ssts t r - PowerPoint PPT Presentation

❚❤❡ ✈✐❝✐ss✐t✉❞❡s ♦❢ t❤❡ ✈❛r✐❛♥❝❡ ❡st✐♠❛t✐♦♥ ♦❢ t❤❡ ●✐♥✐ ✐♥❞❡① ❨✈❡s ❚✐❧❧é ❯♥✐✈❡rs✐t② ♦❢ ◆❡✉❝❤ât❡❧ ❙❡♠✐♥❛r ✷✵✶✽ ❯♥✐✈❡rs✐tà ❞❡❣❧✐ ❙t✉❞✐ ❞✐ ❚r❡♥t♦ ❨✈❡s ❚✐❧❧é ❱❛r✐❛♥❝❡ ❡st✐♠❛t✐♦♥ ♦❢ t❤❡ ●✐♥✐ ✐♥❞❡① ❚r❡♥t♦ ❉❡❝❡♠❜❡r ✷✵✶✽ ✶ ✴ ✷✸

❚❤❡ ✈✐❝✐ss✐t✉❞❡s ♦❢ t❤❡ ✈❛r✐❛♥❝❡ ❡st✐♠❛t✐♦♥ ♦❢ t❤❡ ●✐♥✐ ✐♥❞❡① ❨✈❡s ❚✐❧❧é ❯♥✐✈❡rs✐t② ♦❢ ◆❡✉❝❤ât❡❧ ❙❡♠✐♥❛r ✷✵✶✽ ❯♥✐✈❡rs✐tà ❞❡❣❧✐ ❙t✉❞✐ ❞✐ ❚r❡♥t♦ ❨✈❡s ❚✐❧❧é ❱❛r✐❛♥❝❡ ❡st✐♠❛t✐♦♥ ♦❢ t❤❡ ●✐♥✐ ✐♥❞❡① ❚r❡♥t♦ ❉❡❝❡♠❜❡r ✷✵✶✽ ✷ ✴ ✷✸

■♥tr♦❞✉❝t✐♦♥✱ ❈♦rr❛❞♦ ●✐♥✐ ❚❛❜❧❡ ♦❢ ❝♦♥t❡♥ts ✶ ■♥tr♦❞✉❝t✐♦♥✱ ❈♦rr❛❞♦ ●✐♥✐ ✷ ▲♦r❡♥③ ❝✉r✈❡ ❛♥❞ ●✐♥✐ ❝♦❡✣❝✐❡♥t ✸ ■♥✢✉❡♥❝❡ ❢✉♥❝t✐♦♥ ✹ ❚❤❡ r❡❣r❡ss✐♦♥ ❛♣♣r♦❛❝❤ ✺ ▼♦r❡ ♦♥ t❤❡ ❧✐♥❡❛r✐③❛t✐♦♥ ✻ ▼♦r❡ ♦♥ ❧✐♥❡❛r✐③❛t✐♦♥ ✼ ❈♦♥❝❧✉s✐♦♥s ❨✈❡s ❚✐❧❧é ❱❛r✐❛♥❝❡ ❡st✐♠❛t✐♦♥ ♦❢ t❤❡ ●✐♥✐ ✐♥❞❡① ❚r❡♥t♦ ❉❡❝❡♠❜❡r ✷✵✶✽ ✸ ✴ ✷✸

■♥tr♦❞✉❝t✐♦♥✱ ❈♦rr❛❞♦ ●✐♥✐ ❈♦rr❛❞♦ ●✐♥✐ ❨✈❡s ❚✐❧❧é ❱❛r✐❛♥❝❡ ❡st✐♠❛t✐♦♥ ♦❢ t❤❡ ●✐♥✐ ✐♥❞❡① ❚r❡♥t♦ ❉❡❝❡♠❜❡r ✷✵✶✽ ✹ ✴ ✷✸

