Análise de diagnóstico em modelos de regressão
ZAGA e ZAIG.
SERVIÇO DE PÓS-GRADUAÇÃO DO ICMC-USP Data de Depósito: /02/2016
Assinatura:_______________________
Juliana Scudilio Rodrigues
Análise de diagnóstico em modelos de regressão ZAGA e
ZAIG.
Dissertação apresentada ao Instituto de Ciências Matemáticas e de Computação – ICMC-USP e ao Departamento de Estatística – DEs-UFSCar, como parte dos requisitos para obtenção do título de Mestra em Estatística – Interinstitucional de Pós-Graduação em Estatística. VERSÃO REVISADA.
Área de Concentração: Estatística
Orientador: Prof. Dr. Gustavo Henrique de Araujo Pereira
UFSCAR – São Carlos
Juliana Scudilio Rodrigues
Diagnostic analysis in ZAGA and ZAIG regression models.
Master dissertation submitted to the Instituto de Ciências Matemáticas e de Computação - ICMC-USP and to the Departamento de Estatística – DEs-UFSCar, in partial fulfillment of the requirements for the degree of the Master Joint Graduate Program in Statistics DEs-UFSCar/ICMC-USP. FINAL VERSION
Concentration Area: Statistics
Advisor: Prof. Dr. Gustavo Henrique de Araujo Pereira
Ficha catalográfica elaborada pelo DePT da Biblioteca Comunitária UFSCar Processamento Técnico
com os dados fornecidos pelo(a) autor(a)
R696a
Rodrigues, Juliana Scudilio
Análise de diagnóstico em modelos de regressão ZAGA e ZAIG / Juliana Scudilio Rodrigues. -- São Carlos : UFSCar, 2016.
119 p.
Dissertação (Mestrado) -- Universidade Federal de São Carlos, 2016.
1. Análise de diagnóstico. 2. Fundo de
❆❣r❛❞❡❝✐♠❡♥t♦s
❆ ❉❡✉s ♣♦r t❡r ♠❡ ❞❛❞♦ s❛ú❞❡ ❡ ❢♦rç❛ ♣❛r❛ s✉♣❡r❛r ❛s ❞✐✜❝✉❧❞❛❞❡s✳
➚ ■♥st✐t✉✐çã♦ ♣❡❧♦ ❛♠❜✐❡♥t❡ ❝r✐❛t✐✈♦ ❡ ❛♠✐❣á✈❡❧ q✉❡ ♣r♦♣♦r❝✐♦♥❛✳ ❆ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❙ã♦ ❈❛r❧♦s ✭❯❋❙❈❆❘✮ ❡ ❛ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦ ✭❯❙P✲■▼❊✮ ❡♠ ❡s♣❡❝✐❛❧ ❛♦ ❉❡♣❛r✲ t❛♠❡♥t♦ ❞❡ ❊st❛tíst✐❝❛ ❞❡ ❛♠❜❛s ❛s ✉♥✐✈❡rs✐❞❛❞❡✱ ♣❡❧❛ ♦♣♦rt✉♥✐❞❛❞❡ ❞❡ ❢❛③❡r ♦ ♠❡str❛❞♦ ❡♠ ❊st❛tíst✐❝❛✳
❆♦ ♣r♦❢❡ss♦r ❉r✳ ●✉st❛✈♦ ❍❡♥r✐q✉❡ ❞❡ ❆r❛✉❥♦ P❡r❡✐r❛✱ ♣❡❧❛ ♦r✐❡♥t❛çã♦✱ ♣❡❧♦ ❡♠♣❡♥❤♦ ❞❡❞✐❝❛❞♦ à ❡❧❛❜♦r❛çã♦ ❞❡st❡ tr❛❜❛❧❤♦✱ ♣❡❧♦ ♣❛❝✐❡♥t❡ tr❛❜❛❧❤♦ ❞❡ r❡✈✐sã♦ ❞❛ r❡❞❛çã♦ ❡ ♣❡❧♦ ❛♣♦✐♦ ❡ ❝♦♥✜❛♥ç❛ ♥❡ss❡s ❞♦✐s ❛♥♦s ❞❡ ❝❛♠✐♥❤❛❞❛✳
❆♦s Pr♦❢❡ss♦r❡s ❉r✳ ▲✉ís ❆♣❛r❡❝✐❞♦✱ ❉r✳ ❆❢râ♥✐♦ ▼✳ ❈♦rrê❛ ❱✐❡✐r❛✱ ❉r❛✳ ▼❛r✐❛ ❑❡❧❧② ❱❡♥❡③✉❡❧❛ ❡ ❉r❛✳ ❉❡♥✐s❡ ❆♣❛r❡❝✐❞❛ ❇♦tt❡r ♣❡❧❛s s✉❣❡stõ❡s ♦♣♦rt✉♥❛s ❡ ❝♦rr❡çõ❡s ❢❡✐t❛s ♥❛ q✉❛❧✐✜❝❛çã♦ ❡ ♥❛ ❞❡❢❡s❛ ❞♦ ♠❡str❛❞♦✳
❆❣r❛❞❡ç♦ ❛ t♦❞♦s ♦s ♣r♦❢❡ss♦r❡s ❞♦ ❞❡♣❛rt❛♠❡♥t♦ ❞❡ ❡st❛tíst✐❝❛ ❞❛ ❯❙P ❡ ❯❋❙❈❆❘ ♣♦r ♠❡ ♣r♦♣♦r❝✐♦♥❛r ♦ ❝♦♥❤❡❝✐♠❡♥t♦ ♥ã♦ ❛♣❡♥❛s r❛❝✐♦♥❛❧✱ ♠❛s ❛ ♠❛♥✐❢❡st❛çã♦ ❞♦ ❝❛rát❡r ❡ ❛❢❡t✐✈✐❞❛❞❡ ❞❛ ❡❞✉❝❛çã♦ ♥♦ ♣r♦❝❡ss♦ ❞❡ ❢♦r♠❛çã♦ ♣r♦✜ss✐♦♥❛❧✱ ♣♦r t❛♥t♦ q✉❡ s❡ ❞❡❞✐❝❛r❛♠ ❛ ♠✐♠✱ ♥ã♦ s♦♠❡♥t❡ ♣♦r t❡r❡♠ ♠❡ ❡♥s✐♥❛❞♦✱ ♠❛s ♣♦r t❡r❡♠ ♠❡ ❢❡✐t♦ ❛♣r❡♥❞❡r✳ ❆ ♣❛❧❛✈r❛ ♠❡str❡✱ ♥✉♥❝❛ ❢❛rá ❥✉st✐ç❛ ❛♦s ♣r♦❢❡ss♦r❡s ❞❡❞✐❝❛❞♦s ❛♦s q✉❛✐s s❡♠ ♥♦♠✐♥❛r t❡rã♦ ♦s ♠❡✉s ❡t❡r♥♦s ❛❣r❛❞❡❝✐♠❡♥t♦s✳
❆♦s ♠❡✉s ♣❛✐s✱ ♣❡❧♦ ❛♠♦r✱ ✐♥❝❡♥t✐✈♦ ❡ ❛♣♦✐♦ ✐♥❝♦♥❞✐❝✐♦♥❛❧✳ ❆❣r❛❞❡ç♦ ❛ ♠✐♥❤❛ ♠ã❡ ❋❛t✐♠❛ ❙❝✉❞✐❧✐♦ ❘♦❞r✐❣✉❡s✱ ❤❡r♦í♥❛ q✉❡ ♠❡ ❞❡✉ ❛♣♦✐♦✱ ✐♥❝❡♥t✐✈♦ ♥❛s ❤♦r❛s ❞✐❢í❝❡✐s✱ ❞❡ ❞❡sâ♥✐♠♦ ❡ ❝❛♥s❛ç♦✳ ❆♦ ♠❡✉ ♣❛✐ ▼❛r✐♦ ❏♦sé ❘♦❞r✐❣✉❡s q✉❡ ❛♣❡s❛r ❞❡ t♦❞❛s ❛s ❞✐✜❝✉❧❞❛❞❡s ♠❡ ❢♦rt❛❧❡❝❡✉ ❡ s❡♠♣r❡ ❡st❡✈❡ ❛♦ ♠❡✉ ❧❛❞♦ ❛♣♦✐❛♥❞♦ ♠❡✉ s♦♥❤♦✳
❖❜r✐❣❛❞❛ ♠✐♥❤❛ ✐r♠ã✱ s♦❜r✐♥❤❛ ❡ ♥❛♠♦r❛❞♦ q✉❡ ♥♦s ♠♦♠❡♥t♦s ❞❡ ♠✐♥❤❛ ❛✉sê♥❝✐❛ ❞❡❞✐✲ ❝❛❞♦s ❛♦ ❡st✉❞♦ s✉♣❡r✐♦r✱ s❡♠♣r❡ ✜③❡r❛♠ ❡♥t❡♥❞❡r q✉❡ ♦ ❢✉t✉r♦ é ❢❡✐t♦ ❛ ♣❛rt✐r ❞❛ ❝♦♥st❛♥t❡ ❞❡❞✐❝❛çã♦ ♥♦ ♣r❡s❡♥t❡✦
❖❜r✐❣❛❞❛✦ Pr✐♠♦s ❡ t✐♦s ♣❡❧❛ ❝♦♥tr✐❜✉✐çã♦ ✈❛❧✐♦s❛✳ ▼❡✉s ❛❣r❛❞❡❝✐♠❡♥t♦s ❛♦s ❛♠✐❣♦s✱ ❝♦♠♣❛♥❤❡✐r♦s ❞❡ tr❛❜❛❧❤♦s ❡ ✐r♠ã♦s ♥❛ ❛♠✐③❛❞❡ q✉❡ ✜③❡r❛♠ ♣❛rt❡ ❞❛ ♠✐♥❤❛ ❢♦r♠❛çã♦ ❡ q✉❡ ✈ã♦ ❝♦♥t✐♥✉❛r ♣r❡s❡♥t❡s ❡♠ ♠✐♥❤❛ ✈✐❞❛✳
❆ t♦❞♦s q✉❡ ❞✐r❡t❛ ♦✉ ✐♥❞✐r❡t❛♠❡♥t❡ ✜③❡r❛♠ ♣❛rt❡ ❞❛ ♠✐♥❤❛ ❢♦r♠❛çã♦✱ ♦ ♠❡✉ ♠✉✐t♦ ♦❜r✐❣❛❞♦✳
❘❡s✉♠♦
❘♦❞r✐❣✉❡s✱ ❏✳ ❙✳ ❆♥á❧✐s❡ ❞❡ ❞✐❛❣♥óst✐❝♦ ❡♠ ♠♦❞❡❧♦s ❞❡ r❡❣r❡ssã♦ ❩❆●❆ ❡ ❩❆■●✳
