❛s✮✳ ❉❡st❛ ❢♦r♠❛✱ ♥❡st❡s ♠♦❞❡❧♦s ♣♦❞❡✲s❡ ❢❛③❡r ✐♥❢❡rê♥❝✐❛ t❛♥t♦ ❞❛ ❞✐str✐❜✉✐çã♦ ❞❛s ❝é❧✉❧❛s q✉❡ ♣♦❞❡♠ ♣r♦❞✉③✐r ♦ ❝â♥❝❡r q✉❛♥t♦ ❞❛ ♣r♦❜❛❜✐✲ ❧✐❞❛❞❡ ❞❡ ❛t✐✈❛çã♦ ❞❡ ❝❛❞❛ ❝é❧✉❧❛✳
P♦r ♦✉tr♦ ❧❛❞♦✱ ♥♦ ❝♦♥t❡①t♦ ❡♠ q✉❡ ♦s ♣❛❝✐❡♥t❡s ❢♦r❛♠ tr❛t❛❞♦s ❡♠ ❞✐❢❡r❡♥t❡s ❝❧í♥✐❝❛s✱ é ♥❛t✉r❛❧ s✉♣♦r q✉❡ ❝❛❞❛ ❝❧í♥✐❝❛ ♣♦❞❡ t❡r ✐♥✢✉ê♥❝✐❛ s♦❜r❡ ♦s ♣❛❝✐❡♥t❡s q✉❡ tr❛t❛♠✳ P♦ré♠✱ ♥♦ ❝♦♥t❡①t♦ ❞❡ ❢r❛çã♦ ❞❡ ❝✉r❛ ❤á ❞♦✐s ❣r✉♣♦s ❞❡ ♣❛❝✐❡♥t❡s✿ s✉s❝❡tí✈❡✐s ❡ ❝✉r❛❞♦s✳ P♦rt❛♥t♦✱ ♣♦❞❡✲s❡ ♣❡♥s❛r q✉❡ ❝❛❞❛ ❝❧í♥✐❝❛ ✐♥✢✉✐ t❛♥t♦ ♥♦s ✐♥❞✐✈í❞✉♦s s✉s❝❡tí✈❡✐s q✉❛♥t♦ ♥♦s ✐♥❞✐✈í❞✉♦s ❝✉r❛❞♦s✳ ❈♦♥s✐❞❡r❛♥❞♦ q✉❡ ❛s ❝❧í♥✐❝❛s só r❡♣r❡s❡♥t❛♠ ✉♠❛ ❛✳❛✳ ❞❡ ❝❧í♥✐❝❛s✱ ❡♥tã♦ é ♠❛✐s ❛♣r♦♣r✐❛❞♦ ❝♦♥s✐❞❡r❛r ✉♠ ♠♦❞❡❧♦ ❞❡ ❡❢❡✐✲ t♦s ❛❧❡❛tór✐♦s✱ ✐♥❝❧✉✐♥❞♦ ♣❛r❛ ❝❛❞❛ ❝❧í♥✐❝❛ ✉♠ ❡❢❡✐t♦ ❛❧❡❛tór✐♦ ❛ss♦❝✐❛❞♦ ❛♦s ✐♥❞✐✈í❞✉♦s s✉s❝❡tí✈❡✐s ✭Uj✮ ❡ ✉♠ ❡❢❡✐t♦ ❛❧❡❛tór✐♦ ❛ss♦❝✐❛❞♦ ❛♦s ✐♥❞✐✈í❞✉♦s ❝✉r❛❞♦s ✭Vj✮✱ ❡♠ q✉❡j= 1, . . . , J✱ ❡J r❡♣r❡s❡♥t❛ ♦ ♥ú♠❡r♦ ❞❡ ❝❧í♥✐❝❛s✳
◆❡st❡ ❝♦♥t❡①t♦✱ ❢♦r❛♠ ❡♥❝♦♥tr❛❞♦s ♥❛ ❧✐t❡r❛t✉r❛ só ♦s tr❛❜❛❧❤♦s ❞❡ ▲✐ ❡t ❛❧✳ ❬✷✵✵✶❪ ❡ ▲❛✐ ❡ ❨❛✉