▲♦r❡♥③ ❝✉r✈❡ ❛♥❞ ●✐♥✐ ❝♦❡✣❝✐❡♥t ●✐♥✐ ❝♦❡✣❝✐❡♥t ❨✈❡s ❚✐❧❧é ❱❛r✐❛♥❝❡ ❡st✐♠❛t✐♦♥ ♦❢ t❤❡ ●✐♥✐ ✐♥❞❡① ❚r❡♥t♦ ❉❡❝❡♠❜❡r ✷✵✶✽ ✺ ✴ ✷✸

▲♦r❡♥③ ❝✉r✈❡ ❛♥❞ ●✐♥✐ ❝♦❡✣❝✐❡♥t ●✐♥✐ ❝♦❡✣❝✐❡♥t ●✐♥✐✱ ❈✳ ✭✶✾✶✷✮✳ ❱❛r✐❛❜✐❧✐tà ❡ ▼✉t❛❜✐❧✐tà ✳ ❇♦❧♦❣♥❛✿ ❚✐♣♦❣r❛✜❛ ❞✐ P❛♦❧♦ ❈✉♣♣✐♥✳ ●✐♥✐✱ ❈✳ ✭✶✾✶✹✮✳ ❙✉❧❧❛ ♠✐s✉r❛ ❞❡❧❧❛ ❝♦♥❝❡rtr❛③✐♦♥❡ ❡ ❞❡❧❧❛ ✈❛r✐❛❜✐❧✐tà ❞❡✐ ❝❛r❛tt❡r✐✳ ❆tt✐ ❞❡❧ ❘❡❛❧❡ ■st✐t✉t♦ ❱❡♥❡t♦ ❞✐ ❙❝✐❡♥③❡✱ ▲❡tt❡r❡ ❡ ❆rt✐✱ ▲❳❳■■■ ✼✸ ✱ ✶✷✵✸✕✶✷✹✽✳ ●✐♥✐✱ ❈✳ ✭✶✾✷✶✮✳ ▼❡❛s✉r❡♠❡♥t ♦❢ ✐♥❡q✉❛❧✐t② ❛♥❞ ✐♥❝♦♠❡s✳ ❚❤❡ ❊❝♦♥♦♠✐❝ ❏♦✉r♥❛❧ ✸✶ ✱ ✶✷✹✕✶✷✻✳ ❨✈❡s ❚✐❧❧é ❱❛r✐❛♥❝❡ ❡st✐♠❛t✐♦♥ ♦❢ t❤❡ ●✐♥✐ ✐♥❞❡① ❚r❡♥t♦ ❉❡❝❡♠❜❡r ✷✵✶✽ ✻ ✴ ✷✸

▲♦r❡♥③ ❝✉r✈❡ ❛♥❞ ●✐♥✐ ❝♦❡✣❝✐❡♥t ▲♦r❡♥③ ❝✉r✈❡ ▲♦r❡♥③✱ ▼✳ ❖✳ ✭✶✾✵✺✮✳ ▼❡t❤♦❞s ♦❢ ♠❡❛s✉r✐♥❣ t❤❡ ❝♦♥❝❡♥tr❛t✐♦♥ ♦❢ ✇❡❛❧t❤✳ P✉❜❧✐❝❛t✐♦♥s ♦❢ t❤❡ ❆♠❡r✐❝❛♥ ❙t❛t✐st✐❝❛❧ ❆ss♦❝✐❛t✐♦♥ ✾ ✱ ✷✵✾✕✷✶✾✳ f ( y ) ✿ ♣r♦❜❛❜✐❧✐t② ❞❡♥s✐t② ❢✉♥❝t✐♦♥ ♦❢ ❛ ♣♦s✐t✐✈❡ ❝♦♥t✐♥✉❡ r❛♥❞♦♠ ✈❛r✐❛❜❧❡ X t❤❛t r❡♣r❡s❡♥ts t❤❡ ✐♥❝♦♠❡✳ F ( y ) ✿ ❝✉♠✉❧❛t✐✈❡ ❞✐str✐❜✉t✐♦♥ ❢✉♥❝t✐♦♥✳ ▲♦r❡♥③ ❝✉r✈❡✿ � F − ✶ ( α ) � α yf ( y ) dy = ✶ ✵ F − ✶ ( u ) du , � ∞ L ( α ) = ✵ yf ( y ) dy µ ✵ ✇❤❡r❡ F − ✶ ( . ) ✐s t❤❡ ✐♥✈❡rs❡ ❢✉♥❝t✐♦♥ ♦❢ F ( . ) ❛♥❞ � ∞ µ = yf ( y ) dy . ✵ ❨✈❡s ❚✐❧❧é ❱❛r✐❛♥❝❡ ❡st✐♠❛t✐♦♥ ♦❢ t❤❡ ●✐♥✐ ✐♥❞❡① ❚r❡♥t♦ ❉❡❝❡♠❜❡r ✷✵✶✽ ✼ ✴ ✷✸