❘❡sí❞✉♦s ❞❡s❡♠♣❡♥❤❛♠ ✉♠ ♣❛♣❡❧ ✐♠♣♦rt❛♥t❡ ♥❛ ✈❡r✐✜❝❛çã♦ ❞♦ ❛❥✉st❡ ❞♦ ♠♦❞❡❧♦ ❡ ♥❛ ✐❞❡♥t✐✜❝❛çã♦ ❞❡ ♦❜s❡r✈❛çõ❡s ❞✐s❝r❡♣❛♥t❡s ❡✴♦✉ ✐♥✢✉❡♥t❡s✳ ◆❡st❡ tr❛❜❛❧❤♦✱ ❡st✉❞❛♠♦s ❞✉❛s ❝❧❛ss❡s ❞❡ r❡sí❞✉♦s ♣❛r❛ ♦s ♠♦❞❡❧♦s ❞❡ r❡❣r❡ssã♦ ❣❛♠❛ ✐♥✢❛❝✐♦♥❛❞♦s ♥♦ ③❡r♦ ✭❩❆●❆✮ ❡ ❣❛✉s✲ s✐❛♥❛ ✐♥✈❡rs❛ ✐♥✢❛❝✐♦♥❛❞♦s ♥♦ ③❡r♦ ✭❩❆■●✮✳ ❊ss❛s ❝❧❛ss❡s ❞❡ r❡sí❞✉♦s sã♦ ✉♠❛ ❢✉♥çã♦ ❞❡ ✉♠ r❡sí❞✉♦ ♣❛r❛ ♦ ❝♦♠♣♦♥❡♥t❡ ❝♦♥tí♥✉♦ ❞♦ ♠♦❞❡❧♦ ❡ ❞❛ ❡st✐♠❛t✐✈❛ ❞❡ ♠á①✐♠❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ❞❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❛ ♦❜s❡r✈❛çã♦ ❛ss✉♠✐r ♦ ✈❛❧♦r ③❡r♦✳ ❊st✉❞♦s ❞❡ s✐♠✉❧❛çã♦ ❞❡ ▼♦♥t❡ ❈❛r❧♦ ❢♦r❛♠ r❡❛❧✐③❛❞♦s ♣❛r❛ ❡①❛♠✐♥❛r ❛s ♣r♦♣r✐❡❞❛❞❡s ❞❡ss❛s ❝❧❛ss❡s ❞❡ r❡sí❞✉♦s ❡♠ ❛♠❜♦s ♦s ♠♦✲ ❞❡❧♦s ❞❡ r❡❣r❡ssã♦ ✭❩❆●❆ ❡ ❩❆■●✮✳ ❖s r❡s✉❧t❛❞♦s ♠♦str❛r❛♠ q✉❡ ✉♠ r❡sí❞✉♦ ❞❡ ✉♠❛ ❞❡ss❛s ❝❧❛ss❡s t❡♠ ❛❧❣✉♠❛s ♣r♦♣r✐❡❞❛❞❡s s❡♠❡❧❤❛♥t❡s à ❞❛ ❞✐str✐❜✉✐çã♦ ♥♦r♠❛❧ ♣❛❞rã♦ ♥♦s ♠♦❞❡✲ ❧♦s ❡st✉❞❛❞♦s✳ ❆❧é♠ ❞❡ss❡ ♦❜❥❡t✐✈♦ ♣r✐♥❝✐♣❛❧✱ ❞❡s❝r❡✈❡♠♦s ♦s ♠♦❞❡❧♦s ❞❡ r❡❣r❡ssã♦ ❩❆●❆ ❡ ❩❆■●✱ ❡st✉❞❛♠♦s ♣r♦♣r✐❡❞❛❞❡s ❞❡ ❛❧❣✉♥s r❡sí❞✉♦s ❡♠ ♠♦❞❡❧♦s ❧✐♥❡❛r❡s ❣❡♥❡r❛❧✐③❛❞♦s ❝♦♠ r❡s♣♦st❛ ❣❛♠❛ ❡ ❣❛✉ss✐❛♥❛ ✐♥✈❡rs❛ ❡ ❞✐s❝✉t✐♠♦s ♦✉tr♦s ❛s♣❡❝t♦s ❞❡ ❛♥á❧✐s❡ ❞❡ ❞✐❛❣♥óst✐❝♦ ♥♦s ♠♦❞❡❧♦s ❩❆●❆ ❡ ❩❆■●✳ P❛r❛ ✜♥❛❧✐③❛r✱ ❢♦✐ ❢❡✐t❛ ✉♠❛ ❛♣❧✐❝❛çã♦ ❝♦♠ ❞❛❞♦s r❡❛✐s ❞❡ ❢✉♥❞♦s ❞❡ ✐♥✈❡st✐♠❡♥t♦s✱ ❡♠ q✉❡ ❛❥✉st❛♠♦s ♦ ♠♦❞❡❧♦ ❩❆■●✱ ♣❛r❛ ❡①❡♠♣❧✐✜❝❛r ♦s tó♣✐❝♦s ❞✐s❝✉t✐❞♦s ❡ ♠♦str❛r ❛ ✐♠♣♦rtâ♥❝✐❛ ❞❡ss❡s ♠♦❞❡❧♦s ❡ ❛s ✈❛♥t❛❣❡♥s ❞❡ ✉♠ ❞♦s r❡sí❞✉♦s ❡st✉❞❛❞♦s ♥❛ ❛♥á❧✐s❡ ❞❡ ❞❛❞♦s r❡❛✐s✳
P❛❧❛✈r❛s✲❝❤❛✈❡✿ ❛♥á❧✐s❡ ❞❡ ❞✐❛❣♥óst✐❝♦✱ ❢✉♥❞♦ ❞❡ ✐♥✈❡st✐♠❡♥t♦✱ ♠♦❞❡❧♦s ❞❡ r❡❣r❡ssã♦ ✐♥✢❛✲ ❝✐♦♥❛❞♦ ♥♦ ③❡r♦✱ ♠♦❞❡❧♦ ❩❆●❆✱ ♠♦❞❡❧♦ ❩❆■●✱ r❡sí❞✉♦ q✉❛♥tí❧✐❝♦✳
❆❜str❛❝t
❘♦❞r✐❣✉❡s✱ ❏✳ ❙✳ ❉✐❛❣♥♦st✐❝ ❛♥❛❧②s✐s ✐♥ ❩❆●❆ ❛♥❞ ❩❆■● r❡❣r❡ss✐♦♥ ♠♦❞❡❧s✳
❘❡s✐❞✉❛❧s ♣❧❛② ❛♥ ✐♠♣♦rt❛♥t r♦❧❡ ✐♥ ❝❤❡❝❦✐♥❣ ♠♦❞❡❧ ❛❞❡q✉❛❝② ❛♥❞ ✐♥ t❤❡ ✐❞❡♥t✐✜❝❛t✐♦♥ ♦❢ ♦✉t❧✐❡rs ❛♥❞ ✐♥✢✉❡♥t✐❛❧ ♦❜s❡r✈❛t✐♦♥s✳ ■♥ t❤✐s ♣❛♣❡r✱ ✇❡ st✉❞✐❡❞ t✇♦ ❝❧❛ss ♦❢ r❡s✐❞✉❛❧s ❢♦r t❤❡ ③❡r♦ ❛❞❥✉st❡❞ ❣❛♠♠❛ r❡❣r❡ss✐♦♥ ♠♦❞❡❧ ✭❩❆●❆✮ ❛♥❞ t❤❡ ③❡r♦ ❛❞❥✉st❡❞ ✐♥✈❡rs❡ ●❛✉ss✐❛♥ r❡✲ ❣r❡ss✐♦♥ ♠♦❞❡❧ ✭❩❆■●✮✳ ❚❤❡s❡ ❝❧❛ss❡s ♦❢ r❡s✐❞✉❛❧s ❛r❡ ❢✉♥❝t✐♦♥ ♦❢ ❛ r❡s✐❞✉❛❧ ❢♦r t❤❡ ❝♦♥t✐♥✉♦✉s ❝♦♠♣♦♥❡♥t ♦❢ t❤❡ ♠♦❞❡❧ ❛♥❞ t❤❡ ♠❛①✐♠✉♠ ❧✐❦❡❧✐❤♦♦❞ ❡st✐♠❛t❡ ♦❢ t❤❡ ♣r♦❜❛❜✐❧✐t② ♦❢ t❤❡ ♦❜✲ s❡r✈❛t✐♦♥ ❛ss✉♠✐♥❣ t❤❡ ③❡r♦ ✈❛❧✉❡✳ ▼♦♥t❡ ❈❛r❧♦ s✐♠✉❧❛t✐♦♥ st✉❞✐❡s ❛r❡ ♣❡r❢♦r♠❡❞ t♦ ❡①❛♠✐♥❡ t❤❡ ♣r♦♣❡rt✐❡s ♦❢ t❤✐s ❝❧❛ss ♦❢ r❡s✐❞✉❛❧s ✐♥ ❜♦t❤ ♠♦❞❡❧s ✭❩❆●❆ ❛♥❞ ❩❆■●✮✳ ❘❡s✉❧ts s❤♦✇❡❞ t❤❛t ❛ r❡s✐❞✉❛❧ ♦❢ ♦♥❡ ♦❢ t❤❡s❡ ❝❧❛ss ❤❛s s♦♠❡ s✐♠✐❧❛r ♣r♦♣❡rt✐❡s t♦ t❤❡ st❛♥❞❛r❞ ♥♦r♠❛❧ ❞✐str✐❜✉t✐♦♥ ✐♥ t❤❡ st✉❞✐❡❞ ♠♦❞❡❧s✳ ❲❡ ❛❧s♦ ❞❡s❝r✐❜❡❞ ❩❆●❆ ❛♥❞ ❩❆■● r❡❣r❡ss✐♦♥ ♠♦❞❡❧s✱ st✉❞✐❡❞ ♣r♦♣❡rt✐❡s ♦❢ s♦♠❡ r❡s✐❞✉❛❧s ✐♥ ❣❡♥❡r❛❧✐③❡❞ ❧✐♥❡❛r ♠♦❞❡❧s ✇✐t❤ r❡s♣♦♥s❡ ❣❛♠♠❛ ❛♥❞ ✐♥✈❡rs❡ ●❛✉ss✐❛♥ ❛♥❞ ❞✐s❝✉ss❡❞ ♦t❤❡r ❛s♣❡❝ts ♦❢ ❞✐❛❣♥♦st✐❝ ❛♥❛❧②s✐s ✐♥ ❩❆●❆ ❛♥❞ ❩❆■● ♠♦❞❡❧s✳ ❚♦ ✜♥s✐❤✱ ✇❡ ♣r❡s❡♥t❡❞ ❛ r❡❛❧ ❞❛t❛s❡t ❛♣♣❧✐❝❛t✐♦♥ ❢r♦♠ ✐♥✈❡st♠❡♥t ❢✉♥❞s ♦❢ ❇r❛③✐❧✳ ❲❡ ✜tt❡❞ t❤❡ ❩❆■● ♠♦❞❡❧ t♦ ✐❧❧✉str❛t❡ t❤❡ t♦♣✐❝s ❞✐s❝✉ss❡❞ ❛♥❞ s❤♦✇❡❞ t❤❡ ✐♠♣♦rt❛♥❝❡ ♦❢ t❤❡s❡ ♠♦❞❡❧s ❛♥❞ t❤❡ ❛❞✈❛♥t❛❣❡s ♦❢ ♦♥❡ ♦❢ t❤❡ st✉❞✐❡❞ r❡s✐❞✉❛❧s ✐♥ t❤❡ ❛♥❛❧②s✐s ♦❢ r❡❛❧ ❞❛t❛s❡t✳
❑❡②✇♦r❞s✿ ❞✐❛❣♥♦st✐❝ ❛♥❛❧②s✐s✱ ✐♥✢❛t❡❞ r❡❣r❡ss✐♦♥ ♠♦❞❡❧s✱ ✐♥✈❡st✐♠❡♥t ❢✉♥❞s✱ q✉❛♥t✐❧❡ r❡✲ s✐❞✉❛❧✱ ❩❆●❆ ♠♦❞❡❧s✱ ❩❆■● ♠♦❞❡❧s✳
❙✉♠ár✐♦
▲✐st❛ ❞❡ ❋✐❣✉r❛s ✈✐
▲✐st❛ ❞❡ ❚❛❜❡❧❛s ✈✐✐
✶ ■♥tr♦❞✉çã♦ ✶
✷ ▼♦❞❡❧♦s ❞❡ r❡❣r❡ssã♦ ❩❆●❆ ❡ ❩❆■● ✸
✷✳✶ ❉✐str✐❜✉✐çõ❡s ❝♦♥tí♥✉❛s ✐♥✢❛❝✐♦♥❛❞❛s ♥♦ ③❡r♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹
✷✳✶✳✶ ❉✐str✐❜✉✐çã♦ ❩❆●❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺
✷✳✶✳✷ ❉✐str✐❜✉✐çã♦ ❩❆■● ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼
✷✳✷ ▼♦❞❡❧♦s ❞❡ r❡❣r❡ssã♦ ✐♥✢❛❝✐♦♥❛❞♦s ♥♦ ③❡r♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽
✷✳✷✳✶ ▼♦❞❡❧♦s ❞❡ r❡❣r❡ssã♦ ❣❛♠❛ ✐♥✢❛❝✐♦♥❛❞♦s ♥♦ ③❡r♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾
✷✳✷✳✷ ▼♦❞❡❧♦s ❞❡ r❡❣r❡ssã♦ ❣❛✉ss✐❛♥❛ ✐♥✈❡rs❛ ✐♥✢❛❝✐♦♥❛❞♦s ♥♦ ③❡r♦ ✳ ✳ ✳ ✳ ✳ ✶✶
✷✳✸ ❊st✐♠❛çã♦ ♥♦s ♠♦❞❡❧♦s ❩❆●❆ ❡ ❩❆■● ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷
✷✳✹ ■♥t❡r✈❛❧♦s ❞❡ ❝♦♥✜❛♥ç❛ ❡ t❡st❡s ❞❡ ❤✐♣ót❡s❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸
✷✳✺ ❙❡❧❡çã♦ ❞❡ ♠♦❞❡❧♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹
✸ ❆♥á❧✐s❡ ❞❡ ❞✐❛❣♥óst✐❝♦ ✶✺
✸✳✶ ❆♥á❧✐s❡ ❞❡ ❞✐❛❣♥óst✐❝♦ ❡♠ ▼▲●s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺
✸✳✶✳✶ ❘❡sí❞✉♦ ❞❡s✈✐♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻
✸✳✶✳✷ ❘❡sí❞✉♦ ❞❡ P❡❛rs♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼
✸✳✶✳✸ ❘❡sí❞✉♦ q✉❛♥tí❧✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼
✸✳✶✳✹ ❘❡sí❞✉♦ ❆♥s❝♦♠❜❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽
✸✳✶✳✺ ❘❡sí❞✉♦ ❲✐❧❧✐❛♠s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾
✸✳✷ ❊st✉❞♦s ❞❡ s✐♠✉❧❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾
✸✳✷✳✶ ▼♦❞❡❧♦ ❣❛♠❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵
✸✳✷✳✷ ▼♦❞❡❧♦ ❣❛✉ss✐❛♥❛ ✐♥✈❡rs❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹
✸✳✷✳✸ ❈♦♥s✐❞❡r❛çõ❡s ✜♥❛✐s s♦❜r❡ ♦s ❡st✉❞♦s ❞❡ s✐♠✉❧❛çã♦ ♥♦s ▼▲●s ✳ ✳ ✳ ✳ ✷✻
✸✳✸ ❆♥á❧✐s❡ ❞❡ ❞✐❛❣♥óst✐❝♦ ❡♠ ♠♦❞❡❧♦s ✐♥✢❛❝✐♦♥❛❞♦s
❩❆●❆ ❡ ❩❆■● ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽
✸✳✸✳✶ ■❞❡♥t✐✜❝❛çã♦ ❞❡ ♦❜s❡r✈❛çõ❡s ❞✐s❝r❡♣❛♥t❡s ✲ ❝♦♠♣♦♥❡♥t❡ ❝♦♥tí♥✉♦ ✳ ✳ ✳ ✷✽