❬✷✵✵✽❪✱ ❛♠❜♦s ♣❛r❛ ♦ ♠♦❞❡❧♦ ❞❡ ♠✐st✉r❛ ❡ ❛ss✉♠✐♥❞♦ q✉❡ ♦s ♣❛r❡s(Uj, Vj) t❡♠ ❞✐str✐❜✉✐çã♦ ♥♦r♠❛❧ ❡♠ s✉❛ ✈❡rsã♦ ✐♥❞❡♣❡♥❞❡♥t❡ ❡ ❞❡♣❡♥❞❡♥t❡ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ❛❧é♠ ❞♦ tr❛❜❛❧❤♦ ❞❡ ▲♦♣❡s ❡ ❇♦❧❢❛r✐♥❡
❬✷✵✶✷❪✱ ❡♠ q✉❡ ❢♦✐ tr❛❜❛❧❤❛❞♦ ♦ ♠♦❞❡❧♦ ❞❡ ❈❤❡♥ ❝♦♠ ❡✳❛✳✬s✱ ♠❛s ✐♥❝❧✉✐♥❞♦ ❡❢❡✐t♦s só ♥❛ ♣❛rt❡ ❛ss♦✲ ❝✐❛❞❛ à ❝✉r❛ ✭Vj✮✳ ❊st❡ tr❛❜❛❧❤♦ ❢♦✐ ❢❡✐t♦ ❞❡ ✉♠ ♣♦♥t♦ ❞❡ ✈✐st❛ ❝❧áss✐❝♦ ❡ ❜❛②❡s✐❛♥♦✳ ▼❛s ❝♦♠♦ ♠❡♥❝✐♦♥❛❞♦ ❛♥t❡r✐♦r♠❡♥t❡✱ ❡①✐st❡♠ ♦✉tr♦s ♠♦❞❡❧♦s ❞❡ ❝✉r❛ q✉❡ ♣♦❞❡♠ s❡r ♠❛✐s ✐♥❢♦r♠❛t✐✈♦s ❡ ♠❛✐s ❝♦♠♣❧❡①♦s✱ s♦❜r❡t✉❞♦ ♥♦ ❝♦♥t❡①t♦ ❞❡ ❡st✉❞♦s ❞❡ ❝â♥❝❡r✳
✶✳✷ ❉❡s❝r✐çã♦ ❞♦s ♦❜❥❡t✐✈♦s
❖ ♦❜❥❡t✐✈♦ ❣❡r❛❧ ❞❡st❡ tr❛❜❛❧❤♦ é ♣r♦♣♦r ❡①t❡♥sõ❡s ❡♠ ♠♦❞❡❧♦s ❝♦♠ ❢r❛çã♦ ❞❡ ❝✉r❛✱ ✐♥❝❧✉✐♥❞♦ ❡❢❡✐t♦s ❛❧❡❛tór✐♦s ♥♦s ♠♦❞❡❧♦s ❞❡❈❤❡♥ ❡t ❛❧✳❬✶✾✾✾❛❪ ❡ ♦s ♠♦❞❡❧♦s ❞❡str✉t✐✈♦s ❞❡ P♦✐ss♦♥ ♣♦♥❞❡r❛❞♦ ♣r♦♣♦st♦s ♣♦r❘♦❞r✐❣✉❡s ❡t ❛❧✳❬✷✵✶✶❪✳ ❙❡rá ❝♦♥s✐❞❡r❛❞❛ t❛♥t♦ ✉♠❛ ♣❡rs♣❡❝t✐✈❛ ❝❧áss✐❝❛ q✉❛♥t♦ ✉♠❛ ❜❛②❡s✐❛♥❛✳