▲♦r❡♥③ ❝✉r✈❡ ❛♥❞ ●✐♥✐ ❝♦❡✣❝✐❡♥t ▲♦r❡♥③ ❝✉r✈❡ ✶ G / ✷ ✵ ✶ ❋✐❣✉r❡✿ ▲♦r❡♥③ ❝✉r✈❡ ❛♥❞ ❛r❡❛ ❛ss♦❝✐❛t❡❞ t♦ t❤❡ ●✐♥✐ ❈♦❡✣❝✐❡♥t✱ ✏❚❤❡ ❝✉r✈❡ ✐s ❛ ❣r❛♣❤ s❤♦✇✐♥❣ t❤❡ ♣r♦♣♦rt✐♦♥ ♦❢ ♦✈❡r❛❧❧ ✐♥❝♦♠❡ ♦r ✇❡❛❧t❤ ❛ss✉♠❡❞ ❜② t❤❡ ❜♦tt♦♠ ①✪ ♦❢ t❤❡ ♣❡♦♣❧❡✑ ❲✐❦✐♣❡❞✐❛ ❨✈❡s ❚✐❧❧é ❱❛r✐❛♥❝❡ ❡st✐♠❛t✐♦♥ ♦❢ t❤❡ ●✐♥✐ ✐♥❞❡① ❚r❡♥t♦ ❉❡❝❡♠❜❡r ✷✵✶✽ ✽ ✴ ✷✸

▲♦r❡♥③ ❝✉r✈❡ ❛♥❞ ●✐♥✐ ❝♦❡✣❝✐❡♥t ●✐♥✐ ✐♥❞❡① ●✐♥✐ ✐♥❞❡① ❢r♦♠ t❤❡ ▲♦r❡♥③ ❝✉r✈❡✿ � ✶ � ✶ = ✷ [ α − L ( α )] d α = ✶ − ✷ L ( α ) d α G ✵ ✵ � ∞ ✷ = F ( y ) f ( y ) d ( y ) − ✶ . µ ✵ ❉✐s❝r❡t❡ ✈❡rs✐♦♥✿ y ( i ) , i = ✶ , . . . , n ♦r❞❡r❡❞ ✭❜② ✐♥❝r❡❛s✐♥❣ ♦r❞❡r✮ ✐♥❞❡♣❡♥❞❡♥t r❡❛❧✐③❛t✐♦♥✱ G = ✷ � n i = ✶ iy ( i ) − n + ✶ � n � n . i = ✶ y ( i ) n ❈♦♥tr♦✈❡rs② � G = n � � G / ( n − ✶ ) r❛t❤❡r t❤❛♥ � G ✳ ❨✈❡s ❚✐❧❧é ❱❛r✐❛♥❝❡ ❡st✐♠❛t✐♦♥ ♦❢ t❤❡ ●✐♥✐ ✐♥❞❡① ❚r❡♥t♦ ❉❡❝❡♠❜❡r ✷✵✶✽ ✾ ✴ ✷✸