✸✳✹ ❊st✉❞♦s ❞❡ s✐♠✉❧❛çã♦ ♣❛r❛ ♦s ♠♦❞❡❧♦s ✐♥✢❛❝✐♦♥❛❞♦s ♥♦ ③❡r♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸
❙❯▼➪❘■❖ ✈
✸✳✹✳✶ ❊st✉❞♦s ❞❡ s✐♠✉❧❛çã♦ ♣❛r❛ ♦ ♠♦❞❡❧♦ ❩❆●❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹
✸✳✹✳✷ ❊st✉❞♦s ❞❡ s✐♠✉❧❛çã♦ ♣❛r❛ ♦ ♠♦❞❡❧♦ ❩❆■● ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼
✸✳✹✳✸ ❊st✉❞♦s ❞❡ s✐♠✉❧❛çã♦ ♣❛r❛ ♦ ❝❛s♦ ❞♦ ❛❥✉st❡ ❞♦ ♠♦❞❡❧♦ ✐♥❝♦rr❡t♦ ✳ ✳ ✳ ✹✵
✸✳✺ ❖✉tr♦s ❛s♣❡❝t♦s ❞❛ ❛♥á❧✐s❡ ❞❡ ❞✐❛❣♥óst✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶
✸✳✺✳✶ ❖❜s❡r✈❛çõ❡s ❞✐s❝r❡♣❛♥t❡s ✲ ❝♦♠♣♦♥❡♥t❡ ❞✐s❝r❡t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷
✸✳✺✳✷ P♦♥t♦s ✐♥✢✉❡♥t❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸
✸✳✺✳✸ ●rá✜❝♦s ❞❡ ❞✐❛❣♥óst✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹
✸✳✺✳✹ ❚❡st❡ ❞❡ q✉❛❧✐❞❛❞❡ ❞❡ ❛❥✉st❡ ♣❛r❛ ♦ ❝♦♠♣♦♥❡♥t❡ ❞✐s❝r❡t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼
✹ ❆♣❧✐❝❛çã♦ ✹✾
✹✳✶ ❉❡s❝r✐çã♦ ❞♦s ❞❛❞♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾
✹✳✷ ❆❥✉st❡ ❡ ❛♥á❧✐s❡ ❞❡ ❞✐❛❣♥óst✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸
✹✳✸ ❉✐s❝✉ssã♦ s♦❜r❡ ❛ ✐❞❡♥t✐✜❝❛çã♦ ❞❡ ♦❜s❡r✈❛çõ❡s ♣♦s✐t✐✈❛s ❞✐s❝r❡♣❛♥t❡s✳ ✳ ✳ ✳ ✳ ✺✽
✺ ❈♦♥❝❧✉sõ❡s ❡ tr❛❜❛❧❤♦s ❢✉t✉r♦s ✻✶
✺✳✶ Pró①✐♠♦s ♣❛ss♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷
❆ ❉❡♠♦♥str❛çõ❡s ❞♦s r❡s✉❧t❛❞♦s ❞♦ ❈❛♣ít✉❧♦ ✭✷✮ ✻✸
❆✳✶ ▼♦❞❡❧♦ ❩❆●❆✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸
❆✳✶✳✶ ❖❜t❡♥çã♦ ❞❛ ❢✉♥çã♦ ❡s❝♦r❡ ♣❛r❛ ♦ ♠♦❞❡❧♦ ❩❆●❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸
❆✳✶✳✷ ❖❜t❡♥çã♦ ❞❛ ♠❛tr✐③ ❞❡ ✐♥❢♦r♠❛çã♦ ❞❡ ❋✐s❤❡r ✲ ♠♦❞❡❧♦ ❩❆●❆ ✳ ✳ ✳ ✳ ✻✹
❆✳✷ ▼♦❞❡❧♦ ❩❆■● ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻
❆✳✷✳✶ ❖❜t❡♥çã♦ ❞❛ ❢✉♥çã♦ ❡s❝♦r❡ ♣❛r❛ ♦ ♠♦❞❡❧♦ ❩❆■● ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻
❆✳✷✳✷ ❖❜t❡♥çã♦ ❞❛ ♠❛tr✐③ ❞❡ ✐♥❢♦r♠❛çã♦ ❞❡ ❋✐s❤❡r ✲ ♠♦❞❡❧♦ ❩❆■● ✳ ✳ ✳ ✳ ✳ ✻✼
❇ ❚❛❜❡❧❛s ❞♦s ❡st✉❞♦s ❞❡ s✐♠✉❧❛çã♦ ♥♦ ♠♦❞❡❧♦ ❣❛♠❛ ✻✾
❈ ❚❛❜❡❧❛s ❞♦s ❡st✉❞♦s ❞❡ s✐♠✉❧❛çã♦ ♥♦ ♠♦❞❡❧♦ ❣❛✉ss✐❛♥❛ ✐♥✈❡rs❛ ✼✼
❉ ❚❛❜❡❧❛s ❞♦s ❡st✉❞♦s ❞❡ s✐♠✉❧❛çã♦ ♥♦ ♠♦❞❡❧♦ ❩❆●❆ ✽✺
❊ ❚❛❜❡❧❛s ❞♦s ❡st✉❞♦s ❞❡ s✐♠✉❧❛çã♦ ♥♦ ♠♦❞❡❧♦ ❩❆■● ✾✾
❋ ❚❛❜❡❧❛s ❞♦ ❛❥✉st❡ ❞♦ ♠♦❞❡❧♦ ✐♥❝♦rr❡t♦ ✶✶✸
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✷✳✶ ●rá✜❝♦ ❞❛ ❞✐str✐❜✉✐çã♦ ❩❆●❆ ♣❛r❛ ❞✐❢❡r❡♥t❡s ✈❛❧♦r❡s ❞♦s ♣❛râ♠❡tr♦s ✳ ✳ ✳ ✳ ✻
✷✳✷ ●rá✜❝♦ ❞❛ ❞✐str✐❜✉✐çã♦ ❩❆■● ♣❛r❛ ❞✐❢❡r❡♥t❡s ✈❛❧♦r❡s ❞♦s ♣❛râ♠❡tr♦s ✳ ✳ ✳ ✳ ✳ ✼
✸✳✶ ●rá✜❝♦ ❞♦s r❡sí❞✉♦s ♣❛r❛ ❞✐❢❡r❡♥t❡s ✈❛❧♦r❡s ❞❡ α✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶
✹✳✶ ❍✐st♦❣r❛♠❛ ❞❛ ✈❛r✐á✈❡❧ r❡s♣♦st❛ ✲ ♦❜s❡r✈❛çõ❡s ❞✐❢❡r❡♥t❡s ❞❡ ③❡r♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶
✹✳✷ ❆♥á❧✐s❡ ❞❡ ❞✐❛❣♥óst✐❝♦ ❝♦♠♣♦♥❡♥t❡ ❝♦♥tí♥✉♦ ❞♦ ♠♦❞❡❧♦ ❩❆■●✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸
✹✳✸ ❆♥á❧✐s❡ ❞❡ ❞✐❛❣♥óst✐❝♦ ❝♦♠♣♦♥❡♥t❡ ❞✐s❝r❡t♦ ❞♦ ♠♦❞❡❧♦ ❩❆■●✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹
✹✳✹ ❆♥á❧✐s❡ ❞❡ ❞✐❛❣♥óst✐❝♦ ❞✐stâ♥❝✐❛ ❞❡ ❈♦♦❦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺
✹✳✺ ●rá✜❝♦ ❡♥✈❡❧♦♣❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻
✹✳✻ ❘❡sí❞✉♦s ♣❛r❛ ♦ ❝♦♠♣♦♥❡♥t❡ ❝♦♥tí♥✉♦ ❞♦ ♠♦❞❡❧♦ ❩❆■●✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✸✳✶ ❊str✉t✉r❛s ❞❛s t❛❜❡❧❛s ❛♣r❡s❡♥t❛❞❛s ♥♦ ❆♣ê♥❞✐❝❡ ❇ ❡ ❈ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵
✸✳✷ ❆❧t❡r❛çõ❡s ❢❡✐t❛s ♥♦s ❝❡♥ár✐♦s ❡♠ r❡❧❛çã♦ ❛♦ ❝❡♥ár✐♦ ■✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶
✸✳✸ ❈♦♠♣❛r❛çã♦ ❞❛ ❡st❛tíst✐❝❛ ❞❡ ❆♥❞❡rs♦♥✲❉❛r❧✐♥❣ ♣❛r❛ ♥❂✶✺ ❡ ♥❂✺✵ ♥♦ ♠♦❞❡❧♦ ❣❛♠❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸
✸✳✹ ❆❧t❡r❛çõ❡s ❢❡✐t❛s ♥♦s ❝❡♥ár✐♦s ❡♠ r❡❧❛çã♦ ❛♦ ❝❡♥ár✐♦ ■✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹
✸✳✺ ❈♦♠♣❛r❛çã♦ ❞❛ ❡st❛tíst✐❝❛ ❞❡ ❆♥❞❡rs♦♥✲❉❛r❧✐♥❣ ♣❛r❛ ♥❂✶✺ ❡ ♥❂✺✵ ♥♦ ♠♦❞❡❧♦
❣❛✉ss✐❛♥❛ ✐♥✈❡rs❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼
✸✳✻ ❊str✉t✉r❛ ❞❛s t❛❜❡❧❛s ❛♣r❡s❡♥t❛❞❛s ♥♦s ❛♣ê♥❞✐❝❡s ❉ ❡ ❊✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹
✸✳✼ ❆❧t❡r❛çõ❡s ❢❡✐t❛s ♥♦s ❝❡♥ár✐♦s ❡♠ r❡❧❛çã♦ ❛♦ ❝❡♥ár✐♦ ✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺
✸✳✽ ❆❧t❡r❛çõ❡s ❢❡✐t❛s ♥♦s ❝❡♥ár✐♦s ❡♠ r❡❧❛çã♦ ❛♦ ❝❡♥ár✐♦ ✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾
✹✳✶ ▼❡❞✐❞❛s ❞❡s❝r✐t✐✈❛s ❞❛ ✈❛r✐á✈❡❧ r❡s♣♦st❛ ❨ ❝♦♥s✐❞❡r❛♥❞♦ ❛♣❡♥❛s ❛s ♦❜s❡r✈❛✲
çõ❡s ❞✐❢❡r❡♥t❡s ❞❡ ③❡r♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶
✹✳✷ ▼❡❞✐❞❛s ❞❡s❝r✐t✐✈❛s ❞❛s ❝♦✈❛r✐á✈❡✐s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷
✹✳✸ ❚❛❜❡❧❛ ❞❡ ❢r❡q✉ê♥❝✐❛s ❞❛s ❝♦✈❛r✐á✈❡✐s ❝❛t❡❣♦r✐③❛❞❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷
✹✳✹ ▼♦❞❡❧♦ ✜♥❛❧ ♣❛r❛ ❛ ✈❛r✐á✈❡❧ t❛①❛ ❞❡ ❝r❡s❝✐♠❡♥t♦ ❞♦ ❢✉♥❞♦ r❡❢❡r❡♥❝✐❛❞♦s ❉■
❡①✐st❡♥t❡ ❡♠ ❥✉♥❤♦ ❞❡ ✷✵✶✸ ❛ ❥✉♥❤♦ ❞❡ ✷✵✶✺✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻
✹✳✺ ❚❛❜❡❧❛ ❞❛ ✈❛r✐❛çã♦ ♣❡r❝❡♥t✉❛❧ ❞❛s ❡st✐♠❛t✐✈❛s ❞♦s ♣❛râ♠❡tr♦s ❝♦♠ ❛ r❡t✐r❛❞❛
❞❛s ♦❜s❡r✈❛çõ❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼
✹✳✻ ❱❛❧♦r❡s ❞❛s ✈❛r✐á✈❡✐s ♣❛r❛ ❛ ♦❜s❡r✈❛çã♦ ✶✻✼ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵
✹✳✼ ❱❛❧♦r❡s ❞❛s ✈❛r✐á✈❡✐s ♣❛r❛ ❛ ♦❜s❡r✈❛çã♦ #❡ ∗ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵
❇✳✶ ❘❡s✉❧t❛❞♦s ❞❛ s✐♠✉❧❛çã♦ ♣❛r❛ ♦ ♠♦❞❡❧♦ ❣❛♠❛ ✲ ❝❡♥ár✐♦ ■✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵
❇✳✷ ❘❡s✉❧t❛❞♦s ❞❛ s✐♠✉❧❛çã♦ ♣❛r❛ ♦ ♠♦❞❡❧♦ ❣❛♠❛ ✲ ❝❡♥ár✐♦ ■■✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶
❇✳✸ ❘❡s✉❧t❛❞♦s ❞❛ s✐♠✉❧❛çã♦ ♣❛r❛ ♦ ♠♦❞❡❧♦ ❣❛♠❛ ✲ ❝❡♥ár✐♦ ■■■✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷
❇✳✹ ❘❡s✉❧t❛❞♦s ❞❛ s✐♠✉❧❛çã♦ ♣❛r❛ ♦ ♠♦❞❡❧♦ ❣❛♠❛ ✲ ❝❡♥ár✐♦ ■❱✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸
❇✳✺ ❘❡s✉❧t❛❞♦s ❞❛ s✐♠✉❧❛çã♦ ♣❛r❛ ♦ ♠♦❞❡❧♦ ❣❛♠❛ ✲ ❝❡♥ár✐♦ ❱✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹
❇✳✻ ❘❡s✉❧t❛❞♦s ❞❛ s✐♠✉❧❛çã♦ ♣❛r❛ ♦ ♠♦❞❡❧♦ ❣❛♠❛ ✲ ❝❡♥ár✐♦ ❱■✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺
❇✳✼ ❘❡s✉❧t❛❞♦s ❞❛ s✐♠✉❧❛çã♦ ♣❛r❛ ♦ ♠♦❞❡❧♦ ❣❛♠❛ ✲ ❝❡♥ár✐♦ ❱■■✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻
❈✳✶ ❘❡s✉❧t❛❞♦s ❞❛ s✐♠✉❧❛çã♦ ♣❛r❛ ♦ ♠♦❞❡❧♦ ❣❛✉ss✐❛♥❛ ✐♥✈❡rs❛ ✲ ❝❡♥ár✐♦ ■✳ ✳ ✳ ✳ ✳ ✼✽
❈✳✷ ❘❡s✉❧t❛❞♦s ❞❛ s✐♠✉❧❛çã♦ ♣❛r❛ ♦ ♠♦❞❡❧♦ ❣❛✉ss✐❛♥❛ ✐♥✈❡rs❛ ✲ ❝❡♥ár✐♦ ■■✳ ✳ ✳ ✳ ✳ ✼✾
▲■❙❚❆ ❉❊ ❚❆❇❊▲❆❙ ✈✐✐✐
❈✳✸ ❘❡s✉❧t❛❞♦s ❞❛ s✐♠✉❧❛çã♦ ♣❛r❛ ♦ ♠♦❞❡❧♦ ❣❛✉ss✐❛♥❛ ✐♥✈❡rs❛ ✲ ❝❡♥ár✐♦ ■■■✳ ✳ ✳ ✳ ✽✵
❈✳✹ ❘❡s✉❧t❛❞♦s ❞❛ s✐♠✉❧❛çã♦ ♣❛r❛ ♦ ♠♦❞❡❧♦ ❣❛✉ss✐❛♥❛ ✐♥✈❡rs❛ ✲ ❝❡♥ár✐♦ ■❱✳ ✳ ✳ ✳ ✽✶
❈✳✺ ❘❡s✉❧t❛❞♦s ❞❛ s✐♠✉❧❛çã♦ ♣❛r❛ ♦ ♠♦❞❡❧♦ ❣❛✉ss✐❛♥❛ ✐♥✈❡rs❛ ✲ ❝❡♥ár✐♦ ❱✳ ✳ ✳ ✳ ✳ ✽✷
❈✳✻ ❘❡s✉❧t❛❞♦s ❞❛ s✐♠✉❧❛çã♦ ♣❛r❛ ♦ ♠♦❞❡❧♦ ✐♥✈❡rs❛ ❣❛✉ss✐❛♥❛ ✲ ❝❡♥ár✐♦ ❱■✳ ✳ ✳ ✳ ✽✸
❈✳✼ ❘❡s✉❧t❛❞♦s ❞❛ s✐♠✉❧❛çã♦ ♣❛r❛ ♦ ♠♦❞❡❧♦ ❣❛✉ss✐❛♥❛ ✐♥✈❡rs❛ ✲ ❝❡♥ár✐♦ ❱■■✳ ✳ ✳ ✳ ✽✹
❉✳✶ ❊st❛tíst✐❝❛s ❞❡s❝r✐t✐✈❛s ❞❛ ♣♦r❝❡♥t❛❣❡♠ ♦❜s❡r✈❛❞❛ ❞♦s r❡sí❞✉♦s ♣❛r❛ ❝❛❞❛ ✐♥✲
t❡r✈❛❧♦ ♥♦ ♠♦❞❡❧♦ ❩❆●❆ ✲ ❈❡♥ár✐♦ ✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✻
❉✳✷ ❊st❛tíst✐❝❛s ❞❡s❝r✐t✐✈❛s ❞❛ ♣♦r❝❡♥t❛❣❡♠ ♦❜s❡r✈❛❞❛ ❞♦s r❡sí❞✉♦s ♣❛r❛ ❝❛❞❛ ✐♥✲
t❡r✈❛❧♦ ♥♦ ♠♦❞❡❧♦ ❩❆●❆ ✲ ❈❡♥ár✐♦ ✷❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✼
❉✳✸ ❊st❛tíst✐❝❛s ❞❡s❝r✐t✐✈❛s ❞❛ ♣♦r❝❡♥t❛❣❡♠ ♦❜s❡r✈❛❞❛ ❞♦s r❡sí❞✉♦s ♣❛r❛ ❝❛❞❛ ✐♥✲
t❡r✈❛❧♦ ✲ ❈❡♥ár✐♦ ✷❜✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✽
❉✳✹ ❊st❛tíst✐❝❛s ❞❡s❝r✐t✐✈❛s ❞❛ ♣♦r❝❡♥t❛❣❡♠ ♦❜s❡r✈❛❞❛ ❞♦s r❡sí❞✉♦s ♣❛r❛ ❝❛❞❛ ✐♥✲
t❡r✈❛❧♦ ✲ ❈❡♥ár✐♦ ✸✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾
❉✳✺ ❊st❛tíst✐❝❛s ❞❡s❝r✐t✐✈❛s ❞❛ ♣♦r❝❡♥t❛❣❡♠ ♦❜s❡r✈❛❞❛ ❞♦s r❡sí❞✉♦s ♣❛r❛ ❝❛❞❛ ✐♥✲
t❡r✈❛❧♦ ♥♦ ♠♦❞❡❧♦ ❩❆●❆ ✲ ❈❡♥ár✐♦ ✹❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✵
❉✳✻ ❊st❛tíst✐❝❛s ❞❡s❝r✐t✐✈❛s ❞❛ ♣♦r❝❡♥t❛❣❡♠ ♦❜s❡r✈❛❞❛ ❞♦s r❡sí❞✉♦s ♣❛r❛ ❝❛❞❛ ✐♥✲
t❡r✈❛❧♦ ♥♦ ♠♦❞❡❧♦ ❩❆●❆ ✲ ❈❡♥ár✐♦ ✹❜✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✶
❉✳✼ ❊st❛tíst✐❝❛s ❞❡s❝r✐t✐✈❛s ❞❛ ♣♦r❝❡♥t❛❣❡♠ ♦❜s❡r✈❛❞❛ ❞♦s r❡sí❞✉♦s ♣❛r❛ ❝❛❞❛ ✐♥✲
t❡r✈❛❧♦ ♥♦ ♠♦❞❡❧♦ ❩❆●❆ ✲ ❈❡♥ár✐♦ ✺✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✷
❉✳✽ ❊st❛tíst✐❝❛s ❞❡s❝r✐t✐✈❛s ❞❛ ♣♦r❝❡♥t❛❣❡♠ ♦❜s❡r✈❛❞❛ ❞♦s r❡sí❞✉♦s ♣❛r❛ ❝❛❞❛ ✐♥✲
t❡r✈❛❧♦ ❩❆●❆ ✲ ❈❡♥ár✐♦ ✻❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✸
❉✳✾ ❊st❛tíst✐❝❛s ❞❡s❝r✐t✐✈❛s ❞❛ ♣♦r❝❡♥t❛❣❡♠ ♦❜s❡r✈❛❞❛ ❞♦s r❡sí❞✉♦s ♣❛r❛ ❝❛❞❛ ✐♥✲
t❡r✈❛❧♦ ❩❆●❆ ✲ ❈❡♥ár✐♦ ✻❜✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✹
❉✳✶✵ ❊st❛tíst✐❝❛s ❞❡s❝r✐t✐✈❛s ❞❛ ♣♦r❝❡♥t❛❣❡♠ ♦❜s❡r✈❛❞❛ ❞♦s r❡sí❞✉♦s ♣❛r❛ ❝❛❞❛ ✐♥✲
t❡r✈❛❧♦ ❩❆●❆ ✲ ❈❡♥ár✐♦ ✼❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✺
❉✳✶✶ ❊st❛tíst✐❝❛s ❞❡s❝r✐t✐✈❛s ❞❛ ♣♦r❝❡♥t❛❣❡♠ ♦❜s❡r✈❛❞❛ ❞♦s r❡sí❞✉♦s ♣❛r❛ ❝❛❞❛ ✐♥✲
t❡r✈❛❧♦ ❩❆●❆ ✲ ❈❡♥ár✐♦ ✼❜✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✻
❉✳✶✷ ❊st❛tíst✐❝❛s ❞❡s❝r✐t✐✈❛s ❞❛ ♣♦r❝❡♥t❛❣❡♠ ♦❜s❡r✈❛❞❛ ❞♦s r❡sí❞✉♦s ♣❛r❛ ❝❛❞❛ ✐♥✲
t❡r✈❛❧♦ ❩❆●❆ ✲ ❈❡♥ár✐♦ ✽❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✼
❉✳✶✸ ❊st❛tíst✐❝❛s ❞❡s❝r✐t✐✈❛s ❞❛ ♣♦r❝❡♥t❛❣❡♠ ♦❜s❡r✈❛❞❛ ❞♦s r❡sí❞✉♦s ♣❛r❛ ❝❛❞❛ ✐♥✲
t❡r✈❛❧♦ ❩❆●❆ ✲ ❈❡♥ár✐♦ ✽❜✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✽
❊✳✶ ❊st❛tíst✐❝❛s ❞❡s❝r✐t✐✈❛s ❞❛ ♣♦r❝❡♥t❛❣❡♠ ♦❜s❡r✈❛❞❛ ❞♦s r❡sí❞✉♦s ♣❛r❛ ❝❛❞❛ ✐♥✲
t❡r✈❛❧♦ ❩❆■● ✲ ❈❡♥ár✐♦ ✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✵