◆❡st❡ tr❛❜❛❧❤♦✱ ♣r♦❝✉r❛✲s❡ t❛♠❜é♠ ✐♠♣❧❡♠❡♥t❛r ❛s ♠❡t♦❞♦❧♦❣✐❛s ❞❡s❡♥✈♦❧✈✐❞❛s ❛tr❛✈és ❞❡ s✐✲ ♠✉❧❛çõ❡s ❡ ❛♣❧✐❝❛çã♦ ❛ ❞❛❞♦s r❡❛✐s✱ ❝♦♠♣❛r❛♥❞♦ ❛s ♠❡t♦❞♦❧♦❣✐❛s ❝❧áss✐❝❛s ❡ ❜❛②❡s✐❛♥❛s✳ P❛r❛ ❛t✐♥❣✐r ♦ ♦❜❥❡t✐✈♦ ♣r♦♣♦st♦✱ ❞❡✜♥✐♠♦s ♦s ♦❜❥❡t✐✈♦s ❡s♣❡❝í✜❝♦s ❞❡st❛ t❡s❡✿
✶✳ Pr♦♣♦r ✉♠ ♠ét♦❞♦ ❞❡ ❡st✐♠❛çã♦ ❝❧áss✐❝♦ ♥♦ ♠♦❞❡❧♦ ❞❡ ❈❤❡♥ ❡t ❛❧✳ ❬✶✾✾✾❛❪ ❝♦♠ ❡❢❡✐t♦s ❛❧❡❛✲ tór✐♦s(Uj, Vj)✱j= 1, . . . , J ❝♦♠♦ ❡①♣❧✐❝❛❞♦s ❛♥t❡r✐♦r♠❡♥t❡✳
✷✳ ❊st✉❞❛r ♦ ✐♠♣❛❝t♦ ♥❛s ❡st✐♠❛t✐✈❛s ❞❡ ❝♦♥s✐❞❡r❛r ❞❡ ❢♦r♠❛ ❡rró♥❡❛ ♦ ♠♦❞❡❧♦ ❞❡ ❈❤❡♥ ❡t ❛❧✳
❬✶✾✾✾❛❪ ❝♦♠ ❡❢❡✐t♦s ❛❧❡❛tór✐♦s ❞❡♣❡♥❞❡♥t❡s q✉❛♥❞♦ ❞❡✈❡r✐❛ s❡r ✉s❛❞♦ ♦ ♠♦❞❡❧♦ ❝♦♠ ❡❢❡✐t♦s ❛❧❡❛tór✐♦s ✐♥❞❡♣❡♥❞❡♥t❡s ❡ ✈✐❝❡✈❡rs❛✳
✸✳ Pr♦♣♦r ♠ét♦❞♦s ❞❡ ❡st✐♠❛çã♦ ❝❧áss✐❝♦ ❡ ❜❛②❡s✐❛♥♦ ♥♦s ♠♦❞❡❧♦s ❞❡str✉t✐✈♦s ✭❘♦❞r✐❣✉❡s ❡t ❛❧✳
❬✷✵✶✶❪✮ ❝♦♠ ❡❢❡✐t♦s ❛❧❡❛tór✐♦s(Uj, Vj)✱j= 1, . . . , J✳
✹✳ ❊st✉❞❛r ✈❛♥t❛❣❡♥s ❡ ❞❡s✈❛♥t❛❣❡♥s ❞♦s ❞♦✐s ♠ét♦❞♦s ♣r♦♣♦st♦s ♥♦ ✐t❡♠ ❛♥t❡r✐♦r✳
✶✳✸ ❖r❣❛♥✐③❛çã♦ ❞♦ tr❛❜❛❧❤♦
✹ ▼❖❚■❱❆➬➹❖ ✶✳✸