▲♦r❡♥③ ❝✉r✈❡ ❛♥❞ ●✐♥✐ ❝♦❡✣❝✐❡♥t ●✐♥✐ ✐♥❞❡① ✐♥ s❛♠♣❧✐♥❣ ■♥ ❛ ✜♥✐t❡ ♣♦♣✉❧❛t✐♦♥ U ♦❢ s✐③❡ N ✇✐t❤ Y = � k ∈ U y k . � � � ℓ ∈ U | y k − y ℓ | ✷ ky ( k ) − N + ✶ k ∈ U G = = . YN N ✷ NY k ∈ U ❋r♦♠ ❛ s❛♠♣❧❡ ♦❢ S ⊂ U ✇✐t❤ s❛♠♣❧✐♥❣ ✇❡✐❣❤ts w k ✭✇❡ ❝❛♥ ❤❛✈❡ w k = ✶ /π k ✮ � � � � ✷ ✶ � w k � w ✷ = N k y k − ✶ + G k y k N � � N � � Y Y k ∈ S k ∈ S � � ℓ ∈ S w k w ℓ | y k − y ℓ | k ∈ S = . ✷ � N � Y � � � ✇✐t❤ � w k y k ✱ � w k , � Y = N = N k = w k ✶ { y ℓ ≤ y k } . k ∈ S k ∈ S ℓ ∈ S ❨✈❡s ❚✐❧❧é ❱❛r✐❛♥❝❡ ❡st✐♠❛t✐♦♥ ♦❢ t❤❡ ●✐♥✐ ✐♥❞❡① ❚r❡♥t♦ ❉❡❝❡♠❜❡r ✷✵✶✽ ✶✵ ✴ ✷✸

▲♦r❡♥③ ❝✉r✈❡ ❛♥❞ ●✐♥✐ ❝♦❡✣❝✐❡♥t ●✐♥✐ ✐♥❞❡① ✐♥ s❛♠♣❧✐♥❣ ❙❛♥❞strö♠✱ ❆✳✱ ❲r❡t♠❛♥✱ ❏✳ ❍✳ ✫ ❲❛❧❞é♥✱ ❇✳ ✭✶✾✽✺✮✳ ❱❛r✐❛♥❝❡ ❡st✐♠❛t♦rs ♦❢ t❤❡ ●✐♥✐ ❝♦❡✣❝✐❡♥t✿ ❙✐♠♣❧❡ r❛♥❞♦♠ s❛♠♣❧✐♥❣✳ ▼❡tr♦♥ ✹✸ ✱ ✹✶✕✼✵✳ ❙❛♥❞strö♠✱ ❆✳✱ ❲r❡t♠❛♥✱ ❏✳ ❍✳ ✫ ❲❛❧❞é♥✱ ❇✳ ✭✶✾✽✽✮✳ ❱❛r✐❛♥❝❡ ❡st✐♠❛t♦rs ♦❢ t❤❡ ●✐♥✐ ❝♦❡✣❝✐❡♥t✿ ♣r♦❜❛❜✐❧✐t② s❛♠♣❧✐♥❣✳ ❏♦✉r♥❛❧ ♦❢ ❇✉s✐♥❡ss ❛♥❞ ❊❝♦♥♦♠✐❝ ❙t❛t✐st✐❝s✱ ✻ ✱ ✶✶✸✕✶✶✾✳ ❚❤❡② ❝♦♥s✐❞❡r t❤❛t t❤❡ ●✐♥✐ ❝♦❡✣❝✐❡♥t ✐s ❛ r❛t✐♦ ♦❢ t✇♦ t♦t❛❧s ✭ iy ( i ) ❛♥❞ y ( i ) ✮ G = ✷ � n i = ✶ iy ( i ) − n + ✶ � n � n . i = ✶ y ( i ) n ❚❤❡② ❝♦♠♣✉t❡ t❤❡ ✈❛r✐❛♥❝❡ ♦❢ ❛ r❛t✐♦✳ ❖✈❡r❡st✐♠❛t✐♦♥ ❜② ✶✵ ❝♦♠♣❛r❡❞ t♦ s✐♠✉❧❛t✐♦♥s✳ ❨✈❡s ❚✐❧❧é ❱❛r✐❛♥❝❡ ❡st✐♠❛t✐♦♥ ♦❢ t❤❡ ●✐♥✐ ✐♥❞❡① ❚r❡♥t♦ ❉❡❝❡♠❜❡r ✷✵✶✽ ✶✶ ✴ ✷✸