❊✳✷ ❊st❛tíst✐❝❛s ❞❡s❝r✐t✐✈❛s ❞❛ ♣♦r❝❡♥t❛❣❡♠ ♦❜s❡r✈❛❞❛ ❞♦s r❡sí❞✉♦s ♣❛r❛ ❝❛❞❛ ✐♥✲
t❡r✈❛❧♦ ❩❆■● ✲ ❈❡♥ár✐♦ ✷❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✶
❊✳✸ ❊st❛tíst✐❝❛s ❞❡s❝r✐t✐✈❛s ❞❛ ♣♦r❝❡♥t❛❣❡♠ ♦❜s❡r✈❛❞❛ ❞♦s r❡sí❞✉♦s ♣❛r❛ ❝❛❞❛ ✐♥✲
t❡r✈❛❧♦ ❩❆■● ✲ ❈❡♥ár✐♦ ✷❜✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✷
❊✳✹ ❊st❛tíst✐❝❛ ❉❡s❝r✐t✐✈❛ ❞❛ ♣♦r❝❡♥t❛❣❡♠ ♦❜s❡r✈❛❞❛ ❞♦s r❡sí❞✉♦s ♣❛r❛ ❝❛❞❛ ✐♥✲
▲■❙❚❆ ❉❊ ❚❆❇❊▲❆❙ ✐①
❊✳✺ ❊st❛tíst✐❝❛s ❞❡s❝r✐t✐✈❛s ❞❛ ♣♦r❝❡♥t❛❣❡♠ ♦❜s❡r✈❛❞❛ ❞♦s r❡sí❞✉♦s ♣❛r❛ ❝❛❞❛ ✐♥✲
t❡r✈❛❧♦ ❩❆■● ✲ ❈❡♥ár✐♦ ✹❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✹
❊✳✻ ❊st❛tíst✐❝❛s ❞❡s❝r✐t✐✈❛s ❞❛ ♣♦r❝❡♥t❛❣❡♠ ♦❜s❡r✈❛❞❛ ❞♦s r❡sí❞✉♦s ♣❛r❛ ❝❛❞❛ ✐♥✲
t❡r✈❛❧♦ ❩❆■● ✲ ❈❡♥ár✐♦ ✹❜✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✺
❊✳✼ ❊st❛tíst✐❝❛s ❞❡s❝r✐t✐✈❛s ❞❛ ♣♦r❝❡♥t❛❣❡♠ ♦❜s❡r✈❛❞❛ ❞♦s r❡sí❞✉♦s ♣❛r❛ ❝❛❞❛ ✐♥✲
t❡r✈❛❧♦ ❩❆■● ✲ ❈❡♥ár✐♦ ✺✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✻
❊✳✽ ❊st❛tíst✐❝❛s ❞❡s❝r✐t✐✈❛s ❞❛ ♣♦r❝❡♥t❛❣❡♠ ♦❜s❡r✈❛❞❛ ❞♦s r❡sí❞✉♦s ♣❛r❛ ❝❛❞❛ ✐♥✲
t❡r✈❛❧♦ ❩❆■● ✲ ❈❡♥ár✐♦ ✻❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✼
❊✳✾ ❊st❛tíst✐❝❛s ❞❡s❝r✐t✐✈❛s ❞❛ ♣♦r❝❡♥t❛❣❡♠ ♦❜s❡r✈❛❞❛ ❞♦s r❡sí❞✉♦s ♣❛r❛ ❝❛❞❛ ✐♥✲
t❡r✈❛❧♦ ❩❆■● ✲ ❈❡♥ár✐♦ ✻❜✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✽
❊✳✶✵ ❊st❛tíst✐❝❛s ❞❡s❝r✐t✐✈❛s ❞❛ ♣♦r❝❡♥t❛❣❡♠ ♦❜s❡r✈❛❞❛ ❞♦s r❡sí❞✉♦s ♣❛r❛ ❝❛❞❛ ✐♥✲
t❡r✈❛❧♦ ❩❆■● ✲ ❈❡♥ár✐♦ ✼❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✾
❊✳✶✶ ❊st❛tíst✐❝❛s ❞❡s❝r✐t✐✈❛s ❞❛ ♣♦r❝❡♥t❛❣❡♠ ♦❜s❡r✈❛❞❛ ❞♦s r❡sí❞✉♦s ♣❛r❛ ❝❛❞❛ ✐♥✲
t❡r✈❛❧♦ ❩❆■● ✲ ❈❡♥ár✐♦ ✼❜✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✵
❊✳✶✷ ❊st❛tíst✐❝❛s ❞❡s❝r✐t✐✈❛s ❞❛ ♣♦r❝❡♥t❛❣❡♠ ♦❜s❡r✈❛❞❛ ❞♦s r❡sí❞✉♦s ♣❛r❛ ❝❛❞❛ ✐♥✲
t❡r✈❛❧♦ ❩❆■● ✲ ❈❡♥ár✐♦ ✽❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✶
❊✳✶✸ ❊st❛tíst✐❝❛s ❞❡s❝r✐t✐✈❛s ❞❛ ♣♦r❝❡♥t❛❣❡♠ ♦❜s❡r✈❛❞❛ ❞♦s r❡sí❞✉♦s ♣❛r❛ ❝❛❞❛ ✐♥✲
t❡r✈❛❧♦ ❩❆■● ✲ ❈❡♥ár✐♦ ✽❜✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✷
❋✳✶ ❊st❛tíst✐❝❛s ❞❡s❝r✐t✐✈❛s ❞❛ ♣♦r❝❡♥t❛❣❡♠ ♦❜s❡r✈❛❞❛ ❞♦s r❡sí❞✉♦s ♣❛r❛ ❝❛❞❛ ✐♥✲
t❡r✈❛❧♦ ✲ ❝❡♥ár✐♦ ■ ✿ ●❡r❛♥❞♦ ❩❆■● ❡ ❛❥✉st❛♥❞♦ ❩❆●❆✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✹
❋✳✷ ❊st❛tíst✐❝❛s ❞❡s❝r✐t✐✈❛s ❞❛ ♣♦r❝❡♥t❛❣❡♠ ♦❜s❡r✈❛❞❛ ❞♦s r❡sí❞✉♦s ♣❛r❛ ❝❛❞❛ ✐♥✲
❈❛♣ít✉❧♦ ✶
■♥tr♦❞✉çã♦
▼♦❞❡❧♦s ✉s✉❛✐s ♣❛r❛ ❞❛❞♦s ❛ss✐♠étr✐❝♦s ♥ã♦ ❛❞♠✐t❡♠ ❛ ♦❝♦rrê♥❝✐❛ ❞♦ ✈❛❧♦r ③❡r♦ ❝♦♠ ♣r♦✲ ❜❛❜✐❧✐❞❛❞❡ ♣♦s✐t✐✈❛✳ P♦ré♠✱ ❡♠ ♠✉✐t♦s ❝❛s♦s ❡❧❡ ♣♦❞❡ ❡st❛r ♣r❡s❡♥t❡ ♥❛ ✈❛r✐á✈❡❧ r❡s♣♦st❛✳ P♦r ❡①❡♠♣❧♦✱ ♥♦ ❡st✉❞♦ ❞❡ ♣r❡❝✐♣✐t❛çõ❡s ♣❧✉✈✐♦♠étr✐❝❛s ✭❋❡✉❡r✈❡r❣❡r✱ ✶✾✼✾✮ t❡♠♦s ❛ ♦❝♦rrê♥❝✐❛ ❞♦ ✈❛❧♦r ③❡r♦ ♥❛ ✈❛r✐á✈❡❧ r❡s♣♦st❛ q✉❛♥❞♦ ♥ã♦ t❡♠♦s ❛ ♦❝♦rrê♥❝✐❛ ❞❡ ❝❤✉✈❛✳ P❛r❛ ❡ss❡s ❝❛s♦s✱ t❡♠♦s ♦s ♠♦❞❡❧♦s ❞❡ r❡❣r❡ssã♦ ❝♦♥tí♥✉♦s ✐♥✢❛❝✐♦♥❛❞♦s ♥♦ ③❡r♦✳ ❖s ♠♦❞❡❧♦s ❞❡ r❡❣r❡ssã♦ ❝♦♥✲ tí♥✉♦s ✐♥✢❛❝✐♦♥❛❞♦s ♥♦ ③❡r♦ sã♦ ✉s❛❞♦s q✉❛♥❞♦ ❛ ✈❛r✐á✈❡❧ r❡s♣♦st❛ ♣♦❞❡ ❛ss✉♠✐r ♦ ✈❛❧♦r ③❡r♦ ❝♦♠ ♣r♦❜❛❜✐❧✐❞❛❞❡ ♣♦s✐t✐✈❛✳ ❆ ✈❛r✐á✈❡❧ r❡s♣♦st❛ ❞❡ss❡s ♠♦❞❡❧♦s é ❞✐s❝r❡t❛ ❡♠ ③❡r♦ ❡ ❝♦♥tí♥✉❛ ❡♠ ❛❧❣✉♠ ✐♥t❡r✈❛❧♦ ❞❡ ♥ú♠❡r♦s r❡❛✐s ♣♦s✐t✐✈♦s✳ ❖ ❢♦❝♦ ❞❡ss❡ tr❛❜❛❧❤♦ é ♥❡ss❡s ♠♦❞❡❧♦s✳ ❖s ♠♦❞❡❧♦s ❝♦♥tí♥✉♦s ✐♥✢❛❝✐♦♥❛❞♦s ♥♦ ③❡r♦ tê♠ s✐❞♦s ❛♣❧✐❝❛❞♦s ❡♠ ❞✐✈❡rs❛s ár❡❛s ❝♦♠♦ s❡❣✉r♦s ✭❘❡st✐ ❡t ❛❧✳✱ ✷✵✶✸✮✱ ♥❛ ár❡❛ ✜♥❛♥❝❡✐r❛ ♥❛ ❛♥á❧✐s❡ ❞❡ ❝❛rtõ❡s ❞❡ ❝ré❞✐t♦s ✭❚r♦✐❛♥✐✱ ✷✵✵✾✮✱ ♥❛ ✐♥❛❞✐♠♣❧ê♥❝✐❛ ❡♠ ❡♠♣rést✐♠♦s ❤✐♣♦t❡❝ár✐♦s ✭❚♦♥❣ ❡t ❛❧✳✱ ✷✵✶✸✮✱ ♥❛ s❛ú❞❡ ♣ú❜❧✐❝❛ ♥♦ ❡st✉❞♦ ❞❛ ♠♦rt❛❧✐❞❛❞❡ ♥♦ trâ♥s✐t♦ ✭❱❡♥❡③✉❡❧❛ ❡t ❛❧✳✱ ✷✵✶✹✮ ❡ ♥❛ ♠❡❞✐❝✐♥❛ ♥♦s ❡st✉❞♦s ❞❡ ❞♦❡♥ç❛s ✭❉✐❛s✱ ✷✵✶✹✮✳
❖s r❡sí❞✉♦s ❞❡s❡♠♣❡♥❤❛♠ ✉♠ ♣❛♣❡❧ ✐♠♣♦rt❛♥t❡ ♥❛ ✈❡r✐✜❝❛çã♦ ❞❛ ❛❞❡q✉❛çã♦ ❞♦ ♠♦❞❡❧♦ ❡ ♥❛ ✐❞❡♥t✐✜❝❛çã♦ ❞❡ ✧♦✉t❧✐❡rs✧❡ ♦❜s❡r✈❛çõ❡s ✐♥✢✉❡♥t❡s✳ ❯♠❛ ♠❛♥❡✐r❛ ♣♦ssí✈❡❧ ♣❛r❛ r❡❛❧✐③❛r ❛ ❛♥á❧✐s❡ ❞❡ ❞✐❛❣♥óst✐❝♦ ❡♠ ♠♦❞❡❧♦s ❞❡ r❡❣r❡ssã♦ ❝♦♥tí♥✉♦s ✐♥✢❛❝✐♦♥❛❞♦s ♥♦ ③❡r♦ é ❛ r❡❛❧✐③❛çã♦ ❞❡ ❛♥á❧✐s❡ ❞❡ r❡sí❞✉♦s s❡♣❛r❛❞❛♠❡♥t❡ ♣❛r❛ ❛ ♣❛rt❡ ❞✐s❝r❡t❛ ❡ ♣❛r❛ ♦ ❝♦♠♣♦♥❡♥t❡ ❝♦♥tí♥✉♦ ❞♦ ♠♦❞❡❧♦✳ ◆❡st❡ ❝❛s♦✱ ✉♠ r❡sí❞✉♦ é ✉t✐❧✐③❛❞♦ ♣❛r❛ ❝❛❞❛ ❝♦♠♣♦♥❡♥t❡ ❞♦ ♠♦❞❡❧♦✳ ◆♦ ❡♥t❛♥t♦✱ ❡st❡ ♣r♦❝❡ss♦ t❡♠ ✉♠ ✐♥❝♦♥✈❡♥✐❡♥t❡ ♣r✐♥❝✐♣❛❧✳ P❛r❛ ❝❛❞❛ ♦❜s❡r✈❛çã♦ ♣♦s✐t✐✈❛ t❡♠♦s ❞♦✐s r❡sí❞✉♦s✱ s❡♥❞♦ ❞✐❢í❝✐❧ ❛ss✐♠ ✐❞❡♥t✐✜❝❛r ✈❛❧♦r❡s ❛tí♣✐❝♦s ❝♦♠ ❜❛s❡ ❡♠ ✉♠ ✈❡t♦r ❞❡ r❡sí❞✉♦s✳
❯♠❛ ❛❧t❡r♥❛t✐✈❛ ♣♦ssí✈❡❧ ♣❛r❛ ✐ss♦ é ✉t✐❧✐③❛r ✉♠ ú♥✐❝♦ r❡sí❞✉♦ ♣❛r❛ ❛♥❛❧✐s❛r ❝♦♥❥✉♥t❛✲ ♠❡♥t❡ ♦s ❞♦✐s ❝♦♠♣♦♥❡♥t❡s ❞♦ ♠♦❞❡❧♦✳ ❖ r❡sí❞✉♦ q✉❛♥tí❧✐❝♦ ♣r♦♣♦st♦ ♣♦r ❉✉♥♥ ❡ ❙♠②t❤ ✭✶✾✾✻✮ ♣♦❞❡ s❡r ✉t✐❧✐③❛❞♦ ♣❛r❛ ❡st❡ ✜♠✳ ◆♦ ❡♥t❛♥t♦✱ s❡ ❛ ✈❛r✐á✈❡❧ r❡s♣♦st❛ ❛ss✉♠❡ ✉♠ ✈❛✲ ❧♦r ♣♦s✐t✐✈♦ ♣ró①✐♠♦ ❞❡ ③❡r♦✱ ❡st❡ r❡sí❞✉♦ ♥ã♦ ✈❛✐ ❛ss✉♠✐r ✉♠ ✈❛❧♦r ❡❧❡✈❛❞♦✱ ❡♠ ♠ó❞✉❧♦✱ ❛ ♠❡♥♦s q✉❡ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ✉♠❛ ♦❜s❡r✈❛çã♦ ❛ss✉♠✐r ♦ ✈❛❧♦r ③❡r♦ s❡❥❛ ♠✉✐t♦ ❜❛✐①❛ ✭P❡r❡✐r❛✱ ❇♦tt❡r ❡ ❙❛♥❞♦✈❛❧ ✭✷✵✶✹✮✮✳ ■ss♦ ♥ã♦ é r❛③♦á✈❡❧ ❡♠ ♠✉✐t❛s s✐t✉❛çõ❡s ♣rát✐❝❛s✳ P♦r ❡①❡♠♣❧♦✱ s✉♣♦♥❤❛ q✉❡ ✉♠❛ ✐♥st✐t✉✐çã♦ ✜♥❛♥❝❡✐r❛ t❡♥❤❛ ✐♥t❡r❡ss❡ ♥♦ t♦t❛❧ ❞❡ ✐♥✈❡st✐♠❡♥t♦ ❞❡ ❝❛❞❛ ❝❧✐❡♥t❡✳ ❙❡ ✉♠ ❝❧✐❡♥t❡ t❡♠ ✉♠❛ ❛❧t❛ r❡♥❞❛ ❡ ♣♦ss✉✐ ✉♠ ❜❛✐①♦ ✈❛❧♦r ❞❡ ✐♥✈❡st✐♠❡♥t♦