✉♠❛ r❡✈✐sã♦ ❜✐❜❧✐♦❣rá✜❝❛ ❞♦s ♠♦❞❡❧♦s ❝♦♠ ❢r❛çã♦ ❞❡ ❝✉r❛ ❡ ❛s ♣r✐♥❝✐♣❛✐s ❝❛r❛❝t❡ríst✐❝❛s ❞❡ss❡s ♠♦❞❡❧♦s✳ ❆♣r❡s❡♥t❛✲s❡ ✉♠❛ ❜r❡✈❡ r❡✈✐sã♦ ❞♦s ♠ét♦❞♦s ❇▲❯P ✭❇❡st ▲✐♥❡❛r ❯♥❜✐❛s❡❞ Pr❡❞✐❝t♦r✮ ❡ ❘❊▼▲ ✭❘❡str✐❝t❡❞ ▼❛①✐♠✉♠ ▲✐❦❡❧✐❤♦♦❞✮ ❝♦♠ ❛ ✜♥❛❧✐❞❛❞❡ ❞❡ ❢❛❝✐❧✐t❛r s❡✉ ✉s♦ ❡♠ ❢✉t✉r❛s s❡❝çõ❡s✳ ❋✐♥❛❧♠❡♥t❡✱ ❢❛③✲s❡ ✉♠❛ ✐♥tr♦❞✉çã♦ ❛♦s ♣r♦❝❡ss♦s ❞❡ ❉✐r✐❝❤❧❡t✱ ♦s q✉❡ s❡rã♦ ✉t✐❧✐③❛❞♦s ♣❛r❛ ❢❛③❡r ✉♠❛ ♠♦❞❡❧❛❣❡♠ ♥ã♦ ♣❛r❛♠étr✐❝❛ ❞❛ ❞✐str✐❜✉✐çã♦ ❞♦s ❡❢❡✐t♦s ❛❧❡❛tór✐♦s✳
◆♦ ❝❛♣ít✉❧♦ ✸ ❛♣r❡s❡♥t❛♠♦s ❜r❡✈❡♠❡♥t❡ ♦ ♠♦❞❡❧♦ ❞❡ ♠✐st✉r❛ ❝♦♠ ❡❢❡✐t♦s ❛❧❡❛tór✐♦s ♥♦r♠❛✐s ✐♥❞❡♣❡♥❞❡♥t❡s ❡ ❞❡♣❡♥❞❡♥t❡s ♣r♦♣♦st♦s ❡♠ ▲✐ ❡t ❛❧✳ ❬✷✵✵✶❪ ❡ ▲❛✐ ❡ ❨❛✉ ❬✷✵✵✽❪✱ ❞✐s❝✉t✐♥❞♦ t❛♠❜é♠ ❛ ♠❡t♦❞♦❧♦❣✐❛ ❝❧áss✐❝❛ ❜❛s❡❛❞❛ ♥♦s ❡st✐♠❛❞♦r❡s ❘❊▼▲✳ ❉❡♣♦✐s✱ é ❞❡s❡♥✈♦❧✈✐❞❛ ✉♠❛ ❛❜♦r❞❛❣❡♠ s✐♠✐❧❛r ♣❛r❛ ♦ ♠♦❞❡❧♦ ❞❡❈❤❡♥ ❡t ❛❧✳❬✶✾✾✾❛❪ ❝♦♠ ❡❢❡✐t♦s ❛❧❡❛tór✐♦s ♥♦r♠❛✐s✳ ❙ã♦ ❛♣r❡s❡♥t❛❞♦s ❞♦✐s ❡st✉❞♦s ❞❡ s✐♠✉❧❛çã♦✿ ♦ ♣r✐♠❡✐r♦ ♣❛r❛ ❛✈❛❧✐❛r s❡ ❞❛❞♦ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ♣❛râ♠❡tr♦s ♦ ♠ét♦❞♦ ♣r♦✲ ♣♦st♦ ❝♦♥s❡❣✉❡ ❡st✐♠á✲❧♦s ❡ ♦✉tr♦ ❡♠ q✉❡ ❛✈❛❧✐❛✲s❡ ♦ ❣❛♥❤♦ ♦✉ ♣❡r❞❛ ❞❡ ✉s❛r ❛ ✈❡rsã♦ ❜✐✈❛r✐❛❞❛ ❞❛ ♥♦r♠❛❧ ✈❡rs✉s ❛ ✈❡rsã♦ ✐♥❞❡♣❡♥❞❡♥t❡ ♣❛r❛ ♦s ❡❢❡✐t♦s ❛❧❡❛tór✐♦s✳ ❚❛♠❜é♠ ❢♦✐ ✐♥❝❧✉í❞❛ ✉♠❛ ❞✐s❝✉ssã♦ ❞♦ ♠♦❞❡❧♦ ❞❡ ♠✐st✉r❛ ✉s❛♥❞♦ ♦✉tr❛s ❧✐❣❛çõ❡s ♥❛ ❝✉r❛✱ ❝♦♠♦ sã♦ ❛ ❧✐❣❛çã♦ ♣r♦❜✐t♦ ❡ ❝♦♠♣❧❡♠❡♥t❛r ❧♦❣✲❧♦❣✳
