estatistica

■♥❢❡rê♥❝✐❛ ❊st❛tíst✐❝❛
■♥tr♦❞✉çã♦

❖ q✉❡ é ■♥❢❡rê♥❝✐❛ ❊st❛tíst✐❝❛❄

❆ ♣❛rt❡ ❞❛ ❝✐ê♥❝✐❛ ❡st❛tíst✐❝❛ q✉❡ s❡ ♣r❡♦❝✉♣❛ ❡♠ ❡st✉❞❛r ❛
♣♦♣✉❧❛çã♦ ❛tr❛✈és ❞❡ ✐♥❢♦r♠❛çõ❡s ♦❜t✐❞❛s ♥❛ ❛♠♦str❛✱ é
❝❤❛♠❛❞❛ ❞❡ ■♥❢❡rê♥❝✐❛ ❊st❛tíst✐❝❛✳

➱ ♦ ♥♦♠❡ ❞❛❞♦ ❛♦ ♣r♦❜❧❡♠❛ q✉❡ t❡♠ ♣♦r ♦❜❥❡t✐✈♦ ❡s♣❡❝✐✜❝❛r
✉♠ ♦✉ ♠❛✐s ✈❛❧♦r❡s ♣❛r❛

θ✱

t❡♥❞♦ ❝♦♠♦ ❜❛s❡ ✉♠ ❝♦♥❥✉♥t♦ ❞❡

✈❛❧♦r❡s ♦❜s❡r✈❛❞♦s ♣❛r❛ ❛ ✈❛r✐á✈❡❧ ❛❧❡❛tór✐❛ ❳✳

❆❧❣✉♠❛s s✐t✉❛çõ❡s✳✳✳
❉✉✈✐❞❛✲s❡ ❞❛ ✏❤♦♥❡st✐❞❛❞❡✑ ❞❡ ✉♠ ❞❛❞♦✳
■♥t❡r❡ss❡ ❡♠ ❡st✉❞❛r ❛ ♣r♦♣♦rçã♦ ❞❡ ❛❧✉♥♦s✱ ❡♠ ✉♠❛ ✉♥✐✈❡rs✐✲
❞❛❞❡ ♣ú❜❧✐❝❛✱ q✉❡ ♣r❡t❡♥❞❡♠ ❢❛③❡r ♠❡str❛❞♦✳
❯♠❛ ❡♠♣r❡s❛ q✉❡ ❢❛❜r✐❝❛ ❡q✉✐♣❛♠❡♥t♦s ❡❧❡trô♥✐❝♦s ❞❡s❡❥❛ ✈❡✲ r✐✜❝❛r ❝♦♠♦ s❡ ❝♦♠♣♦rt❛ ❛ r❡s✐stê♥❝✐❛ ❞❡ss❡ ❡q✉✐♣❛♠❡♥t♦ ❡♠ r❡❧❛çã♦ ❛ ❛❧t❡r❛çã♦ ❞❡ ✈♦❧t❛❣❡♠✳
❊♠ ✉♠ ♣♦♥t♦ ❞❡ ô♥✐❜✉s✱ ♦ ✐♥t❡r❡ss❡ é ❡♠ ❡st✉❞❛r ♦ t❡♠♣♦ q✉❡ s❡ ❡s♣❡r❛ ♣❛r❛ q✉❡ ♦ ô♥✐❜✉s ❝❤❡❣✉❡✳

❉❡✜♥✐çã♦ ❞❡ ❛❧❣✉♥s ❝♦♥❝❡✐t♦s

P❛râ♠❡tr♦✿

q✉❛♥t✐❞❛❞❡s ❞❛ ♣♦♣✉❧❛çã♦✱ ❡♠ ❣❡r❛❧ ❞❡s❝♦♥❤❡❝✐✲

❞❛s✱ s♦❜r❡ ❛s q✉❛✐s t❡♠♦s ✐♥t❡r❡ss❡✳ P♦r ❡①❡♠♣❧♦✿

❊st✐♠❛❞♦r✿

❝♦♠❜✐♥❛çã♦ ❞♦s ❡❧❡♠❡♥t♦s ❞❛ ❛♠♦str❛ ❝♦♠ ❛ ✜✲

♥❛❧✐❞❛❞❡ ❞❡ r❡♣r❡s❡♥t❛r ✭❡st✐♠❛r✮ ✉♠ ♣❛râ♠❡tr♦✳ P♦r ❡①❡♠♣❧♦✿

❊st✐♠❛t✐✈❛✿

✈❛❧♦r ♥✉♠ér✐❝♦ ❛ss✉♠✐❞♦ ♣❡❧♦ ❡st✐♠❛❞♦r✳

Pr♦♣r✐❡❞❛❞❡s ❞♦s ❊st✐♠❛❞♦r❡s

◆ã♦ t❡♥❞❡♥❝✐♦s♦✿

❊ (θ) = θ

❈♦♥s✐tê♥❝✐❛✿

❧✐♠

♥−→∞
❊✜❝✐ê♥❝✐❛✿

❊ (θ) = θ

❡

❱❛r (θ✶ ) < ❱❛r (θ✷ )

❧✐♠

♥−→∞

❱❛r (θ) = ✵

❊①❡♠♣❧♦
❯♠ ♣❡sq✉✐s❛❞♦r ❞❡s❡❥❛ ❡st✐♠❛r ❛ ♣r♦❞✉çã♦ ❞❡ ✉♠ ♣r♦❝❡ss♦ q✉í♠✐❝♦
❝♦♠ ❜❛s❡ ♥❛ ♦❜s❡r✈❛çã♦ ❞❡ três r❡❛❧✐③❛çõ❡s

❳✶ ✱ ❳✷

❡

❳✸

❞❡ ✉♠

❡①♣❡r✐♠❡♥t♦ ✐♥❞❡♣❡♥❞❡♥t❡✳ ❈♦♥s✐❞❡r❡ ♦s ❞❛❞♦s ❡st✐♠❛❞♦r❡s ♣❛r❛ ❛
♠é❞✐❛ ♣♦♣✉❧❛❝✐♦♥❛❧✱

θ✶ =

µ✱

❡♠ q✉❡

❳✶ + ❳✷ + ❳✸
✸

❳✐
❡

∼ φ(µ, σ ✷ )✱ ✐ = ✶, ✷, ✸✳ θ✷ =

◗✉❛❧ ❡st✐♠❛❞♦r ❞❡✈❡ s❡r ♦ ♣r❡❢❡r✐❞♦❄

❳✶ + ✷ ❳✷ + ❳✸
✹

❊①❡♠♣❧♦
❙❡❥❛ ❳ ✉♠❛ ♣♦♣✉❧❛çã♦ ❝♦♥st✐t✉í❞❛ ❞♦s ❡❧❡♠❡♥t♦s ✷✱ ✸✱ ✹ ❡ ✺✳

❛✮

◗✉❛❧ ❛ ♠é❞✐❛✱ ❞❡s✈✐♦ ♣❛❞rã♦ ❡ ✈❛r✐â♥❝✐❛ ❞❛ ♣♦♣✉❧❛çã♦❄

❜✮

❙❡❧❡❝✐♦♥❡ ❛♠♦str❛s ❞❡ t❛♠❛♥❤♦ ✷✱ ❝♦♠ r❡♣♦s✐çã♦✱ ❞❛ ♣♦♣✉❧❛çã♦

❡ ❡♥❝♦♥tr❡ ❛ ♠é❞✐❛ ❞❡ ❝❛❞❛ ❛♠♦str❛✳

❝✮

❉❡t❡r♠✐♥❡ ❛