✶✳✵ ✷
é r❛③♦á✈❡❧ ✐♠❛❣✐♥❛r q✉❡ ❡ss❛ ♦❜s❡r✈❛çã♦ s❡❥❛ ❞✐s❝r❡♣❛♥t❡✳ P♦ré♠✱ s❡ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ss❡ ❝❧✐❡♥t❡ ♥ã♦ ♣♦ss✉✐r ✐♥✈❡st✐♠❡♥t♦ ♥❛ ✐♥st✐t✉✐çã♦ ♥ã♦ ❢♦r ❜❛✐①❛✱ ♦✉ s❡❥❛✱ s❡ ♥ã♦ ❢♦r ✐♥❢❡r✐♦r ❛ 2,5%✱ ♦ r❡sí❞✉♦ q✉❛♥tí❧✐❝♦ ♥ã♦ ❝♦♥s✐❞❡r❛r✐❛ ❡ss❛ ♦❜s❡r✈❛çã♦ ❝♦♠♦ ❞✐s❝r❡♣❛♥t❡✳ ❊ é r❛③♦á✈❡❧ ✐♠❛❣✐♥❛r q✉❡ ❡ss❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ♣♦❞❡ ♥ã♦ s❡r tã♦ ❜❛✐①❛✱ ❞❛❞♦ q✉❡ ❝❧✐❡♥t❡s ❞❡ss❡ ♣❡r✜❧ ♣♦❞❡♠ ✐♥✈❡st✐r ❡♠ ♦✉tr❛s ✐♥st✐t✉✐çõ❡s ✜♥❛♥❝❡✐r❛s✳
❯♠❛ ❝❧❛ss❡ ❞❡ r❡sí❞✉♦s ♣❛r❛ ♦s ♠♦❞❡❧♦s ❞❡ r❡❣r❡ssã♦ ❝♦♥tí♥✉♦s ✐♥✢❛❝✐♦♥❛❞♦s ❞❡ ③❡r♦ ❢♦✐ ♣r♦♣♦st❛ ♣♦r P❡r❡✐r❛✱ ❇♦tt❡r ❡ ❙❛♥❞♦✈❛❧ ✭✷✵✶✹✮✳ ❊st❛ ❝❧❛ss❡ ❞❡ r❡sí❞✉♦s é ❢✉♥çã♦ ❞❡ ✉♠ r❡sí❞✉♦ ♣❛r❛ ♦ ❝♦♠♣♦♥❡♥t❡ ❝♦♥tí♥✉♦ ❞♦ ♠♦❞❡❧♦ ❡ ❞❛ ❡st✐♠❛t✐✈❛ ❞❡ ♠á①✐♠❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ❞❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❛ ♦❜s❡r✈❛çã♦ ❛ss✉♠✐r ♦ ✈❛❧♦r ③❡r♦✳ ❘❡sí❞✉♦s ❞❡st❛ ❝❧❛ss❡ ♥ã♦ ❛♣r❡s❡♥t❛♠ ♦s ♣r♦❜❧❡♠❛s ❞♦ r❡sí❞✉♦ q✉❛♥tí❧✐❝♦ ❡ ♦s ❛✉t♦r❡s ❝♦♥❝❧✉ír❛♠ q✉❡ ✉♠ r❡sí❞✉♦ ❞❡st❛ ❝❧❛ss❡ t❡♠ ❜♦❛s ♣r♦♣r✐❡❞❛❞❡s ♥♦s ♠♦❞❡❧♦s ❞❡ r❡❣r❡ssã♦ ❜❡t❛ ✐♥✢❛❝✐♦♥❛❞♦s ♥♦ ③❡r♦✳ ❚❛♠❜é♠ ❞❡✜♥✐♠♦s ✉♠❛ ♦✉tr❛ ❝❧❛ss❡ ❞❡ r❡sí❞✉♦s ❜❛s❡❛❞❛ ♥♦ r❡sí❞✉♦ ♣r♦♣♦st♦ ♣♦r❖s♣✐♥❛ ❡ ❋❡rr❛r✐ ✭✷✵✶✷✮✱ q✉❡ t❛♠❜é♠ é ❢✉♥çã♦ ❞❡ ✉♠ r❡sí❞✉♦ ♣❛r❛ ♦ ❝♦♠♣♦♥❡♥t❡ ❝♦♥tí♥✉♦ ❞♦ ♠♦❞❡❧♦ ❡ ❞❛ ❡st✐♠❛t✐✈❛ ❞❡ ♠á①✐♠❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ❞❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❛ ♦❜s❡r✈❛çã♦ ❛ss✉♠✐r ♦ ✈❛❧♦r ③❡r♦✳
❈❛♣ít✉❧♦ ✷
▼♦❞❡❧♦s ❞❡ r❡❣r❡ssã♦ ❩❆●❆ ❡ ❩❆■●
❊♠ ♠✉✐t❛s s✐t✉❛çõ❡s ♣rát✐❝❛s ♥♦s ❞❡♣❛r❛♠♦s ❝♦♠ ✈❛r✐á✈❡✐s q✉❡ ♣♦❞❡♠ ❛ss✉♠✐r ❝❡rt♦s ✈❛❧♦r❡s ❡s♣❡❝í✜❝♦s ❝♦♠ ✉♠❛ ❞❡t❡r♠✐♥❛❞❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ♦✉ ♣♦❞❡♠ t❡r ✈❛❧♦r❡s q✉❡ ♣❡rt❡♥❝❡♠ ❛ ✉♠ ❞❡t❡r♠✐♥❛❞♦ ✐♥t❡r✈❛❧♦ ❝♦♠ ✉♠❛ ❞❡t❡r♠✐♥❛❞❛ ♣r♦❜❛❜✐❧✐❞❛❞❡✱ ♦✉ s❡❥❛✱ sã♦ ✉♠❛ ❝♦♠❜✐♥❛✲ çã♦ ❞❡ ✈❛r✐á✈❡✐s ❞✐s❝r❡t❛s ❡ ✈❛r✐á✈❡✐s ❝♦♥tí♥✉❛s✳ ❊ss❛s ✈❛r✐á✈❡✐s sã♦ ❝♦♥❤❡❝✐❞❛s ❝♦♠♦ ✈❛r✐á✈❡✐s ♠✐st❛s✳ P♦r ❡①❡♠♣❧♦✱ ♥❛ ár❡❛ ❞❡ s❡❣✉r♦s✱ ♥♦ ❡st✉❞♦ ❞♦ ❝✉st♦ ❞♦ s✐♥✐str♦ ❞❡ ❛✉t♦♠ó✈❡✐s✱ é ♥♦r✲ ♠❛❧ s✉r❣✐r ✈❛r✐á✈❡✐s ❞❡ss❡ t✐♣♦✳ ❊❧❛s s❡ ❝♦♠♣♦rt❛♠ ❝♦♠♦ ✈❛r✐á✈❡✐s ❞✐s❝r❡t❛s ♥♦s ❝❛s♦s ❞❛ ♥ã♦ ♦❝♦rrê♥❝✐❛ ❞❡ s✐♥✐str♦ ✭❝✉st♦ ③❡r♦✮ ❡ s❡ ❝♦♠♣♦rt❛♠ ❝♦♠♦ ✈❛r✐á✈❡✐s ❝♦♥tí♥✉❛s q✉❛♥❞♦ ❛❝♦♥t❡❝❡ ♦ s✐♥✐str♦✳ ◆❡st❡ ú❧t✐♠♦ ❝❛s♦✱ ♦ ❝✉st♦ ❞❛ ♦❝♦rrê♥❝✐❛ ✈❛r✐❛ ♥♦ ✐♥t❡r✈❛❧♦ (0;∞)✱ ✭❘❡st✐ ❡t ❛❧✳✱ ✷✵✶✸✮✳ ◆❛ ár❡❛ ♠é❞✐❝❛✱ é ❝♦♠✉♠ ❛♣❛r❡❝❡r ✈❛r✐á✈❡✐s ♠✐st❛s ❡♠ s✐t✉❛çõ❡s ❡♠ q✉❡ ♦ ✐♥t❡r❡ss❡ é ❞♦s❛r ❛ ❝♦♥❝❡♥tr❛çã♦ ❞❡ ❛❧❣✉♠❛ s✉❜stâ♥❝✐❛ q✉❡ ♣♦❞❡ ♦✉ ♥ã♦ ❡st❛r ♣r❡s❡♥t❡ ♥♦ s❛♥❣✉❡ ✭❆❜❞♦ ❡t ❛❧✳✱✷✵✶✸✮ ♦✉ ♦ ✈♦❧✉♠❡ ❞❡ s❛♥❣✉❡ r❡❝❡❜✐❞♦ ❡♠ ✉♠❛ ❝✐r✉r❣✐❛ ❡s♣❡❝í✜❝❛ ✭❉✐❛s✱✷✵✶✹✮✳ ❊♠ ♠✐❝r♦❜✐♦❧♦❣✐❛✱ é ❝♦♠✉♠ ♦ ✐♥t❡r❡ss❡ ♥♦ ❡st✉❞♦ ❞❛s ✈❛r✐á✈❡✐s q✉❡ ❛❢❡t❛♠ ❛ q✉❛♥t✐❞❛❞❡ ❞❡ ❢✉♥❣♦s ♣r❡s❡♥t❡s ❡♠ ♣❧❛♥t❛çõ❡s ❞❡ ♠✐❧❤♦s ❡ ♦✉tr♦s ❛❧✐♠❡♥t♦s✱ s❡♥❞♦ q✉❡ ❡♠ ❝❛❞❛ ✉♥✐❞❛❞❡ ❛♠♦str❛❧ ❡ss❛ q✉❛♥t✐❞❛❞❡ ♣♦❞❡ s❡r ③❡r♦ ❝♦♠ ♣r♦❜❛❜✐❧✐❞❛❞❡ ♣♦s✐t✐✈❛ ♦✉ q✉❛❧q✉❡r ♦✉tr♦ ✈❛❧♦r ❝♦♥tí♥✉♦ ✭❘♦❝❤❛ ❡t ❛❧✳✱ ✷✵✵✾✮✳ ❊♠ ♣❧✉✈✐♦♠❡tr✐❛✱ ♦ ✐♥t❡r❡ss❡ r❡❝❛✐ ♥❛ q✉❛♥t✐❞❛❞❡ ❞❡ ❝❤✉✈❛ q✉❡ ❝❛✐ ❡♠ ❝❡rt❛ r❡❣✐ã♦✱ ❛ss✉♠✐♥❞♦ ✈❛❧♦r ③❡r♦ ♥♦s ❞✐❛s q✉❡ ♥ã♦ t❡♠ ❝❤✉✈❛ ♦✉ q✉❛❧q✉❡r ♦✉tr♦ ✈❛❧♦r ❝♦♥tí♥✉♦ ♥♦s ❞✐❛s ❡♠ q✉❡ t❡♠♦s ❝❤✉✈❛ ♥❛ r❡❣✐ã♦ ✭❋❡✉❡r✈❡r❣❡r✱ ✶✾✼✾✮✳
P❛r❛ ♦ ❡st✉❞♦ ❞❡ ✈❛r✐á✈❡✐s ♠✐st❛s q✉❡ ❛ss✉♠❡♠ ♦ ✈❛❧♦r ③❡r♦ ❝♦♠ ♣r♦❜❛❜✐❧✐❞❛❞❡ ♣♦s✐t✐✈❛✱ é ♥❡❝❡ssár✐♦ ✉t✐❧✐③❛r ♠ét♦❞♦s q✉❡ ❧❡✈❛♠ ❡♠ ❝♦♥t❛ s✉❛s ♣❡❝✉❧✐❛r✐❞❛❞❡s✱ ♣❛r❛ ❛ss✐♠ ♦❜t❡r ✉♠ ❛❥✉st❡ ❛❞❡q✉❛❞♦✳ ❯♠❛ ♠❡t♦❞♦❧♦❣✐❛ ♣❛r❛ ❛ ♠♦❞❡❧❛❣❡♠ ❞❡ t❛❧ ✈❛r✐á✈❡❧ ❛❧❡❛tór✐❛ é ✉t✐❧✐③❛r ♦s ♠♦❞❡❧♦s ❞❡ r❡❣r❡ssã♦ ❚✇❡❡❞✐❡✳ ❖s ♠♦❞❡❧♦s ❞❡ r❡❣r❡ssã♦ ❝♦♠ ✈❛r✐á✈❡❧ r❡s♣♦st❛ ❚✇❡❡❞✐❡ ♣❡r✲ t❡♥❝❡♠ ❛ ❝❧❛ss❡ ❞♦s ♠♦❞❡❧♦s ❞❡ ❞✐s♣❡rsã♦ ❡①♣♦♥❡♥❝✐❛❧ ✭❏♦r❣❡♥s❡♥✱ ✶✾✾✼✮✳ ❆ ❝❧❛ss❡ ❚✇❡❡❞✐❡ ❞❡ ♠♦❞❡❧♦s ❞❡ ❞✐s♣❡rsã♦ ❡①♣♦♥❡♥❝✐❛❧ é ❞❡✜♥✐❞❛ ❝♦♠♦ ✉♠❛ ❞✐str✐❜✉✐çã♦ ❞❛ ❢❛♠í❧✐❛ ❡①♣♦♥❡♥✲ ❝✐❛❧ ❝♦♠ ♠é❞✐❛ µ ❡ ✈❛r✐â♥❝✐❛ (µp/σ2)✱ ❡♠ q✉❡ pǫ(−∞,0)∪(1,∞) ✭❉✉♥♥ ❡ ❙♠②t❤✱ ✷✵✵✺✮✳
❏ør❣❡♥s❡♥ ❡ P❛❡s ❉❡ ❙♦✉③❛ ✭✶✾✾✹✮ ♣r♦✈❛♠ q✉❡ ♣❛r❛ ❝❛❞❛ p❡①✐st❡ ✉♠❛ ❞✐str✐❜✉✐çã♦ ❞❡ ♣r♦✲
❜❛❜✐❧✐❞❛❞❡✳ ❉❡✈✐❞♦ ❛ ♣♦ss✐❜✐❧✐❞❛❞❡ ❞❡ ✢❡①✐❜✐❧✐❞❛❞❡ ♥❛ ❞✐str✐❜✉✐çã♦ ❞❛ ✈❛r✐á✈❡❧ r❡s♣♦st❛✱ ♦ ♠♦❞❡❧♦ ❚✇❡❞❞✐❡ é ✉♠❛ ❜♦❛ ♦♣çã♦ ♣❛r❛ ♠♦❞❡❧❛r ♦s ✈❛❧♦r❡s ✐❣✉❛✐s ❛ ③❡r♦✳ ❊ss❛ ♠❡t♦❞♦❧♦❣✐❛ ♥ã♦ s❡rá ❛❜♦r❞❛❞❛ ♥❡st❡ tr❛❜❛❧❤♦✳ P❛r❛ ♠❛✐♦r❡s ✐♥❢♦r♠❛çõ❡s s♦❜r❡ ♦s ♠♦❞❡❧♦s ❚✇❡❞❞✐❡ ✈❡r
✷✳✶ ❉■❙❚❘■❇❯■➬Õ❊❙ ❈❖◆❚❮◆❯❆❙ ■◆❋▲❆❈■❖◆❆❉❆❙ ◆❖ ❩❊❘❖ ✹