◆♦ ❝❛♣ít✉❧♦✹❞❡s❡♥✈♦❧✈❡♠♦s ✉♠❛ ♠❡t♦❞♦❧♦❣✐❛ ❝❧áss✐❝❛ s✐♠✐❧❛r à ❞♦ ❝❛♣ít✉❧♦ ❛♥t❡r✐♦r ♣❛r❛ ♦s ♠♦✲ ❞❡❧♦s ❞❡str✉t✐✈♦s ❝♦♠ ❡❢❡✐t♦s ❛❧❡❛tór✐♦s ❜❛s❡❛❞❛ t❛♠❜é♠ ♥♦s ❡st✐♠❛❞♦r❡s ❘❊▼▲✳ ❚❛♠❜é♠ ♣r♦♣õ❡✲s❡ ✉♠❛ ♠❡t♦❞♦❧♦❣✐❛ ❜❛②❡s✐❛♥❛ ♣❛r❛ ❡ss❡ ♠♦❞❡❧♦ ❜❛s❡❛❞❛ ♥♦ ✉s♦ ❞❡ ♣r♦❝❡ss♦s ❞❡ ❉✐r✐❝❤❧❡t ♣❛r❛ ♦s ❡❢❡✐✲ t♦s ❛❧❡❛tór✐♦s✱ ♦ q✉❡ ♣❡r♠✐t❡ ✢❡①✐❜✐❧✐③❛r ❛ ❞✐str✐❜✉✐çã♦ ✉t✐❧✐③❛❞❛ ♣❛r❛ ♦s ❡❢❡✐t♦s ❛❧❡❛tór✐♦s✳ ❆s ❞✉❛s ❛❜♦r❞❛❣❡♥s sã♦ ❝♦♠♣❛r❛❞❛s ❛tr❛✈és ✉♠ ❡st✉❞♦ ❞❡ s✐♠✉❧❛çã♦ ❡♠ q✉❡ ♦s ❡❢❡✐t♦s ❛❧❡❛tór✐♦s ❢♦r❛♠ ❣❡r❛❞♦s ❞❡ ❞✐❢❡r❡♥t❡s ❞✐str✐❜✉✐çõ❡s✱ ✐♥❝❧✉✐♥❞♦ ❛ ❞✐str✐❜✉✐çã♦ ♥♦r♠❛❧✳
❖ ❝❛♣ít✉❧♦ ✺ ❛♣r❡s❡♥t❛ ✉♠❛ ❛♣❧✐❝❛çã♦ ❛♦ ❜❛♥❝♦ ❞❡ ❞❛❞♦s r❡❛❧ ❞❡ ❑❛❧❜✢❡✐s❝❤ ❡ Pr❡♥t✐❝❡ ❬✷✵✵✷❪ ❞✐s❝✉t✐❞♦ ♥♦ ❝♦♠❡ç♦ ❞❡st❡ ❝❛♣ít✉❧♦✳ ■❧✉str❛✲s❡ ❛ ✈❛♥t❛❣❡♠ ✐♥t❡r♣r❡t❛t✐✈❛ ❞❡ ✉t✐❧✐③❛r ♦s ♠♦❞❡❧♦s ❞❡s✲ tr✉t✐✈♦s ❝♦♠ ❡❢❡✐t♦s ❛❧❡❛tór✐♦s ❡♠ r❡❧❛çã♦ ❛♦s ♠♦❞❡❧♦s ❞❡ ❈❤❡♥ ❡t ❛❧✳ ❬✶✾✾✾❛❪ ❡ ❞❡ ♠✐st✉r❛ ❝♦♠ ❡❢❡✐t♦s ❛❧❡❛tór✐♦s✳
