Academia.eduAcademia.edu
❆♣r❡s❡♥t❛çã♦ ❞♦ ❘ ❝♦♠ ✉♠ ❡①❡♠♣❧♦ ❞❡ ❛♥á❧✐s❡ ❞❡ r❡❣r❡ssã♦ ♥ã♦✲❧✐♥❡❛r ∗ ❊❞✉❛r❞♦ ❊st❡✈❡s ✷ ❞❡ ▼❛rç♦ ❞❡ ✷✵✶✶ ■♥st✐t✉t♦ ❙✉♣❡r✐♦r ❞❡ ❊♥❣❡♥❤❛r✐❛✱ ❯♥✐✈❡rs✐❞❛❞❡ ❞♦ ❆❧❣❛r✈❡✱ ❈❛♠♣✉s ❞❛ P❡♥❤❛✱ ✽✵✵✺✲✶✸✾ ❋❛r♦ ❡ ❈❡♥tr♦ ❞❡ ❈✐ê♥❝✐❛s ❞♦ ▼❛r ❈❈▼❆❘ ✲ ❈■▼❆❘✱ ▲❛❜♦r❛tór✐♦ ❆ss♦❝✐❛❞♦✱ ❊❞✐❢í❝✐♦ ✼✱ ❈❛♠♣✉s ❞❡ ●❛♠❜❡❧❛s✱ ✽✵✵✺✲✶✸✾ ❋❛r♦❀ ❊✲♠❛✐❧✿ ❡❡st❡✈❡s❅✉❛❧❣✳♣t❀ ❯❘▲✿ ❤tt♣✿✴✴✇✸✳✉❛❧❣✳♣t✴∼❡❡st❡✈❡s ❘❡s✉♠♦ ◆♦ s❡❣✉✐♠❡♥t♦ ❞✉♠ ❛rt✐❣♦ ❛♥t❡r✐♦r ❛❝❡r❝❛ ❞❛ ❛♥á❧✐s❡ ❞❡ r❡❣r❡ssã♦ ♥ã♦✲❧✐♥❡❛r ✭s✐♠♣❧❡s✮ ✉t✐❧✐✲ ➤ ③❛♥❞♦ ❛ ❢❡rr❛♠❡♥t❛ ❙♦❧✈❡r ❞♦ ❘✱ ➤ ❞♦ ❊①❝❡❧ ✭❊st❡✈❡s✱ ✷✵✶✵✮ ♣r♦♣õ❡✲s❡ ♥❡st❡ ❛rt✐❣♦ ❛ ❛♣r❡s❡♥t❛çã♦ ✉♠❛ ❧✐♥❣✉❛❣❡♠ ❞❡ ♣r♦❣r❛♠❛çã♦ ❡ ✉♠ ❛♠❜✐❡♥t❡ ♣❛r❛ ❝♦♠♣✉t❛çã♦ ❡st❛tíst✐❝❛ ❡ ❣rá✜❝❛✱ ❛tr❛✈és ❞❛ s✉❛ ❛♣❧✐❝❛çã♦ ♥❛ ✏ ❞❡s❝r✐çã♦✑ ❞❡ r❡❧❛çõ❡s ❡st❛tíst✐❝❛s ✭♥ã♦✲❧✐♥❡❛r❡s✮ ❡♥tr❡ ✈❛r✐á✈❡✐s✳ P❛❧❛✈r❛s✲❝❤❛✈❡✿ ❘✱ ❘❡❣r❡ssã♦ ♥ã♦✲❧✐♥❡❛r✳ ■♥tr♦❞✉çã♦ ❖ ❘ ✭❘ ❉❡✈❡❧♦♣♠❡♥t ❈♦r❡ ❚❡❛♠✱ ✷✵✵✼✮ é ❛♦ ♠❡s♠♦ t❡♠♣♦ ✉♠❛ ❧✐♥❣✉❛❣❡♠ ❞❡ ♣r♦❣r❛♠❛çã♦ ❡ ✉♠ ❛♠❜✐❡♥t❡ ♣❛r❛ ❝♦♠♣✉t❛çã♦ ❡st❛tíst✐❝❛ ❡ ❣rá✜❝❛✳ ❚r❛t❛✲s❡ ❞❡ ✉♠❛ ❧✐♥❣✉❛❣❡♠ ❞❡ ♣r♦❣r❛♠❛çã♦ ❡s♣❡❝✐❛❧✐③❛❞❛ ❡♠ ❝♦♠♣✉t❛çã♦ ❝♦♠ ❞❛❞♦s✳ ❯♠❛ ❞❛s s✉❛s ♣r✐♥❝✐♣❛✐s ❝❛r❛❝t❡ríst✐❝❛s é ♦ s❡✉ ❝❛rá❝✲ t❡r ❣r❛t✉✐t♦ ❡ ❛ s✉❛ ❞✐s♣♦♥✐❜✐❧✐❞❛❞❡ ♣❛r❛ ✉♠❛ ❣❛♠❛ ❜❛st❛♥t❡ ✈❛r✐❛❞❛ ❞❡ s✐st❡♠❛s ♦♣❡r❛t✐✈♦s ✭✈❞✳ ❤tt♣✿✴✴✇✇✇✳r✲♣r♦❥❡❝t✳♦r❣✮✳ ❆♣❡s❛r ❞♦ s❡✉ ❝❛rá❝t❡r ❣r❛t✉✐t♦✱ ♦ ❘ é ✉♠❛ ❢❡rr❛♠❡♥t❛ ❜❛st❛♥t❡ ♣♦❞❡✲ r♦s❛ ❝♦♠ ❜♦❛s ❝❛♣❛❝✐❞❛❞❡s ❛♦ ♥í✈❡❧ ❞❛ ♣r♦❣r❛♠❛çã♦ ❡ ✉♠ ❝♦♥❥✉♥t♦ ❜❛st❛♥t❡ ✈❛st♦ ✭❡ ❡♠ ❝♦♥st❛♥t❡ ❝r❡s❝✐♠❡♥t♦✮ ❞❡ ♣❛❝❦❛❣❡s q✉❡ ❛❝r❡s❝❡♥t❛♠ ❜❛st❛♥t❡s ♣♦t❡♥❝✐❛❧✐❞❛❞❡s à ❥á ♣♦❞❡r♦s❛ ✈❡rsã♦ ❜❛s❡ ❞♦ ❘ ✭❚♦r❣♦✱ ✷✵✵✻✮✳ ❈♦♥t✉❞♦✱ ♦ t❡r♠♦ ✏ ❛♠❜✐❡♥t❡✑ ♣r❡t❡♥❞❡ ❝❛r❛❝t❡r✐③❛r ♦ ❘ ❝♦♠♦ ✉♠ s✐st❡♠❛ ❝♦♠✲ ♣❧❡t♦ ❡ ❝♦❡r❡♥t❡ ❛♦ ✐♥✈és ❞✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❢❡rr❛♠❡♥t❛s ♠✉✐t♦ ❡s♣❡❝í✜❝❛s ❡ r❡❧❛t✐✈❛♠❡♥t❡ ✐♥✢❡①í✈❡✐s ✭❱❡♥❛❜❧❡s ❡t ❛❧✳✱ ✷✵✵✻✮✳ ❖ ❘ ♣♦❞❡ s❡r ❡♥t❡♥❞✐❞♦ ❝♦♠♦ ✉♠❛ ✐♠♣❧❡♠❡♥t❛çã♦ ❞❛ ❧✐♥❣✉❛❣❡♠ ❙ ❞❡s❡♥✈♦❧✈✐❞❛ ♣♦r ❘✐❝❦ ❇❡❝✲ ❦❡r✱ ❏♦❤♥ ❈❤❛♠❜❡rs ❡ ❆❧❧❛♥ ❲✐❧❦s ♥♦s ❇❡❧❧ ▲❛❜♦r❛t♦r✐❡s ✭❊✳❯✳❆✳✮✱ q✉❡ t❛♠❜é♠ ❝♦♥st✐t✉✐ ❛ ❜❛s❡ ❞♦ s♦❢t✇❛r❡ ❙✲P❧✉s ➤ ✭■♥s✐❣❤t❢✉❧ ❈♦r♣✳✮✳ ❆ ❡✈♦❧✉çã♦ ❞❛ ❧✐♥❣✉❛❣❡♠ ❞❡ ❏♦❤♥ ❈❤❛♠❜❡rs ❡ ❝♦❧❛❜♦r❛❞♦r❡s✳ ❆s ✏ ❞✐str✐❜✉✐çõ❡s✑ ❞♦ ✭✈❞✳ ❙ ❡stá ❞❡s❝r✐t❛ ❡♠ q✉❛tr♦ ❧✐✈r♦s ❘ ✐♥❝❧✉❡♠ ✉♠ ❜♦♠ ❝♦♥❥✉♥t♦ ❞❡ ♠❛♥✉❛✐s ❤tt♣✿✴✴❝r❛♥✳r✲♣r♦❥❡❝t✳♦r❣✴♠❛♥✉❛❧s✳❤t♠❧✮ ❡ ❡①✐st❡♠✱ ❛❝t✉❛❧♠❡♥t❡✱ ✈ár✐♦s ❧✐✈r♦s q✉❡ ❞❡s❝r❡✲ ✈❡♠ ❛ ✉t✐❧✐③❛çã♦ ❞♦ ❜♦♦❦s✳❤t♠❧✮✱ ❡✳❣✳ ❘ ♣❛r❛ ❛♥á❧✐s❡ ❡st❛tíst✐❝❛ ❞❡ ❞❛❞♦s ✭✈❞✳ ❤tt♣✿✴✴✇✇✇✳r✲♣r♦❥❡❝t✳♦r❣✴❞♦❝✴❜✐❜✴❘✲ ❉❛❧❣❛❛r❞ ✭✷✵✵✷✮ ♦✉ ❈r❛✇❧❡② ✭✷✵✵✼✮✳ ◆❛ ú❧t✐♠❛ r❡✈✐sã♦ ❞❡st❡ ❛rt✐❣♦ ✉s❡✐ ❛ ✈❡rsã♦ ✷✳✶✷✳✵ ✭❡♠❜♦r❛ s❡❥❛♠ ❞✐s♣♦♥✐❜✐❧✐③❛❞❛s r❡❣✉❧❛r♠❡♥t❡ ✏♥♦✈❛s✑ ✈❡rsõ❡s ❞♦ ∗ ❈✐t❛çã♦ r❡❝♦♠❡♥❞❛❞❛✿ ❘✮✳ ❖ ✜❝❤❡✐r♦ ❞❡ ❊st❡✈❡s✱ ❊✳ ✭✷✵✶✶✮ ❆♣r❡s❡♥t❛çã♦ ❞♦ ❘ ❝♦♠ ✉♠ ❡①❡♠♣❧♦ ❞❡ ❛♥á❧✐s❡ ❞❡ r❡❣r❡s✲ sã♦ ♥ã♦✲❧✐♥❡❛r✳ ■♥st✐t✉t♦ ❙✉♣❡r✐♦r ❞❡ ❊♥❣❡♥❤❛r✐❛ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❞♦ ❆❧❣❛r✈❡✱ ❋❛r♦✱ ✶✵ ♣✳ ❬❞✐s♣♦♥í✈❡❧ ❡♠ ❤tt♣✿✴✴✇✸✳✉❛❧❣✳♣t✴∼❡❡st❡✈❡s✱ ❝♦♥s✉❧t❛❞♦ ❡♠ ❞❛t❛ ❪ ✶ ✐♥st❛❧❛çã♦ ✭❘✲❳✳❳❳✳❳✲✇✐♥✸✷✳❡①❡✮ ♣❛r❛ ▼✐❝r♦s♦❢t ❲✐♥❞♦✇s ➤ ♣♦❞❡ s❡r ♦❜t✐❞♦ ❡♠ ❤tt♣✿✴✴❝r❛♥✳❛t✳r✲ ♣r♦❥❡❝t✳♦r❣✴❜✐♥✴✇✐♥❞♦✇s✴❜❛s❡✴ ❡ ♦ ♣r♦❝❡ss♦ ❞❡ ✐♥st❛❧❛çã♦ é s✐♠♣❧❡s✳ ❚❛♠❜é♠ ❡①✐st❡♠ ✏ ✈❡rsõ❡s✑ ♣❛r❛ ▼❛❝ ❖❙ ❡ ❯♥✐①✴▲✐♥✉①✱ ❡ ✻✹✲❜✐t ♣❛r❛ ❲✐♥❞♦✇s✳ ❖ sít✐♦ ❡❧❡❝tró♥✐❝♦ ❞♦ ♣r♦❥❡❝t♦ ❝♦♥st✐t✉✐ ❛ ♣r✐♥❝✐♣❛❧ r❡❢❡rê♥❝✐❛ ❞♦ ❘ ❡ ❢✉♥❝✐♦♥❛ ❝♦♠♦ ♣♦♥t♦ ❞❡ ♣❛rt✐❞❛ ♣❛r❛ ❡①♣❧♦r❛r ♠❛✐s ❡st❡ s✐st❡♠❛✳ ❇♦❛ ♣❛rt❡ ❞❛s ♣❡ss♦❛s ✉t✐❧✐③❛ ♦ ❘ ❝♦♠♦ ✉♠ s✐st❡♠❛ ♣❛r❛ ❛♥á❧✐s❡ ❡st❛tíst✐❝❛ ❞❡ ❞❛❞♦s✱ ✉♠❛ ✈❡③ q✉❡ ❛ ♠❛✐♦r✐❛ ❞❛s ✏ ❡st❛tíst✐❝❛s ❝❧áss✐❝❛s✑ ❡ ♠✉✐t❛s ❞❛s ♠❡t♦❞♦❧♦❣✐❛s ♠❛✐s r❡❝❡♥t❡s ❡stã♦ ❞✐s♣♦♥í✈❡✐s✱ ❡♠❜♦r❛ ♦s ♣r♦♠♦t♦r❡s ♣r❡✜r❛♠ ✏ ♣❡♥s❛r✑ ♦ ✐♠♣❧❡♠❡♥t❛❞❛s ✭❱❡♥❛❜❧❡s ❡t ❛❧✳✱ ✷✵✵✻✮✳ ❘ ❝♦♠♦ ✉♠ ❛♠❜✐❡♥t❡ ♥♦ q✉❛❧ ❡ss❛s té❝♥✐❝❛s tê♠ s✐❞♦ ❈❡r❝❛ ❞❡ ✷✺ ♣❛❝♦t❡s ✭✐✳❡✳ ❝♦♥❥✉♥t♦s ❞❡ ❢✉♥çõ❡s✮ ❢❛③❡♠ ♣❛rt❡ ❞♦ s✐st❡♠❛ ❜ás✐❝♦ ✭♦s ✏ r❡❝♦♠♠❡♥❞❡❞✑ ♣❛❝❦❛❣❡s✮✱ ♠❛s ♠✉✐t♦s ♦✉tr♦s ❡stã♦ ❞✐s♣♦♥í✈❡✐s ❛tr❛✈és ❞♦ ❈❘❆◆ ✭✈✐❛ ❤tt♣✿✴✴❈❘❆◆✳❘✲♣r♦❥❡❝t✳♦r❣✮ ♣❛r❛ ✐♥st❛❧❛çã♦✳ ❯♠❛ ✐♠♣♦rt❛♥t❡ ❞✐❢❡r❡♥ç❛ ❡♥tr❡ ❛ ❧✐♥❣✉❛❣❡♠ ❙❆❙ ➤ ❙ ✭❡ ♦ ❘✮ ❡ ♦✉tr♦s s✐st❡♠❛s ✭❡✳❣✳ ➤ ❙P❙❙ ♦✉ ✮ r❡s✐❞❡ ♥❛ ✭♠✉✐t♦✮ ♠❡♥♦r q✉❛♥t✐❞❛❞❡ ❞❡ r❡s✉❧t❛❞♦s ❛♣r❡s❡♥t❛❞♦s ♣❛r❛ ✉♠❛ q✉❛❧q✉❡r ❛♥á❧✐s❡ ❡st❛tíst✐❝❛✱ ❡♠❜♦r❛ ♦s r❡s✉❧t❛❞♦s s❡❥❛♠ ❣✉❛r❞❛❞♦s ❡♠ ♦❜❥❡❝t♦s ♣❛r❛ ♣♦st❡r✐♦r ❝♦♥s✉❧t❛ ♦✉ ✉t✐❧✐③❛çã♦ ♣❡❧♦ ❘ ♥♦✉tr❛s ❢✉♥çõ❡s ✭❱❡♥❛❜❧❡s ❡t ❛❧✳✱ ✷✵✵✻✮✳ ◆❡st❡ ❛rt✐❣♦✱ ♣r❡t❡♥❞❡✲s❡ ❛♣r❡s❡♥t❛r ✭♠✉✐t♦ s✉❝✐♥t❛♠❡♥t❡✮ ♦ ❘✱ ✉♠❛ ❧✐♥❣✉❛❣❡♠ ❞❡ ♣r♦❣r❛♠❛çã♦ ❡s♣❡❝✐❛❧✐③❛❞❛ ❡♠ ❝♦♠♣✉t❛çã♦ ❝♦♠ ❞❛❞♦s✱ ✉t✐❧✐③❛♥❞♦✲❛ ♣❛r❛ ❛♥❛❧✐s❛r ♣r♦❜❧❡♠❛s ❝✉❥♦ ♦❜❥❡❝t✐✈♦ é ✏ ❞❡s❝r❡✈❡r✑ r❡❧❛çõ❡s ❡st❛tíst✐❝❛s ✭♥ã♦✲❧✐♥❡❛r❡s✮ ❡♥tr❡ ✈❛r✐á✈❡✐s✳ ❛s♣❡❝t♦s ❡st❛tíst✐❝♦s ❞♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s✱ ❛♣❡♥❛s ♦ ◆ã♦ s❡ ♣r❡t❡♥❞❡ ❞✐s❝✉t✐r ❛q✉✐ ♦s ♠♦❞✉s ♦♣❡r❛♥❞✐ ✭❛✐♥❞❛ q✉❡ ❞❡ ❢♦r♠❛ s✐♠♣❧✐✲ ✜❝❛❞❛✮✳ ❘❡❣r❡ssã♦ ♥ã♦✲❧✐♥❡❛r ✭s✐♠♣❧❡s✮ ❖s ✈ár✐♦s ❛s♣❡❝t♦s r❡❧❛❝✐♦♥❛❞♦s ❝♦♠ ❛ r❡❣r❡ssã♦ ♥ã♦✲❧✐♥❡❛r ✭s✐♠♣❧❡s✮ q✉❡ s❡r✈❡♠ ❞❡ ❜❛s❡ ❛ ❡st❡ ❛rt✐❣♦ ❢♦r❛♠ ❛❜♦r❞❛❞♦s✱ ❛✐♥❞❛ q✉❡ ❞❡ ❢♦r♠❛ ✐♥❢♦r♠❛❧ ❡ ♣♦ss✐✈❡❧♠❡♥t❡ ✐♥❝♦♠♣❧❡t❛✱ ♥✉♠ ❛rt✐❣♦ ❛♥t❡r✐♦r ✭❊st❡✈❡s✱ ✷✵✶✵✮✳ ❊♠ ✈ár✐♦s ❞♦♠í♥✐♦s ❞♦ ❝♦♥❤❡❝✐♠❡♥t♦✱ ❡✳❣✳ ❜✐♦❧♦❣✐❛✱ ❢ís✐❝❛✱ q✉í♠✐❝❛✱ ❡♥❣❡♥❤❛r✐❛✱ ❡t❝✳✱ sã♦ ✉s❛❞♦s ♠♦❞❡❧♦s ♠❛t❡♠át✐❝♦s ♣❛r❛ ❞❡s❝r❡✈❡r ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s ❡♠♣ír✐❝♦s✱ ❣❡♥❡r✐❝❛♠❡♥t❡ y = f (x) + ǫ ❡♠ q✉❡ ② é ❛ ✈❛r✐á✈❡❧ ❞❡♣❡♥❞❡♥t❡✱ ① é ❛ ✈❛r✐á✈❡❧ ✏ ✐♥❞❡♣❡♥❞❡♥t❡✑ ✕ ♣♦r ✈❡③❡s✱ ❝♦♥tr♦❧❛❞❛ ♣❡❧♦ ✐♥✈❡st✐❣❛❞♦r ✕ ❡ ❢✭①✮ é ✉♠❛ ❢✉♥çã♦ q✉❡ ♣♦❞❡ ✐♥❝❧✉✐r ✉♠ ♦✉ ♠❛✐s ♣❛râ♠❡tr♦s θ ❡ ǫ sã♦ ♦s ❡rr♦s ❛❧❡❛tór✐♦s✱ ✐♥❞❡♣❡♥❞❡♥t❡s ❡ ❝♦♠ ❞✐str✐❜✉✐çã♦ ♥♦r♠❛❧✳ ❖✉tr❛ ❢♦r♠✉❧❛çã♦✱ ❡q✉✐✈❛❧❡♥t❡✱ é ✭❡♠ q✉❡ ŷ s❡ ❧ê ✈❛❧♦r ❡s♣❡r❛❞♦✱ ♦✉ ❡st✐♠❛❞♦✱ ❞❡ ŷ = f (x) ② ✮✳ ◗✉❛♥t♦ ♠❡❧❤♦r ❢✭①✮ s❡ ❛❥✉st❛r ❛♦s ❞❛❞♦s✱ ♠❛✐s ✏ r✐❣♦r♦s❛♠❡♥t❡✑ ❞❡s❝r❡✈❡rá ❛q✉❡❧❛ r❡❧❛çã♦ ✭❇r♦✇♥✱ ✷✵✵✶✮✳ Pr❡t❡♥❞❡✲s❡ ❛❥✉st❛r ❛ ❢✉♥çã♦ ❛♦s ❞❛❞♦s ❡♠♣ír✐❝♦s ❞❡ ❢♦r♠❛ ❛ ♠✐♥✐♠✐③❛r ♦s ❡rr♦s ♦✭s✮ ♣❛râ♠❡tr♦✭s✮ ❞❛ ❢✉♥çã♦ ǫi = (yi − ŷ)✳ ❢✭①✮ ❉❡ ❢❛❝t♦✱ ♦ ♦❜❥❡❝t✐✈♦ é ❡st✐♠❛r ❢✭①✮ ❞❡ ♠♦❞♦ ❛ ♠✐♥✐♠✐③❛r ❛ s♦♠❛ ❞♦s q✉❛❞r❛❞♦s ❞♦s ❡rr♦s✱ ❙◗❊ ✕ ♠ét♦❞♦ ❞♦s ♠í♥✐♠♦s q✉❛❞r❛❞♦s✳ ◆♦ ❝❛s♦ ❞❡ ❢✉♥çõ❡s ✭♦✉ ♠♦❞❡❧♦s✮ ♥ã♦✲❧✐♥❡❛r❡s✱ ❡✳❣✳ y = aexp(bx)✱ ♥ã♦ é ♣♦ssí✈❡❧ ♦❜t❡r ❛s ❡st✐♠❛t✐✈❛s ❞♦s ♣❛râ♠❡tr♦s ♥✉♠ ú♥✐❝♦ ♣❛ss♦✱ ❝♦♠♦ ♥♦ ❝❛s♦ ❞❡ r❡❣r❡ssõ❡s ❧✐♥❡❛r❡s✱ ♣❡❧♦ q✉❡ ❛ ❙◗❊ é ♠✐♥✐♠✐③❛❞❛ ❛tr❛✈és ❞✉♠ ♣r♦❝❡ss♦ ✐t❡r❛t✐✈♦ ✭❝í❝❧✐❝♦✮ ✉t✐❧✐③❛♥❞♦ ✉♠ ❛❧❣♦r✐t♠♦ ❛♣r♦♣r✐❛❞♦ q✉❡ ♥❡❝❡ss✐t❛ ❞♦s ✈❛❧♦r❡s ✐♥✐❝✐❛✐s ❞♦s ♣❛râ♠❡tr♦s θ0 ✭❇♦✇❡♥ ❛♥❞ ❏❡r♠❛♥✱ ✶✾✾✺✮✳ ❚r❛❞✐❝✐♦♥❛❧♠❡♥t❡✱ tr❛♥s❢♦r♠❛♠✲s❡ ❛s ✈❛r✐á✈❡✐s ❞❡ ❛❧❣✉♥s ♠♦❞❡❧♦s ♥ã♦✲❧✐♥❡❛r❡s ❞❡ ❢♦r♠❛ ❛ ❧✐♥❡❛r✐③❛r ❛ r❡❧❛çã♦ ❡ ❛ ♣❡r♠✐t✐r ❛ s✉❛ ❛♥á❧✐s❡ ❛tr❛✈és ❞❛ r❡❣r❡ssã♦ ❧✐♥❡❛r✳ ❈♦♥t✉❞♦✱ ❡st❛ ❛❜♦r❞❛❣❡♠ é ✈á❧✐❞❛ s❡ ❛✭s✮ ✈❛r✐á✈❡❧✭✐s✮ tr❛♥s❢♦r♠❛❞❛s s❡ ✈❡r✐✜❝❛♠ ♦s ♣r❡ss✉♣♦st♦s ❞❛ ❛♥á❧✐s❡ ❞❡ r❡❣r❡sã♦ ❧✐♥❡❛r✳ ✷ ❋✐❣✉r❛ ✶✿ ❆s♣❡❝t♦ ❞❛ ❥❛♥❡❧❛ ❘ ❈♦♥s♦❧❡✳ ❊①❡♠♣❧♦ ❘ ❆ ✉t✐❧✐③❛çã♦ ❞♦ ❢❡rr❛♠❡♥t❛ ❙♦❧✈❡r ❝♦♠ ✉♠ ❡①❡♠♣❧♦ ❝♦♥❝r❡t♦ ✭❡♥tr❡t❛♥t♦ ❛❜♦r❞❛❞♦ ♣♦r ❊st❡✈❡s ✭✷✵✶✵✮ ✉s❛♥❞♦ ❛ ➤ ❞♦ ▼✐❝r♦s♦❢t ❊①❝❡❧ ❝❛♣❛❝✐❞❛❞❡s ❞♦ s♦❢t✇❛r❡✳ ➤ ✮ ♣❡r♠✐t✐rá ♠♦str❛r ♦ ❢✉♥❝✐♦♥❛♠❡♥t♦ ❡ ❞❡♠♦♥str❛r ❛s ❈♦♠♦ s❡ ✐♠❛❣✐♥❛✱ ❛s ❢✉♥❝✐♦♥❛❧✐❞❛❞❡s ♥ã♦ s❡ ❡s❣♦t❛♠ ♥♦ q✉❡ ❛q✉✐ s❡ ❛♣r❡s❡♥t❛✳ ❖ ❛s♣❡❝t♦ ❞♦ ❘ ❛♦ ✐♥✐❝✐❛r ✉♠❛ s❡ssã♦ ❞❡ tr❛❜❛❧❤♦ ❡♠ ❛♠❜✐❡♥t❡ ❲✐♥❞♦✇s ➤ ✐❧✉str❛✲s❡ ♥❛ ❋✐❣✉r❛ ✶✳ P❛r❛ ❛❧é♠ ❞❛ ❜❛rr❛ ❞❡ ❢❡rr❛♠❡♥t❛s ♥♦ t♦♣♦ ✭q✉❡ ♣❡r♠✐t❡ r❡❛❧✐③❛r ❛s t❛r❡❢❛s ❝♦♠✉♥s✿ ❛❜r✐r✴❣r❛✈❛r ✜❝❤❡✐r♦s✱ ❝♦rt❛r✴❝♦❧❛r t❡①t♦✱ ✐♥st❛❧❛r ♣❛❝♦t❡s✱ ✏ ❣❡r✐r✑ ❛s ❥❛♥❡❧❛s✱ ❡t❝✳✮ s✉r❣❡ ✉♠❛ ❥❛♥❡❧❛ ✭ ♥❛ q✉❛❧ s❡ ✐♥tr♦❞✉③❡♠ ♦s ❝♦♠❛♥❞♦s✱ ❛ s❡❣✉✐r ❛♦ s✐♥❛❧ ❃✳ ❆❞♠✐t❛✲s❡ q✉❡ ♦s ❞❛❞♦s q✉❡ s❡ ♣r❡t❡♥❞❡♠ ❛♥❛❧✐s❛r ❡stã♦ ♥✉♠ ✜❝❤❡✐r♦ ❞♦ ❊①❝❡❧ ❧✉❣❛r✱ s❡rá ♥❡❝❡ssár✐♦ ❣✉❛r❞❛r ✉♠❛ ✈❡rsã♦ ✭✯✳t①t ❘ ❈♦♥s♦❧❡ ✮ ➤ ✳ ❊♠ ♣r✐♠❡✐r♦ ✶ ♦✉ ✯✳❝s✈✮ ❞❡ss❡ ✜❝❤❡✐r♦ ✉t✐❧✐③á✈❡❧ ♣❡❧♦ ❘ ✭❞❡✈❡♠ ✉s❛r✲s❡ ♣♦♥t♦s✱ ❡♠ ✈❡③ ❞❡ ✈ír❣✉❧❛s✱ ❝♦♠♦ s❡♣❛r❛❞♦r❡s ❞❡❝✐♠❛✐s✮✳ ◆❛ ❝♦♥s♦❧❛ ❞♦ ❘ ❡s❝r❡✈❡r ✭❢❛③❡♥❞♦ ❊♥t❡r ♥♦ ✜♠✮✱ ❃ ❞❛❞♦s❁✲r❡❛❞✳t❛❜❧❡✭❢✐❧❡❂✧●✿✴▼②❆rt✐❝❧❡s✴❆rt✐❣♦s❘❡❣r❡ss❛♦◆❛♦▲✐♥❡❛r❊①❝❡❧✴❘❡❣r❡ ss❛♦◆❛♦▲✐♥❡❛r✳t①t✧✱❤❡❛❞❡r❂❚✱s❡♣❂✧❭t✧✮ ❘❡❣r❡ss❛♦◆❛♦▲✐♥❡❛r✳t①t ♣❛r❛ ♦ ♦❜❥❡❝t♦ ❞❛❞♦s✳ ❤❡❛❞❡r ❡ s❡♣ ♣❡r♠✐t❡♠ ❝♦♥s✐❞❡r❛r ♦s rót✉❧♦s ❞♦s ❞❛❞♦s ♣❛r❛ ✏ ❝❛rr❡❣❛r✑ ❛ ✐♥❢♦r♠❛çã♦ ❝♦♥t✐❞❛ ♥♦ ✜❝❤❡✐r♦ ✭❛t❡♥t❡✲s❡ ♥❛ ♥♦t❛çã♦ ❁✲✮✳ ❖s ♣❛râ♠❡tr♦s ❡ ♦ t✐♣♦ ❞❡ ✜❝❤❡✐r♦ ❞❡ t❡①t♦ ✭♥❡st❡ ❝❛s♦ s❡♣❛r❛❞♦ ♣♦r t❛❜✉❧❛çõ❡s✮✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ P♦r s✐♥❛❧✱ ❛ q✉❛♥t✐❞❛❞❡ ❞❡ ❞❛❞♦s ❡♥✈♦❧✈✐❞❛ ♣♦❞❡r✐❛ ♠✉✐t♦ ❜❡♠ s❡r ✐♥tr♦❞✉③✐❞❛ ❞✐r❡❝t❛♠❡♥t❡ ♥♦ ❘ ❛tr❛✈és ❞❡ ❃ ❈❖✷❁✲❝✭✶✹✶✱✶✼✷✱✶✽✶✱✷✷✼✱✸✵✾✱✹✶✹✱✻✹✶✱ ✾✸✻✮ ❃ Pr♦♣❁✲❝✭✵✳✷✺✱✵✳✸✹✱✵✳✸✹✱✵✳✻✽✱✵✳✽✺✱✵✳✾✾✱✵✳✾✽✱✵✳✾✾✮ ❡♠ q✉❡ ❝✭✳✳✳✮ ♣❡r♠✐t❡ ❝♦♥❝❛t❡♥❛r ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s ♥✉♠ ♦❜❥❡❝t♦ ✭♥❡st❡ ❝❛s♦✱ P♦❞❡♠♦s ✈✐s✉❛❧✐③❛r ❛ ✐♥❢♦r♠❛çã♦ ✉s❛♥❞♦ ❛ ❢✉♥çã♦ ❈❖✷ ❡ Pr♦♣✮ ✳ ♣❧♦t ✶ ❆ ❡①t❡♥sã♦ t①t ❞✐③ r❡s♣❡✐t♦ ❛ ✜❝❤❡✐r♦s ❞❡ t❡①t♦ s❡♣❛r❛❞♦ ♣♦r t❛❜✉❧❛çõ❡s ❡♥q✉❛♥t♦ ❛ ❡①t❡♥sã♦ ❝s✈ ❡stá r❡❧❛❝✐♦♥❛❞❛ ❝♦♠ ✜❝❤❡✐r♦s ❞❡ t❡①t♦ s❡♣❛r❛❞♦s ♣♦r ✈ír❣✉❧❛s✳ ✸ ❃ ♣❧♦t✭Pr♦♣⑦❈❖✷✱ ❧❛s❂✶✱①❧✐♠❂❝✭✵✱✶✵✵✵✮✱②❧✐♠❂❝✭✵✱✶✮✱♣❝❤❂✶✻✱❝❡①❂ ✶✳✺✱ ①❧❛❜❂✧❈❖✷ ✭♣♣♠✮✧✱ ②❧❛❜❂✧Pr♦♣♦rçã♦ ❞❡ r❡s♣♦st❛s ❝♦rr❡❝t❛s✧✮ Pr♦♣⑦❈❖✷ ❡♠ q✉❡ ❈❖✷✮ ❞❡ ❞❡s❝r❡✈❡ ♦ ✏ ♠♦❞❡❧♦✑ q✉❡ s❡ ♣r❡t❡♥❞❡ r❡♣r❡s❡♥t❛r ✭♥❡st❡ ❝❛s♦ Pr♦♣ ❡♠ ❢✉♥çã♦ ❡ ❝✉❥♦s r❡st❛♥t❡s ♣❛râ♠❡tr♦s ❡s♣❡❝✐✜❝❛♠ ❛s ✈ár✐❛s ❝❛r❛❝t❡ríst✐❝❛s ❞♦ ❣rá✜❝♦ ✭❧❛s ♣❛r❛ ②②✱ ①❧✐♠ ❡ ②❧✐♠ ♣❛r❛ ❞❡t❡r♠✐♥❛r ♦s ❧✐♠✐t❡s ❞♦s ❡✐①♦s✱ ♣❝❤ ♣❛r❛ ❝❡① ♣❛r❛ ❛✉♠❡♥t❛r ♦ t❛♠❛♥❤♦ r❡❧❛t✐✈♦ ❞♦s ❝❛r❛❝t❡r❡s✱ ❡ ①❧❛❜ ❡ ②❧❛❜ ♣❛r❛ ♦r✐❡♥t❛çã♦ ❞♦s rót✉❧♦s ❞♦ ❡✐①♦ ❞♦s ❞❡✜♥✐r ♦ sí♠❜♦❧♦ ✉s❛❞♦✱ ✏ ❧❡❣❡♥❞❛r✑ ♦s ❡✐①♦s✮ ✭❋✐❣✉r❛ ✷❛✮✳ P❛r❛ ♠❛✐s ✐♥❢♦r♠❛çõ❡s ❛❝❡r❝❛ ❞❡st❛ ✭♦✉ q✉❛❧q✉❡r ♦✉tr❛✮ ❢✉♥çã♦ ♣♦❞❡ ❢❛③❡r✲s❡ ❃ ❄♣❧♦t ✭♦✉ ❡♥tã♦ ♣r♦❝✉r❛r ❆♣r♦♣♦s✳✳✳✮✳ ❝♦♠ ❃❤❡❧♣✳s❡❛r❝❤✭✏t❡r♠♦✑✮ ♦✉✱ ❛✐♥❞❛✱ ✉s❛r ❛ ♦♣çã♦ ❍❡❧♣❃ ❯s❛♥❞♦ ♦ ❜♦tã♦ ❞✐r❡✐t♦ ❞♦ r❛t♦ s♦❜r❡ ♦ ❣rá✜❝♦✱ é ♣♦ssí✈❡❧ ❝♦♣✐❛r ❛ ✜❣✉r❛ ✭❝♦♠♦ ♠❡t❛✜❝❤❡✐r♦ ❲✐♥❞♦✇s ➤ ♣♦r ❡①❡♠♣❧♦✮ ♣❛r❛ ✐♥❝❧✉sã♦ ♥✉♠ ✜❝❤❡✐r♦ ❞♦ ▼✐❝r♦s♦❢t ❲♦r❞ ➤ ✳ ❆❞♠✐t❛✲s❡ ✭♣♦r r❛③õ❡s ❝✐❡♥tí✜❝❛s✮ q✉❡ ✉♠ ♠♦❞❡❧♦ ✏ ❞♦s❡✲r❡s♣♦st❛✑ ✭❧♦❣íst✐❝♦ ♠♦❞✐✜❝❛❞♦✮ P = ❡♠ q✉❡ Pi ❡stí♠✉❧♦ 1 3 + exp(B(T − log(x)) 1 + exp(T − log(x)) é ❛ ♣r♦♣♦rçã♦ ❞❡ r❡s♣♦st❛s ♣♦s✐t✐✈❛s ❞♦ ♣r♦✈❛❞♦r ✐✱ log(x) é ♦ ❧♦❣❛r✐t♠♦ ❞♦ ✈❛❧♦r ❞♦ ①✱ ❇ é ♦ ✧❞❡❝❧✐✈❡✧ ❡ ❚ é ♦ ❧✐♠✐❛r ♣❛r❛ ♦ ♣r♦✈❛❞♦r ✐ ✭❡♠ log(x)✮✱ é ❛❞❡q✉❛❞♦ ♣❛r❛ ❞❡s❝r❡✈❡r ♦s ❞❛❞♦s✳ P❛r❛ ❛❥✉st❛r ♦ ♠♦❞❡❧♦ ❜❛st❛ ❢❛③❡r ❃ ❛❥✉st❡❁✲♥❧s✭Pr♦♣⑦✭✶✴✸✰❡①♣✭❇✯✭❚✲❧♦❣✶✵✭❈❖✷✮✮✮✮✴✭✶✰❡①♣✭❇✯✭❚✲❧♦❣✶✵✭❈❖✷✮✮✮✮✱ ❞❛t❛❂❞❛t❛✳❢r❛♠❡✭❈❖✷❂❈❖✷✱Pr♦♣❂Pr♦♣✮✱st❛rt❂❧✐st✭❇❂✲✶✵✱❚❂✷✳✺✮✮ ❛❥✉st❡ ✐♥❝❧✉✐rá ♦s r❡s✉❧t❛❞♦s ❞✉♠❛ r❡❣r❡ssã♦ ♥ã♦✲❧✐♥❡❛r ✭❛tr❛✈és ❞❛ ❢✉♥çã♦ ♥❧s✮✷ ✸ ❞♦ ♠♦❞❡❧♦ Pr♦♣⑦✭✶✴✸✰❡①♣✭❇✯✭❚✲❧♦❣✶✵✭❈❖✷✮✮✮✮✴✭✶✰❡①♣✭❇✯✭❚✲❧♦❣✶✵✭❈❖✷✮✮✮ ❝♦♥s✐❞❡r❛♥❞♦ ♦s ✹ ❞❛❞♦s ✭✐♥❞✐❝❛❞♦s ♣❛r❛ ♦ ♣❛râ♠❡tr♦ ❞❛t❛ s♦❜ ❛ ❢♦r♠❛ ❞❡ ✉♠❛ ❞❛t❛✳❢r❛♠❡ ✮ ❡ ❛s ❡st✐♠❛t✐✈❛s ✐♥✐❝✐❛✐s ❞♦s ♣❛râ♠❡tr♦s ❞♦ ♠♦❞❡❧♦ ❞❡s❝r✐t❛s ❡♠ st❛rt ✭❛tr❛✈és ❞✉♠❛ ❧✐st✮✳ ❖s r❡s✉❧t❛❞♦s ❞♦ ❛❥✉st❡ ❡♠ q✉❡ ♦ ♦❜❥❡❝t♦ ✭❋✐❣✉r❛ ✸✮ ♣♦❞❡♠ s❡r ❝♦♥s✉❧t❛❞♦s ❢❛③❡♥❞♦ ❃ s✉♠♠❛r②✭❛❥✉st❡✮ ➱ ♣♦ssí✈❡❧ ✐❧✉str❛r ♦ ❢✉♥çã♦ ♣r❡❞✐❝t✮ ❛❥✉st❡✱ ♦❜t❡♥❞♦ ♣r✐♠❡✐r♦ ❛s ❡st✐♠❛t✐✈❛s ❞❛ ✈❛r✐á✈❡❧ Pr♦♣ ✭❛tr❛✈és ❞❛ ❡ ✏ ❞❡s❡♥❤❛♥❞♦✲❛s✑ ✱ ❡♠ s❡❣✉✐❞❛✱ s♦❜r❡ ♦ ❣rá✜❝♦ ❡♥tr❡t❛♥t♦ ♦❜t✐❞♦ ✭❋✐❣✉r❛ ✷❛ ✈s ❋✐❣✉r❛ ✷❜✮ ✉s❛♥❞♦ ❛ ❢✉♥çã♦ ❧✐♥❡s✱ ♦✉ s❡❥❛ ❃ Pr♦♣❊s♣❁✲♣r❡❞✐❝t✭❛❥✉st❡✱♥❡✇❞❛t❛❂❧✐st✭❈❖✷❂s❡q✭✵✱✶✵✵✵✱❧❡♥❣t❤❂✶✵✵✮✮✱s❡✳❢✐t❂❚✮ ❃ ❧✐♥❡s✭Pr♦♣❊s♣⑦s❡q✭✵✱✶✵✵✵✱❧❡♥❣t❤❂✶✵✵✮✱❧✇❞❂✷✱❝♦❧❂✻✮ ❛❥✉st❡ ♣❡r♠✐t❡ ♦❜t❡r ❛s ❡st✐♠❛t✐✈❛s ♣❛r❛ ✶✵✵ ✈❛❧♦r❡s ❞❡ ❈❖✷ ❡♥tr❡ ✵ ❡ ✶✵✵✵ ✭❞❛í ♦ ♣❛râ♠❡tr♦ s❡q✭✶✱✶✵✵✵✱❧❡♥❣t❤❂✶✵✵✮ ♥♦ ❝♦♠❛♥❞♦ ❛❝✐♠❛✮ ❛ss✐♠ ❝♦♠♦ ♦s r❡s♣❡❝t✐✈♦s ❡rr♦s✲♣❛❞rã♦ ✭s❡✳❢✐t❂❚✮ q✉❡ s❡rã♦ ❣✉❛r❞❛❞❛s ♥♦ ♦❜❥❡❝t♦ ❞❡s✐❣♥❛❞♦ Pr♦♣❊s♣✳ ❆ ❛❞✐çã♦ ❞✉♠❛ ❧✐♥❤❛ ❡s♣❡ss❛ ❡ ♠❛❣❡♥t❛ ✭❧✇❞❂✷ ❡ ❝♦❧❂✻✮ à ❋✐❣✉r❛ ✷❛ é r❡❧❛t✐✈❛♠❡♥t❡ ❢á❝✐❧ ✭❋✐❣✉r❛ ✷❜✮✳ ❆ ✐♥❢♦r♠❛çã♦ ❝♦♥t✐❞❛ ♥♦ ♦❜❥❡❝t♦ ✷ ❖✉tr❛s ❢✉♥çõ❡s ✭♠✉✐t♦✮ ✉s❛❞❛s sã♦ ❧♠ ❡ ❛♦✈ ♣❛r❛ r❡❣r❡ssã♦ ❧✐♥❡❛r ✭✐✳❡✳ ♠♦❞❡❧♦s ❧✐♥❡❛r❡s✮ ❡ ❛♥á❧✐s❡ ❞❡ ✈❛r✐â♥❝✐❛✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ✸ ❆ ❞❡✜♥✐çã♦ ❞♦s ♠♦❞❡❧♦s ❡♠ ❙ ❡stá ♠✐♥✉❝✐♦s❛♠❡♥t❡ ❞❡s❝r✐t❛ ❡♠ ❈❤❛♠❜❡rs ❛♥❞ ❍❛st✐❡ ✭✶✾✾✷✮✳ ✹ ◆❡st❡ ❝❛s♦✱ ❝♦♥s✐❞❡r♦✉✲s❡ q✉❡ ♦ ✉t✐❧✐③❛❞♦r ✐♥tr♦❞✉③✐✉ ❞✐r❡❝t❛♠❡♥t❡ ♥♦ s✐st❡♠❛ ♦s ❞❛❞♦s ❛♦ ✐♥✈és ✜❝❤❡✐r♦ ❞♦s ❞❛❞♦s ✭s❡♥❞♦ q✉❡ ❜❛st❛r✐❛ ❛♣❡♥❛s ✐♥❞✐❝❛r ❞❛t❛❂❞❛❞♦s✱ ✹ ♥♦ ❝♦♠❛♥❞♦✮✳ ❞❡ ✏ ❝❛rr❡❣❛r✑ ♦ ❋✐❣✉r❛ ✷✿ ❉✐❛❣r❛♠❛s ❞❡ ❞✐s♣❡rsã♦ ❞❛ ♣r♦♣♦rçã♦ ❞❡ r❡s♣♦st❛s ✈s✳ ❝♦♥❝❡♥tr❛çã♦ ❞❡ ❈❖✷✿ ❞❛❞♦s ♦r✐❣✐✲ ♥❛✐s ✭❛✮❀ ♠♦❞❡❧♦ ✏❞♦s❡✲r❡s♣♦st❛✑ ✭❧♦❣íst✐❝♦ ♠♦❞✐✜❝❛❞♦✮ ✭❜✮❀ ♠♦❞❡❧♦ ✏❞♦s❡✲r❡s♣♦st❛✑ ❝♦♠ ✐♥t❡r✈❛❧♦s ❞❡ ✾✺✪ ❞❡ ❝♦♥✜❛♥ç❛ ✭❝✮❀ ❡ ♠♦❞❡❧♦ ❧♦❣íst✐❝♦ ✭✈❡r t❡①t♦ ♣r✐♥❝✐♣❛❧✮ ✭❞✮✳ ❋✐❣✉r❛ ✸✿ ❆s♣❡❝t♦ ❞❛ ❡①❡❝✉çã♦ ❞❡ ❝♦♠❛♥❞♦s ❡ r❡s♣❡❝t✐✈♦s r❡s✉❧t❛❞♦s ♥❛ ❥❛♥❡❧❛ ✺ ❘ ❈♦♥s♦❧❡✳ P♦❞❡♠✱ ❛✐♥❞❛✱ ♦❜t❡r✲s❡ ❡ ✏ ❞❡s❡♥❤❛r✲s❡✑ ♦s ✐♥t❡r✈❛❧♦s ❞❡ ❝♦♥✜❛♥ç❛ ✭✉♣■❈ ❡ ❛tr❛✈és ❞❡ ŷ ± t · se(Y )✱ r❡❝♦rr❡♥❞♦ às ❢✉♥çõ❡s qt ❧♦■❈✮ q✉❡ s❡ ❝❛❧❝✉❧❛♠ ✭♣❛r❛ ♦❜t❡r ♦s ✈❛❧♦r❡s ✏ t❡ór✐❝♦s✑ ❞❡ t✲❙t✉❞❡♥t 1 − α/2✱ ♥❡st❡ ❝❛s♦ ✵✳✾✼✺✱ ❡ ♦s ❣r❛✉s ❞❡ ❧✐❜❡r❞❛❞❡ ❞♦ ❡rr♦✱ q✉❡ s❡ ♦❜tê♠ s✉♠♠❛r②✭❛❥✉st❡✮✩❞❢❬✷❪✮✱ s✉♠♠❛r②✭❛❥✉st❡✮✩s✐❣♠❛ ♣❛r❛ ♦❜t❡r ♦ ❡rr♦✲♣❛❞rã♦ ❞❛s ❡st✐♠❛t✐✈❛s ❧✐♥❡s✱ r❡s♣❡❝t✐✈❛♠❡♥t❡ ✭❋✐❣✉r❛ ✷❝✮✳ ❡ ❝✉❥♦s ♣❛râ♠❡tr♦s sã♦ ❞❡ ❡ ❃ ❃ ❃ ❃ ✉♣■❈❁✲Pr♦♣❊s♣✰qt✭✳✾✼✺✱s✉♠♠❛r②✭❛❥✉st❡✮✩❞❢❬✷❪✮✯s✉♠♠❛r②✭❛❥✉st❡✮✩s✐❣♠❛ ❧♦■❈❁✲Pr♦♣❊s♣✲qt✭✳✾✼✺✱s✉♠♠❛r②✭❛❥✉st❡✮✩❞❢❬✷❪✮✯s✉♠♠❛r②✭❛❥✉st❡✮✩s✐❣♠❛ ❧✐♥❡s✭✉♣■❈⑦s❡q✭✵✱✶✵✵✵✱❧❡♥❣t❤❂✶✵✵✮✱❝♦❧❂✹✮ ❧✐♥❡s✭❧♦■❈⑦s❡q✭✵✱✶✵✵✵✱❧❡♥❣t❤❂✶✵✵✮✱❝♦❧❂✹✮ ❖ ♠♦❞♦ ♠❛✐s s✐♠♣❧❡s ❞❡ ✏ t❡st❛r✑ ❛ ❜♦♥❞❛❞❡ ❞♦ ❛❥✉st❡ é r❡♣r❡s❡♥t❛r ❣r❛✜❝❛♠❡♥t❡ ♦s ❞❛❞♦s ❡ ♦ ♠♦✲ ❞❡❧♦ ❛❥✉st❛❞♦ ✭❜❡♠ ❝♦♠♦ ♦s r❡s♣❡❝t✐✈♦s ✐♥t❡r✈❛❧♦s ❞❡ ❝♦♥✜❛♥ç❛✮✱ ❞❡ ♠♦❞♦ ❛ ✈❡r✐✜❝❛r ✭✈✐s✉❛❧♠❡♥t❡✮ s❡ ♦s ♣❛râ♠❡tr♦s ♦❜t✐❞♦s ♥✉♠❡r✐❝❛♠❡♥t❡ ❞❡s❝r❡✈❡♠✱ ❞❡ ❢❛❝t♦✱ ❛ r❡❧❛çã♦ ❡♥tr❡ ✈❛r✐á✈❡✐s ✭❋✐❣✉r❛ ✷❝✮✳ P♦r ♦✉tr♦ ❧❛❞♦✱ ❛ ❛♥á❧✐s❡ ❣rá✜❝❛ ❞♦s r❡sí❞✉♦s✱ ❡✳❣✳ r❡sí❞✉♦s ✈s✳ ✈❛❧♦r❡s ♦❜s❡r✈❛❞♦s ❞❡ ❳✱ ♣❡r♠✐t❡ ✏ ✈❡r✐✜❝❛r✑ s❡ ♦ ♠♦❞❡❧♦ é ❛❞❡q✉❛❞♦ ✭♦s r❡sí❞✉♦s r❡♣r❡s❡♥t❛♠ ❛♣❡♥❛s ♦ ❡rr♦ ❡①♣❡r✐♠❡♥t❛❧ s❡ ♥ã♦ ❛♣r❡s❡♥t❛♠ t❡♥❞ê♥❝✐❛s ♦✉ ♣❛❞rõ❡s✮✳ ❙❡♥❞♦ ❛ss✐♠✱ ♦❜t❡r ♦s r❡sí❞✉♦s ❛tr❛✈és ❞❡ ❃ r❡s✐❞✉♦s❁✲s✉♠♠❛r②✭❛❥✉st❡✮✩r❡s✐❞ ❡✱ ❡♠ s❡❣✉✐❞❛✱ r❡♣r❡s❡♥t❛r ❡ss❡ ❣rá✜❝♦ ❡♠ ❝♦♥❥✉♥t♦ ❝♦♠ ♦ ♥♦r♠❛❧ ♣r♦❜❛❜✐❧✐t② ♣❧♦t ❞♦s r❡sí❞✉♦s ✭❋✐❣✉r❛ ✹✮ ❃ ♦♣❁✲♣❛r✭♠❢r♦✇❂❝✭✷✱✶✮✱♣t②❂✧s✧✱❧❛s❂✶✮ ❃ ♣❧♦t✭r❡s✐❞✉♦s⑦♣r❡❞✐❝t✭❛❥✉st❡✮✱♣❝❤❂✶✻✱❝♦❧❂✸✱①❧❛❜❂✧❊④Pr♦♣♦rçã♦ ❞❡ r❡s♣♦st❛s ❝♦rr❡❝t❛s⑥✧✱②❧❛❜❂✧❘❡sí❞✉♦s✧✮ ❃ ❛❜❧✐♥❡✭❤❂✵✮ ❃ qq♥♦r♠✭r❡s✐❞✉♦s✱♣❝❤❂✶✻✱❝♦❧❂✷✱①❧❛❜❂ ✧◗✉❛♥t✐s ❞❛ ❉✐str✐❜✉✐çã♦ ◆♦r♠❛❧✧✱ ②❧❛❜❂✧◗✉❛♥t✐s ❆♠♦str❛✐s✧✱♠❛✐♥❂✧✧✮ ❃ qq❧✐♥❡✭r❡s✐❞✉♦s✮ ❃ ♣❛r✭♦♣✮ ♣❛r ♣❡r♠✐t❡ ❡st❛❜❡❧❡❝❡r ♦ ✏ ❡sq✉❡♠❛✑ ❞❛ ✜❣✉r❛✱ ♥❡st❡ ❝❛s♦✱ ♦s ❣rá✜❝♦s ✜❝❛♠ ✏ ❛rr❛♥❥❛❞♦s✑ ❡♠ ✷ ❧✐♥❤❛s ♣♦r ✶ ❝♦❧✉♥❛ ✕ ♠❢r♦✇❂❝✭✷✱✶✮ ✕✱ ❛ss✐♠ ❝♦♠♦ ❞❡✜♥✐r ❛ r❡s♣❡❝t✐✈❛ ❢♦r♠❛ ✭q✉❛❞r❛❞❛✱ ❛tr❛✈és ❞❡ ♣t②❂✧s✧ ✲ ✏s✑ ❞❡ ✏sq✉❛r❡✑✮✳ ❆♦ ❣rá✜❝♦ ❞♦s r❡sí❞✉♦s ✈s✳ ✈❛❧♦r❡s ❡s♣❡r❛❞♦s ❞❡ Pr♦♣ ✭❛tr❛✈és ❞❡ ♣❧♦t✮ ❛❝r❡s❝❡♥tá♠♦s ✉♠❛ ❧✐♥❤❛ ❤♦r✐③♦♥t❛❧ ❛♦ ♥í✈❡❧ ❞❡ ③❡r♦ ✭❛tr❛✈és ❞❡ ❛❜❧✐♥❡✮ ❡✱ ♣♦r ✜♠✱ ❞❡s❡♥❤❛♠♦s ♦ ♥♦r♠❛❧ ♣r♦❜❛❜✐❧✐t② ♣❧♦t ❞♦s r❡sí❞✉♦s ✭❝♦♠ qq♥♦r♠ ❡ qq❧✐♥❡✮✳ ❖ ❝♦♠❛♥❞♦ ➱ ♣♦ssí✈❡❧ t❡st❛r s❡ ♦s r❡sí❞✉♦s s❡ ❞✐str✐❜✉❡♠ ♥♦r♠❛❧♠❡♥t❡ ❛tr❛✈és✱ ♣♦r ❡①❡♠♣❧♦✱ ❞❡ ❃ s❤❛♣✐r♦✳t❡st✭r❡s✐❞✉♦s✮ ❖ r❡s✉❧t❛❞♦ ❞❡st❡ ❝♦♠❛♥❞♦ é ❙❤❛♣✐r♦✲❲✐❧❦ ♥♦r♠❛❧✐t② t❡st ❞❛t❛✿ r❡s✐❞✉♦s ❲ ❂ ✵✳✾✸✻✱ ♣✲✈❛❧✉❡ ❂ ✵✳✺✼✶✾ ❖ t❡st❡ ❞❡ s❡q✉ê♥❝✐❛s ✭♦✉ ✏ r✉♥s t❡st✑ ♥♦s ♠❛♥✉❛✐s ❛♥❣❧ó❢♦♥♦s✮ ♣❡r♠✐t❡ t❡st❛r✱ ❞❡ ❢♦r♠❛ s✐♠♣❧❡s ❡ r♦❜✉st❛✱ s❡ ♦s ♣♦♥t♦s ✭❞❛❞♦s✮ ❞✐❢❡r❡♠ s✐st❡♠❛t✐❝❛♠❡♥t❡ ❞❛ ❝✉r✈❛ ❛❥✉st❛❞❛ ✭♠♦❞❡❧♦✮ ❝♦♠♣❧❡✲ ♠❡♥t❛♥❞♦ ❛ ✐♥❢♦r♠❛çã♦ ❞♦ ❞✐❛❣r❛♠❛ ❞♦s r❡sí❞✉♦s ✈s ✈❛❧♦r❡s ♦❜s❡r✈❛❞♦s ❞❡ ❳✳ ❈♦♥♦✈❡r ✭✶✾✾✾✮ ✻ ❋✐❣✉r❛ ✹✿ ❆♥á❧✐s❡ ❣rá✜❝❛ ❞❡ r❡sí❞✉♦s✿ r❡sí❞✉♦s ❞♦s r❡sí❞✉♦s ✭❞✐r✳✮✳ ✈s✳ ✈❛❧♦r❡s ❡s♣❡r❛❞♦s ✭❡sq✳✮❀ ❡ ♥♦r♠❛❧ ♣r♦❜❛❜✐❧✐t② ♣❧♦t ❛❧❡rt❛ ♣❛r❛ ❛ r❡❞✉③✐❛ ♣♦tê♥❝✐❛ ❡st❛tíst✐❝❛ ❞♦ t❡st❡s ❜❛s❡❛❞♦s ❡♠ s❡q✉ê♥❝✐❛s✳ ◆♦ ❘✱ s❡rá ♥❡❝❡ssá✲ r✐♦ ❝❛rr❡❣❛r ❛❧❣✉♥s ♣❛❝♦t❡s✱ ts❡r✐❡s✱ q✉❛❞♣r♦❣ ❡ ③♦♦ ✭♣r❡✈✐❛♠❡♥t❡ ✐♥st❛❧❛❞♦s✱ ❛tr❛✈és ❞❛ ❜❛rr❛ ❞❡ ❢❡rr❛♠❡♥t❛s✱ ❛ ♣❛rt✐r ❞♦s ✜❝❤❡✐r♦s ✯✳③✐♣ ❞✐s♣♦♥í✈❡✐s ♣❛r❛ ♦ ❲✐♥❞♦✇s ❡♠ ❤tt♣✿✴✴❝r❛♥✳❛t✳r✲ ♣r♦❥❡❝t✳♦r❣✴❜✐♥✴✇✐♥❞♦✇s✴❝♦♥tr✐❜✴✮ ❢❛③❡♥❞♦ ❡✳❣✳ ➤ ❃ ❧✐❜r❛r②✭ts❡r✐❡s✮ ❉❡♣♦✐s ❜❛st❛ ❢❛③❡r ❃ r✉♥s✳t❡st✭❢❛❝t♦r✭s✐❣♥✭r❡s✐❞✉♦s✮✮✮ ♣❛r❛ s❡ ♦❜t❡r ♦ s❡❣✉✐♥t❡ r❡s✉❧t❛❞♦ ❘✉♥s ❚❡st ❞❛t❛✿ ❢❛❝t♦r✭s✐❣♥✭r❡s✐❞✉♦s✮✮ ❙t❛♥❞❛r❞ ◆♦r♠❛❧ ❂ ✵✳✺✼✼✹✱ ♣✲✈❛❧✉❡ ❂ ✵✳✺✻✸✼ ❛❧t❡r♥❛t✐✈❡ ❤②♣♦t❤❡s✐s✿ t✇♦✳s✐❞❡❞ P♦❞❡ ❝♦♠♣❛r❛r✲s❡ ♦ ❛❥✉st❡ ❞❡ ❞♦✐s ♠♦❞❡❧♦s ❞✐st✐♥t♦s ❛ ✉♠ ❞❛❞♦ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s ❝♦♥❢r♦♥t❛♥❞♦ ❛s ❙◗❊ ❞♦s ♠♦❞❡❧♦s ❛❥✉st❛❞♦s ❛tr❛✈és ❞♦ t❡st❡ ❞❡ ❋✳ ❙❡♥❞♦ ❛ss✐♠✱ ❞❡♣♦✐s ❞❡ ❛❥✉st❛r ✉♠ ♠♦❞❡❧♦ ❧♦❣íst✐❝♦✱ ŷ = C/[1 + Aexp(−Bx)] ✭❋✐❣✉r❛ ✷❞✮✺ ✱ ❞❡ ❢♦r♠✉❧❛çã♦ ♠❛✐s ❣❡♥❡r❛❧✐③❛❞❛ ❞♦ q✉❡ ♦ ♠♦❞❡❧♦ ✺ ❊st❛ ✜❣✉r❛ ❢♦✐ ♦❜t✐❞❛ ❛tr❛✈és ❞❡ ❃ ♣❧♦t✭Pr♦♣⑦❈❖✷✱❧❛s❂✶✱①❧✐♠❂❝✭✵✱✶✵✵✵✮✱ ②❧✐♠❂❝✭✵✱✶✮✱♣❝❤❂✶✻✱❝❡①❂✶✳✺✱ ①❧❛❜❂✧❈❖✷ ✭♣♣♠✮✧✱②❧❛❜❂✧Pr♦♣♦r çã♦ ❞❡ r❡s♣♦st❛s ❝♦rr❡❝t❛s✧✮ ❃ Pr♦♣❊s♣❡r❁✲♣r❡❞✐❝t✭❛❥✉st❡s✱♥❡✇❞❛t❛❂ ❧✐st✭❈❖✷❂s❡q✭✵✱✶✵✵✵✱❧❡♥❣t❤❂✶✵✵✮✮✱s❡✳❢✐t❂❚✮ ❃ ❧✐♥❡s✭Pr♦♣❊s♣❡r⑦s❡q✭✵✱✶✵✵✵✱❧❡♥❣t❤❂ ✶✵✵✮✱❧✇❞❂✷✱❝♦❧❂✻✮ ❃ ✉♣♣■❈❁✲Pr♦♣❊s♣❡r✰qt✭✳✾✼✺✱s✉♠♠❛r②✭ ❛❥✉st❡s✮✩❞❢❬✷❪✮✯s✉♠♠❛r②✭❛❥✉st❡s✮✩s✐❣♠ ❃ ❧♦✇■❈❁✲Pr♦♣❊s♣❡r✲qt✭✳✾✼✺✱s✉♠♠❛r②✭ ❛❥✉st❡s✮✩❞❢❬✷❪✮✯s✉♠♠❛r②✭❛❥✉st❡s✮✩s✐❣♠ ❃ ❧✐♥❡s✭✉♣♣■❈⑦s❡q✭✵✱✶✵✵✵✱❧❡♥❣t❤❂✶✵✵✮✱ ❝♦❧❂✹✮ ❃ ❧✐♥❡s✭❧♦✇■❈⑦s❡q✭✵✱✶✵✵✵✱❧❡♥❣t❤❂✶✵✵✮✱ ❝♦❧❂✹✮ ✼ ❋✐❣✉r❛ ✺✿ ❆s♣❡❝t♦ ❞✉♠❛ s❡ssã♦ ❞❡ tr❛❜❛❧❤♦ ♥♦ ❘✳ ✏ ❞♦s❡✲r❡s♣♦st❛✑ ❛♥t❡r✐♦r✱ ❛tr❛✈és ❞❡ ❃ ❛❥✉st❡s❁✲♥❧s✭Pr♦♣⑦❈✴✭✶✰❆✯❡①♣✭✲❇✯❈❖✷ ✮✮✱❞❛t❛❂❞❛t❛✳❢r❛♠❡✭❈❖✷❂❈❖✷✱Pr♦♣❂Pr♦♣✮✱ st❛rt❂❧✐st✭❆❂✶✵✱❇❂✳✵✵✷✺✱❈❂✶✮✮ ❃ s✉♠♠❛r②✭❛❥✉st❡s✮ ♦s r❡s✉❧t❛❞♦s ❞♦ t❡st❡ ❞❡ ❋ ♦❜tê♠✲s❡ ❢❛❝✐❧♠❡♥t❡ ❛tr❛✈és ❞❡ ❃ ❛♥♦✈❛✭❛❥✉st❡✱❛❥✉st❡s✮ ❖s ♣❛ss♦s ❞❡s❝r✐t♦s ❛♥t❡r✐♦r♠❡♥t❡✱ ✐✳❡✳ ✉♠❛ s❡ssã♦ ❞❡ tr❛❜❛❧❤♦ ✭❋✐❣✉r❛ ✺✮✱ ♣♦❞❡♠ ✭❡✱ ♥❛ ♠✐♥❤❛ ♦♣✐♥✐ã♦✱ ❞❡✈❡♠✮ s❡r ✏ ❣✉❛r❞❛❞♦s✑ ✳ s❝r✐♣t✮✱ s❝r✐♣t P❛r❛ ✐ss♦✱ ❝r✐❛r ✉♠ ✜❝❤❡✐r♦ ❞❡ ❞❡ ❢❛❝t♦ ✉♠ ✜❝❤❡✐r♦ t❡①t♦✱ ♦♥❞❡ sã♦ ✏ ❣✉❛r❞❛❞♦s✑ ♦s ❝♦♠❛♥❞♦s✳ ❝❛rr❡❣❛❞♦ ♥♦✉tr❛ s❡ssã♦ ❞❡ tr❛❜❛❧❤♦ ✭❛tr❛✈és ❞❡ ♣♦❞❡♠ s❡r r❡♣❡t✐❞♦s ♥✲✈❡③❡s ✭❥❛♥❡❧❛ ❘ ❊❞✐t♦r ✮✳ ❖ ❋✐❧❡❃❖♣❡♥ s❝r✐♣t✳✳✳✮ s❝r✐♣t ✭❛tr❛✈és ❞❡ ❋✐❧❡❃◆❡✇ ❊st❡ ✜❝❤❡✐r♦ ♣♦❞❡ s❡r ❡ ❛s ❛♥á❧✐s❡s ❡ ❣rá✜❝♦s ❞♦ ❡①❡♠♣❧♦ ❞❡s❝r✐t♦ ❛q✉✐ ♣♦❞❡ s❡r ♦❜t✐❞♦ ♥♦ sít✐♦ ❡❧❡❝tró♥✐❝♦ ❞♦ ❛✉t♦r✳ P❛r❛ t❡r♠✐♥❛r ✉♠❛ s❡ssã♦ ❞❡ tr❛❜❛❧❤♦✱ ♣r✐♠❡✐r♦ ✏ ❧✐♠♣❛r✑ ❞❛ ♠❡♠ór✐❛ ♦s ♦❜❥❡❝t♦s ❝r✐❛❞♦s ✭❝♦♠ ❛ ❢✉♥çã♦ r♠✮ ❡✱ ❞❡♣♦✐s✱ ❡♥❝❡rr❛r ♦ ♣r♦❣r❛♠❛ ✭❣❡r❛❧♠❡♥t❡ ♥ã♦ ❣✉❛r❞♦ ✉♠❛ ✏ ✐♠❛❣❡♠✑ ❞♦ ❛♠❜✐❡♥t❡ ❞❡ tr❛❜❛❧❤♦✮✿ ❃ r♠✭❧✐st❂❧s✭✮✮ ❀ q✭✮ ❈♦♥s✐❞❡r❛çõ❡s ✜♥❛✐s ➤ ❆s ✏ ❞✐✜❝✉❧❞❛❞❡s ❡st❛tíst✐❝❛s✑ r❡❧❛❝✐♦♥❛❞❛s ❝♦♠ ❛ ✉t✐❧✐③❛çã♦ ❞♦ ❊①❝❡❧ t✐✈❛ ❢❡rr❛♠❡♥t❛ ❙♦❧✈❡r ➤ ❞❛ ▼✐❝r♦s♦❢t ✭❡ ❞❛ r❡s♣❡❝✲ ✮ ♣❛r❛ ❛♥á❧✐s❡ ❞❡ r❡❣r❡ssã♦ ♥ã♦✲❧✐♥❡❛r ✭✈❞✳ ❊st❡✈❡s✱ ✷✵✶✵✮ ❧✐♠✐t❛♠ ❛ s✉❛ ✉t✐❧✐③❛çã♦ ❛♦s ❝❛s♦s ✏ ♠❛✐s s✐♠♣❧❡s✑ ♦✉ ♣❛r❛ ❡❢❡✐t♦s ♣❡❞❛❣ó❣✐❝♦s✳ ❊♠ s✐t✉❛çõ❡s ✏ ♣r♦✜ss✐♦♥❛✐s✑ ❞❡✈❡ ✉s❛r✲s❡ s♦❢t✇❛r❡ ❞❡❞✐❝❛❞♦✱ ♣♦r ❡①❡♠♣❧♦ ❙P❙❙ ➤ ♦✉ ✽ ❘✳ ❊♠❜♦r❛ ❛s ❝❛r❛❝t❡ríst✐❝❛s ❞♦ ❘ t♦r♥❡♠ ✭♠❛✐s✮ ❞✐❢í❝✐❧ ❛ ❛♣r❡♥❞✐③❛❣❡♠✱ ♦ s❡✉ ❝❛rá❝t❡r ❣r❛t✉✐t♦✱ ♦ ❢❛❝t♦ ❞❡ s❡r ✉♠❛ ❢❡rr❛♠❡♥t❛ ❜❛st❛♥t❡ ♣♦❞❡r♦s❛ ❝♦♠ ❜♦❛s ❝❛♣❛❝✐❞❛❞❡s ❛♦ ♥í✈❡❧ ❞❛ ♣r♦❣r❛♠❛✲ çã♦ ❡ ✉♠ ❝♦♥❥✉♥t♦ ❜❛st❛♥t❡ ✈❛st♦ ✭❡ ❡♠ ❝♦♥st❛♥t❡ ❝r❡s❝✐♠❡♥t♦✮ ❞❡ ♣❛❝❦❛❣❡s q✉❡ ❛❝r❡s❝❡♥t❛♠ ❜❛st❛♥t❡s ♣♦t❡♥❝✐❛❧✐❞❛❞❡s ❡st❛tíst✐❝❛s ❡ ❣rá✜❝❛s✱ ♦ ❝r❡s❝❡♥t❡ ✐♥t❡r❡ss❡ ❞❡ ✉t✐❧✐③❛❞♦r❡s ❞❛s ♠❛✐s ✈❛r✐❛❞❛s ❢♦r♠❛çõ❡s ✭q✉❡ s❡ r❡ú♥❡♠ ❛♥✉❛❧♠❡♥t❡ ❞❡s❞❡ ✷✵✵✹ ♥❛s ❝♦♥❢❡rê♥❝✐❛s ✉s❡❘✦ ✕ ❡♠ ✷✵✶✶ ❛ ✉s❡❘✦✷✵✶✶ ❞❡❝♦rr❡rá ♥♦ ❘❡✐♥♦✲❯♥✐❞♦✱ ❝❢✳ ❤tt♣✿✴✴✇✇✇✳✇❛r✇✐❝❦✳❛❝✳✉❦✴st❛ts❞❡♣t✴✉s❡❘✲✷✵✶✶✴✮ ❡ ❛ ❞✐s♣♦♥✐❜✐❧✐❞❛❞❡ ❞♦s ♣r♦♠♦t♦r❡s ✭❘ ❉❡✈❡❧♦♣♠❡♥t ❈♦r❡ ❚❡❛♠✮ ❡ ❞❛ ✏ ❝♦♠✉♥✐❞❛❞❡✑ ❞❡ ✉t✐❧✐③❛❞♦r❡s✱ ♠❛✐s ♦✉ ♠❡♥♦s ❛✈❛♥ç❛❞♦s✱ ❛❥✉❞❛♠ ✭❡ ♠✉✐t♦✮ ❡ss❡ ♣r♦❝❡ss♦✳ ❖s ✈ár✐♦s ♠❛♥✉❛✐s ✭❤tt♣✿✴✴❝r❛♥✳r✲ ♣r♦❥❡❝t✳♦r❣✴♠❛♥✉❛❧s✳❤t♠❧✮✱ ❛ ♣á❣✐♥❛ ✇✐❦✐ ✭❤tt♣✿✴✴✇✐❦✐✳r✲♣r♦❥❡❝t✳♦r❣✴✮ ❡ ❛ ♠❛✐❧✐♥❣ ❧✐st ❞❡ ❛❥✉❞❛ ✭❤tt♣✿✴✴st❛t✳❡t❤③✳❝❤✴♠❛✐❧♠❛♥✴❧✐st✐♥❢♦✴r✲❤❡❧♣✮ ♣❡r♠✐t❡♠ ✉❧tr❛♣❛ss❛r ❛ ✭❡s♠❛❣❛❞♦r❛✮ ♠❛✐♦r✐❛ ❞❛s ❞✐✜❝✉❧❞❛❞❡s s✉r❣✐❞❛s ❞✉r❛♥t❡ ❛ ✉t✐❧✐③❛çã♦ ❞♦ ❘✳ ❆❣r❛❞❡❝✐♠❡♥t♦s ❊st❡ ❛rt✐❣♦ ♠✉✐t♦ ❜❡♥❡✜❝✐♦✉ ❞♦s ❝♦♠❡♥tár✐♦s✱ ❝♦rr❡❝çõ❡s ❡ s✉❣❡stõ❡s ❞♦s ❝♦❧❡❣❛s ❡ ❧❡✐t♦r❡s✳ ❘❡❢❡rê♥❝✐❛s ❇♦✇❡♥✱ ❲✳✱ ❏❡r♠❛♥✱ ❏✳✱ ✶✾✾✺✳ ◆♦♥❧✐♥❡❛r r❡❣r❡ss✐♦♥ ✉s✐♥❣ s♣r❡❛❞s❤❡❡ts✳ ❚r❡♥❞s ✐♥ P❤❛r♠❛❝♦❧♦❣✐❝❛❧ ❙❝✐❡♥❝❡s ✶✻✱ ✹✶✸✕✹✶✼✳ ❇r♦✇♥✱ ❆✳ ▼✳✱ ✷✵✵✶✳ ❆ st❡♣✲❜②✲st❡♣ ❣✉✐❞❡ t♦ ♥♦♥✲❧✐♥❡❛r r❡❣r❡ss✐♦♥ ❛♥❛❧②s✐s ♦❢ ❡①♣❡r✐♠❡♥t❛❧ ❞❛t❛ ✉s✐♥❣ ❛ ♠✐❝r♦s♦❢t ❡①❝❡❧ s♣r❡❛❞s❤❡❡t✳ ❈♦♠♣✉t❡r ♠❡t❤♦❞s ❛♥❞ Pr♦❣r❛♠s ✐♥ ❇✐♦♠❡❞✐❝✐♥❡ ✻✺✱ ✶✾✶✕ ✷✵✵✳ ❈❤❛♠❜❡rs✱ ❏✳ ▼✳✱ ❍❛st✐❡✱ ❚✳ ❏✳✱ ✶✾✾✷✳ ❙t❛t✐st✐❝❛❧ ♠♦❞❡❧s ✐♥ ❙✳ ❈❤❛♣♠❛♥ ✫ ❍❛❧❧✱ ▲♦♥❞♦♥✳ ❈♦♥♦✈❡r✱ ❲✳✱ ✶✾✾✾✳ Pr❛❝t✐❝❛❧ ♥♦♥♣❛r❛♠❡tr✐❝ st❛t✐st✐❝s✳ ❏♦❤♥ ❲✐❧❡② ✫ ❙♦♥s✳ ■♥❝✳✱ ◆❡✇ ❨♦r❦✳ ❈r❛✇❧❡②✱ ▼✳✱ ✷✵✵✼✳ ❚❤❡ ❘ ❜♦♦❦✳ ❲✐❧❡②✱ ◆❨✳ ❯❘▲ ❤tt♣✿✴✴✇✇✇✳❣♦♦❣❧❡✳❝♦♠✴❜♦♦❦s❄✐❞❂✽❉✹❍❱①✵❛♣❩◗❈ ❉❛❧❣❛❛r❞✱ P✳✱ ✷✵✵✷✳ ■♥tr♦❞✉❝t♦r② st❛t✐st✐❝s ✇✐t❤ ❘✳ ❙♣r✐♥❣❡r✲❱❡r❧❛❣ ◆❡✇ ❨♦r❦ ■♥❝✳✱ ◆❡✇ ❨♦r❦✳ ❊st❡✈❡s✱ ❊✳✱ ✷✵✶✵✳ ❘❡❣r❡ssã♦ ♥ã♦✲❧✐♥❡❛r ✉t✐❧✐③❛♥❞♦ ❛ ❢❡rr❛♠❡♥t❛ s♦❧✈❡r ➤ ❞♦ ♠✐❝r♦s♦❢t ❡①❝❡❧ ➤ ✳ ■♥st✐t✉t♦ ❙✉♣❡r✐♦r ❞❡ ❊♥❣❡♥❤❛r✐❛✱ ❯♥✐✈❡rs✐❞❛❞❡ ❞♦ ❆❧❣❛r✈❡✱ ❋❛r♦✱ P♦rt✉❣❛❧ ❬❞✐s♣♦♥í✈❡❧ ❡♠ ❤tt♣✿✴✴✇✸✳✉❛❧❣✳♣t✴ ❡❡st❡✈❡s✳❪✳ ❯❘▲ ❤tt♣✿✴✴✇✸✳✉❛❧❣✳♣t✴⑦❡❡st❡✈❡s✳ ❘ ❉❡✈❡❧♦♣♠❡♥t ❈♦r❡ ❚❡❛♠✱ ✷✵✵✼✳ ❘✿ ❆ ▲❛♥❣✉❛❣❡ ❛♥❞ ❊♥✈✐r♦♥♠❡♥t ❢♦r ❙t❛t✐st✐❝❛❧ ❈♦♠♣✉t✐♥❣✳ ❘ ❋♦✉♥❞❛t✐♦♥ ❢♦r ❙t❛t✐st✐❝❛❧ ❈♦♠♣✉t✐♥❣✱ ❱✐❡♥♥❛✱ ❆✉str✐❛✱ ■❙❇◆ ✸✲✾✵✵✵✺✶✲✵✼✲✵✳ ❯❘▲ ❤tt♣✿✴✴✇✇✇✳❘✲♣r♦❥❡❝t✳♦r❣ ❚♦r❣♦✱ ▲✳✱ ✷✵✵✻✳ ■♥tr♦❞✉çã♦ à ♣r♦❣r❛♠❛çã♦ ❡♠ ❘✳ ❋❛❝✉❧❞❛❞❡ ❞❡ ❊❝♦♥♦♠✐❛ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❞♦ P♦rt♦✱ P♦rt♦✳ ❱❡♥❛❜❧❡s✱ ❲✳ ◆✳✱ ❙♠✐t❤✱ ❉✳ ▼✳✱ ❚❡❛♠✱ ❘✳ ❉✳ ❈✳✱ ✷✵✵✻✳ ❆♥ ■♥tr♦❞✉❝t✐♦♥ t♦ ❘ ✭◆♦t❡s ♦♥ ❘✿ ❆ Pr♦❣r❛♠♠✐♥❣ ❊♥✈✐r♦♥♠❡♥t ❢♦r ❉❛t❛ ❆♥❛❧②s✐s ❛♥❞ ●r❛♣❤✐❝s✮✳ ❚❤❡ ❘ ❋♦✉♥❞❛t✐♦♥ ❢♦r ❙t❛t✐st✐❝❛❧ ❈♦♠♣✉t✐♥❣✱ ❱✐❡♥♥❛✱ ❆✉str✐❛✳ ❯❘▲ ❤tt♣✿✴✴❝r❛♥✳r✲♣r♦❥❡❝t✳♦r❣✴❞♦❝✴♠❛♥✉❛❧s✴❘✲✐♥tr♦✳♣❞❢ ✾