❇♦rt♦❧✉③③♦ ❡t ❛❧✳ ✭✷✵✶✶✮✱ P♦✉s✐♥❤♦ ✭✷✵✶✸✮ ❡ ❋❡rr❡✐r❛ ✭✷✵✵✺✮✳ ❖✉tr❛ ♠❡t♦❞♦❧♦❣✐❛ ❡✜❝❛③ é ❛ ♠✐st✉r❛ ❡♥tr❡ ❞✉❛s ❞✐str✐❜✉✐çõ❡s ♣❛r❛ ❛ ✈❛r✐á✈❡❧ r❡s♣♦st❛✱ ✉♠❛ ❞✐str✐❜✉✐çã♦ ❞❡❣❡♥❡r❛❞❛ ♥♦ ③❡r♦ ❡ ✉♠❛ ❞✐str✐❜✉✐çã♦ ❝♦♥tí♥✉❛✳ ❊ss❛s ♠✐st✉r❛s ❞❡ ❞✐str✐❜✉✐çã♦ ❞ã♦ ♦r✐❣❡♠ ❛♦s ♠♦❞❡❧♦s ❞❡ r❡❣r❡ssã♦ ✐♥✢❛❝✐♦♥❛❞♦s ♥♦s ③❡r♦✳ ◆❡st❡ tr❛❜❛❧❤♦✱ t❡♠♦s ✐♥t❡r❡ss❡ ♥♦s ❝❛s♦s ❡♠ q✉❡ ❛ ✈❛r✐á✲ ✈❡❧ r❡s♣♦st❛ ❛♣r❡s❡♥t❛ ✉♠❛ ❞✐str✐❜✉✐çã♦ ❝♦♥tí♥✉❛ ♥♦ ❝♦♥❥✉♥t♦ ❞♦s ♥ú♠❡r♦s r❡❛✐s ♣♦s✐t✐✈♦s ❡ ❛ss✉♠❡ ♦ ✈❛❧♦r ③❡r♦ ❝♦♠ ♣r♦❜❛❜✐❧✐❞❛❞❡ ♣♦s✐t✐✈❛✳
❖ ♣r✐♠❡✐r♦ ♠♦❞❡❧♦ ❞❡ r❡❣r❡ssã♦ ✐♥✢❛❝✐♦♥❛❞♦ ♥♦ ③❡r♦ ♣❛r❛ ✈❛r✐á✈❡✐s ♠✐st❛s ❢♦✐ ♣r♦♣♦st♦ ♣♦r❋❡✉❡r✈❡r❣❡r✭✶✾✼✾✮✱ q✉❡ ✉t✐❧✐③♦✉ ❛ ❞✐str✐❜✉✐çã♦ ❣❛♠❛ ♣❛r❛ ♦ ❡st✉❞♦ ❞❡ ♣r❡❝✐♣✐t❛çõ❡s ♣❧✉✲ ✈✐♦♠étr✐❝❛s✳ ❆♣ós ♦ tr❛❜❛❧❤♦ ❞❡ ❋❡✉❡r✈❡r❣❡r✱ ✈ár✐♦s tr❛❜❛❧❤♦s ♥❡ss❛ ár❡❛ ❢♦r❛♠ ❛♣❛r❡❝❡♥❞♦✱ ❡♥tr❡ ❡❧❡s✱ ❍❡❧❧❡r ❡t ❛❧✳ ✭✷✵✵✻✮ q✉❡ ♣r♦♣ôs ✉♠ ♠♦❞❡❧♦ q✉❡ ❝♦♥s✐❞❡r♦✉ ❛ ❞✐str✐❜✉✐çã♦ ❣❛✉ss✐✲ ❛♥❛ ✐♥✈❡rs❛ ✐♥✢❛❝✐♦♥❛❞❛ ♥♦ ③❡r♦ ♥♦ ❛❥✉st❡ ❞♦ ❝✉st♦ ❞♦ s✐♥✐str♦ ❞❡ ❛✉t♦♠ó✈❡✐s✳ ▼♦❞❡❧♦s ❝♦♠ ✈❛r✐á✈❡❧ r❡s♣♦st❛ ❞♦ t✐♣♦ ♣r♦♣♦rçã♦ ❢♦r❛♠ ♣r♦♣♦st♦s ♣♦r ❈♦♦❦ ❡t ❛❧✳ ✭✷✵✵✽✮✱ ❍♦✛ ✭✷✵✵✼✮✱ ❖s♣✐♥❛ ❡ ❋❡rr❛r✐✭✷✵✶✷✮ ❡P❡r❡✐r❛ ❡t ❛❧✳✭✷✵✶✷✮ q✉❡ ♣r♦♣✉s❡r❛♠ ♦s ♠♦❞❡❧♦s ❞❡ r❡❣r❡ssã♦ ❜❡t❛ ✐♥✢❛❝✐♦♥❛❞♦s ♥♦ ③❡r♦✱ ❜❡t❛ ✐♥✢❛❝✐♦♥❛❞♦s ♥♦ ✉♠✱ ❜❡t❛ ✐♥✢❛❝✐♦♥❛❞♦s ♥♦ ✉♠ ♦✉ ♥♦ ③❡r♦ ❡ ❜❡t❛ ✐♥✢❛❝✐♦♥❛❞♦s ♥♦ ③❡r♦✱ ♥♦ ✉♠ ❡ ❡♠ ✉♠ ♣♦♥t♦c∈(0,1)✳
❖ ♣r✐♥❝✐♣❛❧ ✐♥t❡r❡ss❡ ❞❡st❡ ❝❛♣ít✉❧♦ é ❛♣r❡s❡♥t❛r ♦s ♠♦❞❡❧♦s ❞❡ r❡❣r❡ssã♦ ❝♦♠ r❡s♣♦st❛ ❣❛♠❛ ✐♥✢❛❝✐♦♥❛❞♦s ♥♦ ③❡r♦ ❡ ❣❛✉ss✐❛♥❛ ✐♥✈❡rs❛ ✐♥✢❛❝✐♦♥❛❞♦s ♥♦ ③❡r♦ ♣❛r❛✱ ♥♦ ♣ró①✐♠♦ ❝❛♣í✲ t✉❧♦ ✭❈❛♣ít✉❧♦ ✸✮✱ tr❛t❛r♠♦s s♦❜r❡ ❛ ❛♥á❧✐s❡ ❞❡ ❞✐❛❣♥óst✐❝♦ ♥❡ss❡s ♠♦❞❡❧♦s✳
✷✳✶ ❉✐str✐❜✉✐çõ❡s ❝♦♥tí♥✉❛s ✐♥✢❛❝✐♦♥❛❞❛s ♥♦ ③❡r♦
❆s ❞✐str✐❜✉✐çõ❡s ❝♦♥tí♥✉❛s ✐♥✢❛❝✐♦♥❛❞❛s ♥♦ ③❡r♦ sã♦ ❛q✉❡❧❛s ❞✐str✐❜✉✐çõ❡s ❡♠ q✉❡ ❛ ✈❛✲ r✐á✈❡❧ r❡s♣♦st❛ ❛♣r❡s❡♥t❛ ✉♠❛ ❞✐str✐❜✉✐çã♦ ❝♦♥tí♥✉❛ ♥♦ ❝♦♥❥✉♥t♦ ❞♦s ♥ú♠❡r♦s r❡❛✐s ♣♦s✐t✐✈♦s ❡ ♣♦❞❡ ❛ss✉♠✐r ♦ ✈❛❧♦r ③❡r♦ ❝♦♠ ♣r♦❜❛❜✐❧✐❞❛❞❡ ♣♦s✐t✐✈❛✳ P♦❞❡♠♦s ❞❡✜♥✐r ❡ss❛ ❝❧❛ss❡ ❞❡ ❞✐str✐❜✉✐çõ❡s ✐♥✢❛❝✐♦♥❛❞❛s ♥♦ ③❡r♦ ❞❛ s❡❣✉✐♥t❡ ❢♦r♠❛✿
❉❡✜♥✐çã♦ ✶✳ ❙❡❥❛ y ✉♠❛ ✈❛r✐á✈❡❧ ❛❧❡❛tór✐❛ ❝♦♠ s✉♣♦rt❡ ❡♠ {0} ∪(0,∞)✳ ❉✐③❡♠♦s q✉❡ y
♣❡rt❡♥❝❡ ❛ ❝❧❛ss❡ ❞❡ ❞✐str✐❜✉✐çõ❡s ❝♦♥tí♥✉❛s ♣♦s✐t✐✈❛s tr✐♣❛r❛♠étr✐❝❛ ✐♥✢❛❝✐♦♥❛❞❛s ♥♦ ③❡r♦ ❝♦♠ ✈❡t♦r ❞❡ ♣❛râ♠❡tr♦ (α, µ, σ)✱ s❡ s✉❛ ❢✉♥çã♦ ❞❡♥s✐❞❛❞❡ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ é ❞❛❞❛ ♣♦r
g(y;α, µ, σ) =
0, se y <0;
α, se y = 0
(1−α)f(y;µ, σ), se y >0,
✭✷✳✶✮
❡♠ q✉❡ 0 < α < 1 ❡ f(y;µ, σ) é ❛ ❢✉♥çã♦ ❞❡♥s✐❞❛❞❡ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ✉♠❛ ❞✐str✐❜✉✐çã♦ ❝♦♥tí♥✉❛ ❝♦♠ ♣❛râ♠❡tr♦s µ ❡ σ ❡ s✉♣♦rt❡ ❡♠ (0,∞)✳ ❖❜s❡r✈❡ q✉❡ α=P(y= 0)✳
❆ ❢✉♥çã♦ ❞❡♥s✐❞❛❞❡ ❞❡ y ♣♦❞❡ s❡r r❡❡s❝r✐t❛ ❝♦♠♦✿
g(y;α, µ, σ) = {αI(0)(y)(1−α)(1−I(0)(y))}{f(y;µ, σ)(1−I(0)(y))}, ✭✷✳✷✮
✷✳✶ ❉■❙❚❘■❇❯■➬Õ❊❙ ❈❖◆❚❮◆❯❆❙ ■◆❋▲❆❈■❖◆❆❉❆❙ ◆❖ ❩❊❘❖ ✺
❡♠ ✭✷✳✷✮ ♣♦❞❡ s❡r ❢❛t♦r❛❞❛ ❡♠ ❞♦✐s t❡r♠♦s✿ ♦ ♣r✐♠❡✐r♦ ❞❡♣❡♥❞❡ ❛♣❡♥❛s ❞❡α ❡ ♦ s❡❣✉♥❞♦ q✉❡
❞❡♣❡♥❞❡ ❞❡ (µ;σ) ❡ ❡♥✈♦❧✈❡ ❛♣❡♥❛s ❛ ♣❛rt❡ ❝♦♥tí♥✉❛ ❞❛ ✈❛r✐á✈❡❧✳
◆❡st❡ tr❛❜❛❧❤♦✱ ✐r❡♠♦s ✉t✐❧✐③❛r ❝♦♠♦ f(y;µ, σ)✱ ❛ ❢✉♥çã♦ ❞❡♥s✐❞❛❞❡ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❛ ❞✐str✐❜✉✐çã♦ ❣❛♠❛ ❡ ❛ ❢✉♥çã♦ ❞❡♥s✐❞❛❞❡ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❛ ❞✐str✐❜✉✐çã♦ ❣❛✉ss✐❛♥❛ ✐♥✈❡rs❛✱ ❞❡✜♥✐❞❛s ❛ s❡❣✉✐r✳
✷✳✶✳✶ ❉✐str✐❜✉✐çã♦ ❩❆●❆
❆ ❞✐str✐❜✉✐çã♦ ❣❛♠❛ ✐♥✢❛❝✐♦♥❛❞❛ ♥♦ ③❡r♦ ✭③❡r♦ ❛❞❥✉st❡❞ ❣❛♠♠❛✱ ❩❆●❆✶✮ é ✉♠❛ ❞✐s✲ tr✐❜✉✐çã♦ ❝♦♠ três ♣❛râ♠❡tr♦s✱ s❡♥❞♦ ✉♠❛ ❡①t❡♥sã♦ ❞❛ ❞✐str✐❜✉✐çã♦ ❣❛♠❛✱ q✉❡ ♣❡r♠✐t❡ ❛ ♦❝♦rrê♥❝✐❛ ❞♦ ✈❛❧♦r ③❡r♦ ❝♦♠ ♣r♦❜❛❜✐❧✐❞❛❞❡ ♣♦s✐t✐✈❛✳
❆ ❞✐str✐❜✉✐çã♦ ❣❛♠❛ é ✉♠❛ ❞✐str✐❜✉✐çã♦ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❝♦♥tí♥✉❛ q✉❡ t❡♠ ❞♦✐s ♣❛râ✲ ♠❡tr♦s ❡ ❡♠ s✉❛ ♣❛r❛♠❡tr✐③❛çã♦ ♠❛✐s ✉s✉❛❧ ♣♦ss✉✐ ❢✉♥çã♦ ❞❡♥s✐❞❛❞❡ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❛❞❛ ♣♦r
f(y;a, b) = a
Γ(b)(ay)
(b−1)e−ay ✭✷✳✸✮
❡♠ q✉❡ Γ(.) é ❛ ❢✉♥çã♦ ❣❛♠❛ ❞❡✜♥✐❞❛ ❝♦♠♦ Γ(k) = R∞
0 t
k−1e−tdt✱ a >0 ❡ b > 0 sã♦ ♦s ♣❛✲
râ♠❡tr♦s ❞❡ ❡s❝❛❧❛ ❡ ♣❛râ♠❡tr♦ ❞❡ ❢♦r♠❛✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ❊♥tr❡t❛♥t♦ ❡ss❛ ♣❛r❛♠❡tr✐③❛çã♦ ♥ã♦ é ♠✉✐t♦ ❛❞❡q✉❛❞❛ ♣❛r❛ ♦ ✉s♦ ❡♠ ♠♦❞❡❧♦s ❞❡ r❡❣r❡ssã♦✱ ♣♦✐s ♦s ♣❛râ♠❡tr♦s ♥ã♦ sã♦ ❢❛❝✐❧✲ ♠❡♥t❡ ✐♥t❡r♣r❡tá✈❡✐s✳ ❊♥tã♦ ❞❡✜♥✐♥❞♦ µ =b/a ❡ σ =p1/b✱ ♦❜té♠✲s❡ ✉♠❛ ♣❛r❛♠❡tr✐③❛çã♦
❛❧t❡r♥❛t✐✈❛ q✉❡ é ✉s❛❞❛ ♥♦ ♣❛❝♦t❡ ❣❛♠❧ss ❞♦ s♦❢t✇❛r❡ ❘ ✭❙t❛s✐♥♦♣♦✉❧♦s ❡t ❛❧✳✱ ✷✵✶✹✮ ❞❛❞❛ ♣♦r
f(y;µ, σ) =
exp−σy2µ
Γ(σ12)
y(σ12−1)
(µσ2)σ12
, ✭✷✳✹✮
❡♠ q✉❡ y > 0✱ µ > 0 ❡ σ > 0✳ ❆q✉✐ E(y) = µ ❡ V ar(y) = σ2µ2 sã♦ ❛ ♠é❞✐❛ ❡ ❛ ✈❛r✐â♥❝✐❛
r❡s♣❡❝t✐✈❛♠❡♥t❡ ❞❛ ❞✐str✐❜✉✐çã♦ ❣❛♠❛✳
❆ ❞✐str✐❜✉✐çã♦ ❣❛♠❛ ✐♥✢❛❝✐♦♥❛❞❛ ♥♦ ③❡r♦ é ✉♠❛ ♠✐st✉r❛ ❞❛ ❞✐str✐❜✉✐çã♦ ❞❡❣❡♥❡r❛❞❛ ♥♦ ③❡r♦ ❡ ❞❛ ❞✐str✐❜✉✐çã♦ ❣❛♠❛✳ ❯t✐❧✐③❛♥❞♦ ❛ ♣❛r❛♠❡tr✐③❛çã♦ ❞❛ ❡q✉❛çã♦ ✭✷✳✹✮✱ ♣♦❞❡♠♦s ❞❡✜♥✐✲❧❛ ❞❛ ❢♦r♠❛ ❛ s❡❣✉✐r✳