P♦r ú❧t✐♠♦✱ ♦ ❝❛♣ít✉❧♦ ✻ ❞✐s❝✉t❡ ❛s ♣r✐♥❝✐♣❛✐s ❝♦♥❝❧✉sõ❡s ❞❡st❡ tr❛❜❛❧❤♦ ❡ ♣❡rs♣❡❝t✐✈❛s ❢✉t✉r❛s ❞❡ ♣❡sq✉✐s❛✳
P❛rt❡ ❞❡st❡ tr❛❜❛❧❤♦ ❥á ❢♦✐ ❛❝❡✐t♦ ❡♠ ♣❡r✐ó❞✐❝♦s ❞❡ ❝✐r❝✉❧❛çã♦ ✐♥t❡r♥❛❝✐♦♥❛❧ ✭●❛❧❧❛r❞♦ ❡t ❛❧✳
❈❛♣ít✉❧♦ ✷
Pr❡❧✐♠✐♥❛r❡s
❊st❡ ❝❛♣ít✉❧♦ ❡stá ❝❡♥tr❛❞♦ ♥❛ ❛♣r❡s❡♥t❛çã♦ ❞❛s ❞✐str✐❜✉✐çõ❡s ❛ s❡r❡♠ ✉t✐❧✐③❛❞❛s ♥❡st❡ tr❛❜❛❧❤♦✱ ❛❧❣✉♠❛s té❝♥✐❝❛s ❞❡ ❡st✐♠❛çã♦ q✉❡ s❡rã♦ ✉t✐❧✐③❛❞❛s ❡♠ ❢✉t✉r♦s ❝❛♣ít✉❧♦s ❞❡s❡♥✈♦❧✈✐❞♦s ❡ ✐♥tr♦❞✉③✐r ❛ ❝❧❛ss❡ ❞❡ ♠♦❞❡❧♦s ❝♦♠ ❢r❛çã♦ ❞❡ ❝✉r❛ ♥♦ ❝♦♥t❡①t♦ ❞❡ ❛♥á❧✐s❡ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛✳
◆❛ s❡çã♦ ✷✳✶ ❛♣r❡s❡♥t❛♠✲s❡ ❛s ❞✐str✐❜✉✐çõ❡s ❲❡✐❜✉❧❧ ❡ ❊①♣♦♥❡♥❝✐❛❧ ❙❡❣♠❡♥t❛❞❛✱ ❞✐str✐❜✉✐çõ❡s ♠✉✐t♦ ✐♠♣♦rt❛♥t❡s ♥❡st❡ tr❛❜❛❧❤♦ ♣♦✐s ♣❡rt❡♥❝❡♠ à r❡❞✉③✐❞❛ ❝❧❛ss❡ ❞❡ ♠♦❞❡❧♦s ♣❛r❛♠étr✐❝♦s ❞❡ r✐s✲ ❝♦s ♣r♦♣♦r❝✐♦♥❛✐s✱ ❛❧é♠ ❞❡ ✐♥tr♦❞✉③✐r ❛ ❞✐str✐❜✉✐çã♦ ❲✐s❤❛rt ❡ ❲✐s❤❛rt ■♥✈❡rt✐❞❛✳ P♦st❡r✐♦r♠❡♥t❡✱ ♥❛ s❡çã♦ ✷✳✷❢❛③✲s❡ ✉♠❛ rá♣✐❞❛ r❡✈✐sã♦ ❞♦s ♣r✐♥❝✐♣❛✐s ♠♦❞❡❧♦s ❝♦♠ ❢r❛çã♦ ❞❡ ❝✉r❛ ♥❛ ❧✐t❡r❛t✉r❛✳ ◆❛ s❡çã♦✷✳✸sã♦ ❛♣r❡s❡♥t❛❞♦ ♦s ❡st✐♠❛❞♦r❡s ❇▲❯P ✭❇❡st ▲✐♥❡❛r ❯♥❜✐❛s❡❞ Pr❡❞✐❝t✐♦♥✮ ❡ ♦s ❡st✐♠❛❞♦r❡s ❘❊▼▲ ✭❘❡str✐❝t❡❞ ▼❛①✐♠✉♠ ▲✐❦❡❧✐❤♦♦❞✮ ❡♠ ✉♠ ♠♦❞❡❧♦ ❞❡ ❡❢❡✐t♦s ❛❧❡❛tór✐♦s✱ ❡♥✉♥❝✐❛♥❞♦ ❛❧❣✉♠❛s ♣r♦♣r✐❡❞❛❞❡s ❞❡❧❡s✳ ❋✐♥❛❧♠❡♥t❡✱ ♥❛ s❡çã♦✷✳✹❛♣r❡s❡♥t❛✲s❡ ✉♠❛ ❜r❡✈❡ ✐♥tr♦❞✉çã♦ ❛♦s Pr♦❝❡ss♦s ❉✐r✐✲ ❝❤❧❡t ✭P✳❉✳✬s✮✱ ✐♥❝❧✉✐♥❞♦ ❛❧❣✉♥s ♠ét♦❞♦s ❞❡ ❛♠♦str❛❣❡♠ ♣❛r❛ ❡st❡s ♣r♦❝❡ss♦s ❡♠ ♠♦❞❡❧♦s ❝♦♥❥✉❣❛❞♦s ❡ ♥ã♦ ❝♦♥❥✉❣❛❞♦s✱ ❛❧é♠ ❞❡ ✐♥tr♦❞✉③✐r ❛ ♥♦çã♦ ❞❡ Pr♦❝❡ss♦s ❉✐r✐❝❤❧❡t ❈❡♥tr❛❞♦s ✭P✳❉✳❈✳✬s✮✳
✷✳✶ ❆❧❣✉♠❛s ❞✐str✐❜✉✐çõ❡s ❞❡ ✐♥t❡r❡ss❡
❊st❛ s❡çã♦ ✈✐s❛ ❛❥✉❞❛r ❛♦ ❧❡✐t♦r ❛♦ ❡♥t❡♥❞✐♠❡♥t♦ ❞❡ ❞✉❛s ❞✐str✐❜✉✐çõ❡s ✉t✐❧✐③❛❞❛s ♥❡st❡ tr❛❜❛✲ ❧❤♦✿ ❛s ❞✐str✐❜✉✐çõ❡s ❲❡✐❜✉❧❧ ❡ ❊①♣♦♥❡♥❝✐❛❧ ❙❡❣♠❡♥t❛❞❛✳ ❙❡rã♦ ✐♥❞✐❝❛❞❛s ❛❧❣✉♠❛s ❝❛r❛❝t❡ríst✐❝❛s ❡ ♣r♦♣r✐❡❞❛❞❡s ❞❡ ❝❛❞❛ ✉♠❛ ❞❡❧❛s✱ ❛❧é♠ ❞❡ ✉♥✐✜❝❛r ❛ ♥♦t❛çã♦ ❞❛s ❞✉❛s ❞✐str✐❜✉✐çõ❡s✱ ❛❥✉❞❛♥❞♦ ❛♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡st❡ tr❛❜❛❧❤♦✳ ❚❛♠❜é♠ s❡rã♦ ✐♥tr♦❞✉③✐❞❛s ❛s ❞✐str✐❜✉✐çõ❡s ❲✐s❤❛rt ❡ ❲✐s❤❛rt✲ ■♥✈❡rt✐❞❛✱ ❡st❛ ú❧t✐♠❛ ❞❡ ❣r❛♥❞❡ r❡❧❡✈â♥❝✐❛ ♥❛ ■♥❢❡rê♥❝✐❛ ❜❛②❡s✐❛♥❛ ♣♦✐s ♣❡r♠✐t❡ ❛ ❝♦♥❥✉❣❛çã♦ ❞❛ ♠❛tr✐③ ❞❡ ✈❛r✐â♥❝✐❛✲❝♦✈❛r✐â♥❝✐❛ ♥♦ ♠♦❞❡❧♦ ◆♦r♠❛❧✳