❉❡✜♥✐çã♦ ✷✳ ❙❡❥❛ y ✉♠❛ ✈❛r✐á✈❡❧ ❛❧❡❛tór✐❛ ❝♦♠ s✉♣♦rt❡ ❡♠ {0} ∪(0;∞)✳ ❉✐③❡♠♦s q✉❡ y
t❡♠ ❞✐str✐❜✉✐çã♦ ❣❛♠❛ ✐♥✢❛❝✐♦♥❛❞❛ ♥♦ ③❡r♦ ❝♦♠ ✈❡t♦r ❞❡ ♣❛râ♠❡tr♦s (α, µ, σ) s❡ s✉❛ ❢✉♥çã♦ ❞❡♥s✐❞❛❞❡ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ é ❞❛❞❛ ♣❡❧❛ ❡q✉❛çã♦ ✭✷✳✶✮ ❡ ♥♦ ❧✉❣❛r ❞❛ ❢✉♥çã♦ ❞❡♥s✐❞❛❞❡ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡f(y;µ, σ)❝♦♥s✐❞❡r❛♠♦s ❛ ❢✉♥çã♦ ❞❡ ❞❡♥s✐❞❛❞❡ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❛ ❞✐str✐❜✉✐çã♦ ❣❛♠❛ ❞❡✜♥✐❞❛ ♥❛ ❡q✉❛çã♦ ✭✷✳✹✮✳
✷✳✶ ❉■❙❚❘■❇❯■➬Õ❊❙ ❈❖◆❚❮◆❯❆❙ ■◆❋▲❆❈■❖◆❆❉❆❙ ◆❖ ❩❊❘❖ ✻
0 2 4 6 8 10
0.0
0.1
0.2
0.3
0.4
0.5
0.6
y
σ =0.5
σ =0.3
σ =0.1
Distribuição ZAGA µ =4 e α =0.4
✭❛✮
0 2 4 6 8 10
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
y
µ =4
µ =2
µ =6
Distribuição ZAGA σ =0.2 e α =0.4
✭❜✮
0 2 4 6 8 10
0.0
0.2
0.4
0.6
0.8
y
pdf α =0.2
α =0.8
α =0.5
Distribuição ZAGA σ =0.2 e µ =4
✭❝✮
❋✐❣✉r❛ ✷✳✶✿ ●rá✜❝♦ ❞❛ ❞✐str✐❜✉✐çã♦ ❩❆●❆ ♣❛r❛ ❞✐❢❡r❡♥t❡s ✈❛❧♦r❡s ❞♦s ♣❛râ♠❡tr♦s
❆ ❡s♣❡r❛♥ç❛ ❡ ❛ ✈❛r✐â♥❝✐❛ ❞❛ ❞✐str✐❜✉✐çã♦ ❩❆●❆ ✭❙t❛s✐♥♦♣♦✉❧♦s ❡t ❛❧✳✱ ✷✵✶✹✮ sã♦ ❞❛❞❛s ♣♦r
E(y) = (1−α)µ ✭✷✳✺✮
V ar(y) = (1−α)µ2(α+σ2). ✭✷✳✻✮
❆ ❞✐str✐❜✉✐çã♦ ❩❆●❆ é ✉♠❛ ❞✐str✐❜✉✐çã♦ ❛ss✐♠étr✐❝❛✱ ♣❡❧♦ ❢❛t♦ ❞❛ ❞✐str✐❜✉✐çã♦ ❣❛♠❛ s❡r ❛ss✐♠étr✐❝❛✳ ❈♦♠♦ ❞✐t♦✱ ❛ ❞✐str✐❜✉✐çã♦ ❣❛♠❛ ✐♥✢❛❝✐♦♥❛❞❛ ♥♦ ③❡r♦ ♣♦ss✉✐ três ♣❛râ♠❡tr♦s✱µ
❛ ♠é❞✐❛ ❞❛ ❞✐str✐❜✉✐çã♦ ❣❛♠❛✱ σ ♦ ♣❛râ♠❡tr♦ ❞❡ ❡s❝❛❧❛ ♦✉ ♣❛râ♠❡tr♦ ❞❡ ❞✐s♣❡rsã♦ ❡ α é ❛
♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ♦❝♦rr❡r ♦ ✈❛❧♦r ③❡r♦✳ ❆ ❋✐❣✉r❛ ✭✷✳✶✮ ❛♣r❡s❡♥t❛ ❣rá✜❝♦s ❞❛ ❢✉♥çã♦ ❞❡♥s✐❞❛❞❡ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❛ ❞✐str✐❜✉✐çã♦ ❩❆●❆ ♣❛r❛ ❞✐❢❡r❡♥t❡s ✈❛❧♦r❡s ❞♦s ♣❛râ♠❡tr♦s✳ ◆❛ ❋✐❣✉r❛
✭✷✳✶✭❛✮✮ t❡♠♦s ❛ ❢✉♥çã♦ ❞❡♥s✐❞❛❞❡ ❞❛ ❞✐str✐❜✉✐çã♦ ❩❆●❆ ♣❛r❛ ♦s ♣❛râ♠❡tr♦sµ= 4❡α= 0,4
❡ ✈❛r✐❛♠♦s ♦s ✈❛❧♦r❡s ❞❡σ✱ ❝♦♥s✐❞❡r❛♥❞♦ 0,1✱ 0,3 ❡0,5✳ ❆ ✈❛r✐❛çã♦ ❞♦ ♣❛râ♠❡tr♦σ✱ ♣r♦✈♦❝❛
✉♠❛ ❛❧t❡r❛çã♦ ♥❛ ❡s❝❛❧❛ ❞♦ ❣rá✜❝♦✳ ❆♦ ❞✐♠✐♥✉✐r♠♦sσ ♣❛r❛0,1t❡♠♦s ✉♠❛ ❝♦♥❝❡♥tr❛çã♦ ❞♦s ✈❛❧♦r❡s ♣ró①✐♠♦ ❞❛ ♠é❞✐❛ ✭❝✉r✈❛ ❛③✉❧✮✱ ❛♦ ❛✉♠❡♥t❛r♠♦s σ ♣❛r❛ 0,5 ❛s ♦❜s❡r✈❛çõ❡s ❡stã♦ ♠❛✐s ❡s♣❛❧❤❛❞❛s ❛♦ ❧♦♥❣♦ ❞♦ s✉♣♦rt❡ ❞❛ ❞✐str✐❜✉✐çã♦ ✭❝✉r✈❛ ♣r❡t❛✮✳ ❆❧é♠ ❞✐ss♦✱ ♥♦t❛♠♦s q✉❡ ♦ ❛✉♠❡♥t♦ ❞❡ ✈❛❧♦r❡s ♣❛r❛ σ✱ ❛✉♠❡♥t❛ ❛ ❛ss✐♠❡tr✐❛ ❞❛ ❞✐str✐❜✉✐çã♦✱ ✐ss♦ ♦❝♦rr❡ ❞❡✈✐❞♦
❛♦ ❢❛t♦ ❞❛ ❛ss✐♠❡tr✐❛ ❞❛ ❞✐str✐❜✉✐çã♦ ❣❛♠❛ ❡stá ❛ss♦❝✐❛❞❛ ❛♦ ♣❛râ♠❡tr♦ σ✳ ❏á ♥❛ ❋✐❣✉r❛
✭✷✳✶✭❜✮✮ ❝♦♥s✐❞❡r❛♠♦s σ = 0,2 ❡ α = 0,4 ❡ ✈❛r✐❛♠♦s ♦s ✈❛❧♦r❡s ❞❡ µ✳ ❆ ♠✉❞❛♥ç❛ ♥❛ ♠é❞✐❛
❛❧t❡r❛ ♦s ♣♦♥t♦s ❞❡ ❝♦♥❝❡♥tr❛çã♦ ❞♦s ❞❛❞♦s✳ ❖❜s❡r✈❛♠♦s q✉❡ q✉❛♥❞♦ ❛ ♠é❞✐❛ é4♦s ❞❛❞♦s s❡ ❝♦♥❝❡♥tr❛♠ ♥♦ ♣♦♥t♦ ❞❡ y= 4 ✭❝✉r✈❛ ♣r❡t❛✮✱ s❡ µ= 2 ♦s ❞❛❞♦s s❡ ❝♦♥❝❡♥tr❛♠ ❡♠ t♦r♥♦ ❞♦ ♣♦♥t♦y= 2 ✭❝✉r✈❛ ✈❡r♠❡❧❤❛✮✳ ❆ ✈❛r✐❛çã♦ ❞♦ ♣❛râ♠❡tr♦α✱ ♠♦❞✐✜❝❛ ❛ ❝♦♥❝❡♥tr❛çã♦ ❞❡ ③❡r♦s
✷✳✶ ❉■❙❚❘■❇❯■➬Õ❊❙ ❈❖◆❚❮◆❯❆❙ ■◆❋▲❆❈■❖◆❆❉❆❙ ◆❖ ❩❊❘❖ ✼
❩❆●❆✱ ❞❡♣❡♥❞❡♥❞♦ ❞♦ ✈❛❧♦r ❞♦s ♣❛râ♠❡tr♦s t❡♠♦s ❞❡♥s✐❞❛❞❡s ❜❡♠ ❞✐st✐♥t❛s✳
✷✳✶✳✷ ❉✐str✐❜✉✐çã♦ ❩❆■●
❆ ❞✐str✐❜✉✐çã♦ ❣❛✉ss✐❛♥❛ ✐♥✈❡rs❛ ✐♥✢❛❝✐♦♥❛❞❛ ♥♦ ③❡r♦ ✭③❡r♦ ❛❞❥✉st❡❞ ✐♥✈❡rs❡ ❣❛✉ss✐❛♥✱ ❩❆■● ✷✮ é ✉♠❛ ❡①t❡♥sã♦ ❞❛ ❞✐str✐❜✉✐çã♦ ❣❛✉ss✐❛♥❛ ✐♥✈❡rs❛ ♣❛r❛ ❛s s✐t✉❛çõ❡s ❡♠ q✉❡ ❛ ✈❛r✐á✈❡❧ ❞❡ ✐♥t❡r❡ss❡ ❛ss✉♠❡ ♦ ✈❛❧♦r ③❡r♦ ❝♦♠ ♣r♦❜❛❜✐❧✐❞❛❞❡ ♣♦s✐t✐✈❛✳ ❊①✐st❡♠ ❞✐❢❡r❡♥t❡s ♣❛r❛♠❡tr✐③❛çõ❡s ♣❛r❛ ❛ ❞✐str✐❜✉✐çã♦ ❣❛✉ss✐❛♥❛ ✐♥✈❡rs❛✳ ❯s❛r❡♠♦s ❛q✉✐ ❛ ♣❛r❛♠❡tr✐③❛çã♦ ✉t✐✲ ❧✐③❛❞❛ ♥♦ ♣❛❝♦t❡ ❣❛♠❧ss ❞♦ s♦❢t✇❛r❡ ❘ ✭❙t❛s✐♥♦♣♦✉❧♦s ❡t ❛❧✳✱ ✷✵✶✹✮ ❝✉❥❛ ❢✉♥çã♦ ❞❡♥s✐❞❛❞❡ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ é ❞❛❞❛ ♣♦r
f(y;µ, σ) = p 1
(2πy3σ2)exp
−(y−µ)
2
2µ2σ2y
✭✷✳✼✮
❡♠ q✉❡ y >0✱µ >0 ❡ σ >0✳ ❆q✉✐ E(y) =µ ❡V ar(y) = σ2µ3 sã♦ ❛ ♠é❞✐❛ ❡ ❛ ✈❛r✐â♥❝✐❛ ❞❛
❢✉♥çã♦ ❞❡♥s✐❞❛❞❡ ❞❛ ❣❛✉ss✐❛♥❛ ✐♥✈❡rs❛ r❡s♣❡❝t✐✈❛♠❡♥t❡✳
0 2 4 6 8 10
0.0
0.2
0.4
0.6
0.8
y
pdf σ =0.08
σ =0.05
σ =0.03
Distribuição ZAIG µ =5 e α =0.4
✭❛✮
0 2 4 6 8 10
0.0
0.2
0.4
0.6
0.8
1.0
y
µ =5
µ =3
µ =8
Distribuição ZAIG σ =0.05 e α =0.4
✭❜✮
0 2 4 6 8 10
0.0
0.2
0.4
0.6
0.8
y
α =0.2
α =0.8
α =0.5
Distribuição ZAIG σ =0.05 e µ =5
✭❝✮
❋✐❣✉r❛ ✷✳✷✿ ●rá✜❝♦ ❞❛ ❞✐str✐❜✉✐çã♦ ❩❆■● ♣❛r❛ ❞✐❢❡r❡♥t❡s ✈❛❧♦r❡s ❞♦s ♣❛râ♠❡tr♦s
❆ ❞✐str✐❜✉✐çã♦ ❣❛✉ss✐❛♥❛ ✐♥✈❡rs❛ ✐♥✢❛❝✐♦♥❛❞❛ ♥♦ ③❡r♦ é ✉♠❛ ♠✐st✉r❛ ❞❛ ❞✐str✐❜✉✐çã♦ ❞❡❣❡♥❡r❛❞❛ ♥♦ ③❡r♦ ❡ ❞❛ ❞✐str✐❜✉✐çã♦ ❣❛✉ss✐❛♥❛ ✐♥✈❡rs❛✳ ❯t✐❧✐③❛♥❞♦ ❛ ♣❛r❛♠❡tr✐③❛çã♦ ❞❛ ❡q✉❛çã♦ ✭✷✳✼✮✱ ♣♦❞❡♠♦s ❞❡✜♥✐✲❧❛ ❞❛ ❢♦r♠❛ ❛ s❡❣✉✐r
❉❡✜♥✐çã♦ ✸✳ ❙❡❥❛ y ✉♠❛ ✈❛r✐á✈❡❧ ❛❧❡❛tór✐❛ ❝♦♠ s✉♣♦rt❡ ❡♠ {0} ∪(0;∞)✳ ❉✐③❡♠♦s q✉❡ y
t❡♠ ❞✐str✐❜✉✐çã♦ ❣❛✉ss✐❛♥❛ ✐♥✈❡rs❛ ✐♥✢❛❝✐♦♥❛❞❛ ♥♦ ③❡r♦ ❝♦♠ ✈❡t♦r ❞❡ ♣❛râ♠❡tr♦s (α, µ, σ) s❡ s✉❛ ❢✉♥çã♦ ❞❡♥s✐❞❛❞❡ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ é ❞❛❞❛ ♣❡❧❛ ❡q✉❛çã♦ ✭✷✳✶✮ ❡ ♥♦ ❧✉❣❛r ❞❛ ❢✉♥çã♦