✷✳✶✳✶ ❉✐str✐❜✉✐çã♦ ❲❡✐❜✉❧❧
❆ ❞✐str✐❜✉✐çã♦ ❲❡✐❜✉❧❧ t❡♠ s✐❞♦ ❛♠♣❧❛♠❡♥t❡ ✉t✐❧✐③❛❞❛ ♥❛ ❛♥á❧✐s❡ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛✳ ❋♦✐ ❛♣r❡s❡♥✲ t❛❞❛ ♦r✐❣✐♥❛❧♠❡♥t❡ ♣♦r ❲❡✐❜✉❧❧ ❬✶✾✸✾❪ ❡ ✉t✐❧✐③❛❞❛ ♥❛ ❛♥á❧✐s❡ ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ♣♦st❡r✐♦r♠❡♥t❡ ♣♦r
❲❡✐❜✉❧❧ ❬✶✾✺✶❪✳ ❉❡s❞❡ ❡♥tã♦✱ t❡♠ s✐❞♦ ❡①t❡♥s❛♠❡♥t❡ ✉t✐❧✐③❛❞❛ ❝♦♠♦ ♠♦❞❡❧♦ ❡♠ ❛♣❧✐❝❛çõ❡s ❜✐♦♠é✲ tr✐❝❛s✱ ✐♥❞✉str✐❛✐s ❡ ♠✉✐t❛s ♦✉tr❛s ár❡❛s✳ ❯♠❛ ❞❛s ♣r✐♥❝✐♣❛✐s ❝❛r❛❝t❡ríst✐❝❛s ❞❡st❛ ❞✐str✐❜✉✐çã♦ ♥❛ ♠♦❞❡❧❛❣❡♠ é s✉❛ ✢❡①✐❜✐❧✐❞❛❞❡ ❡♠ ❛❝♦♠♦❞❛r ❞✐❢❡r❡♥t❡s ❢♦r♠❛s ♥❛ t❛①❛ ❞❡ ❢❛❧❤❛ ✭❢✉♥çã♦ ❞❡ r✐s❝♦✮✱ ❛♣❡♥❛s ✈❛r✐❛♥❞♦ ♦ ✈❛❧♦r ❞♦ ♣❛râ♠❡tr♦ ❞❡ ❢♦r♠❛✳
❆ ✈❛r✐á✈❡❧ T t❡♠ ❞✐str✐❜✉✐çã♦ ❲❡✐❜✉❧❧ ❝♦♠ ♣❛râ♠❡tr♦ ❞❡ ❢♦r♠❛ ν > 0 ❡ ♣❛râ♠❡tr♦ ❞❡ ❡s❝❛❧❛ λ >0 ✭❞❡♥♦t❛♠♦s T ∼❲❡✐❜✉❧❧(λ, ν)✮ s❡ ❛ ❢✉♥çã♦ ❞❡ ❞❡♥s✐❞❛❞❡ é ❞❛❞❛ ♣♦r
f(t|λ, ν) =λνtν−1exp{−λtν}, t >0. ✭✷✳✶✮ ❆s ❢✉♥çõ❡s ❞❡ s♦❜r❡✈✐✈ê♥❝✐❛ ❡ ❞❡ r✐s❝♦ sã♦ ❞❛❞❛s r❡s♣❡❝t✐✈❛♠❡♥t❡ ♣♦r
