❈♦❧❧❡❝t✐✈❡ ❇✐♦❣r❛♣❤✐❡s ✲ t❤❡ ❉❛t❛❜❛s❡ ❇❇■ ✲ ❇✐♦❣r❛♣❤✐❝❛❧ ❇❛❝❦❣r♦✉♥❞ ■♥❢♦r♠❛t✐♦♥ ❲♦❧❢❣❛♥❣ ❑❛r❧ ❍är❞❧❡✱ ❈❤❡♥ ❍✉❛♥❣ ❆♥❞r✐❥❛ ▼✐❤♦❝✐✱ ❆❧❧❛ P❡t✉❦❤✐♥❛ ❆♥♥❡tt❡ ❇✳ ❱♦❣t ▲❛❞✐s❧❛✉s ✈♦♥ ❇♦rt❦✐❡✇✐❝③ ❈❤❛✐r ♦❢ ❙t❛t✐st✐❝s ❈✳❆✳❙✳❊✳ ✕ ❈❡♥t❡r ❢♦r ❆♣♣❧✐❡❞ ❙t❛t✐st✐❝s ❛♥❞ ❊❝♦♥♦♠✐❝s ❍✉♠❜♦❧❞t✕❯♥✐✈❡rs✐tät ③✉ ❇❡r❧✐♥ ▼❛① P❧❛♥❝❦ ■♥st✐t✉t❡ ❢♦r t❤❡ ❍✐st♦r② ♦❢ ❙❝✐❡♥❝❡ ❧✈❜✳✇✐✇✐✳❤✉✲❜❡r❧✐♥✳❞❡ ❝❛s❡✳❤✉✲❜❡r❧✐♥✳❞❡ ♠♣✐✇❣✲❜❡r❧✐♥✳♠♣❣✳❞❡
▼♦t✐✈❛t✐♦♥ ✶✲✶ ❈❛r❧ ❋r✐❡❞r✐❝❤ ●❛✉ss 0.4 ϕ ( z ) 0.2 0 −5 0 5 z � � ✶ − ✶ ✷ ③ ✷ ♥♦r♠ ϕ ( ③ ) = ❡①♣ √ ✷ π ✶✼✼✼✕✶✽✺✺ ❈❛r❧ ❋r✐❡❞r✐❝❤ ●❛✉ss ♦♥ ❇❇■✿ ❇❇■ ✲ ❇✐♦❣r❛♣❤✐❝❛❧ ❇❛❝❦❣r♦✉♥❞ ■♥❢♦r♠❛t✐♦♥
▼♦t✐✈❛t✐♦♥ ✶✲✷ ❊♠✐❧ ❏✉❧✐✉s ●✉♠❜❡❧ 0.4 f(k; 0.61) f(x) 0.2 0 5 −5 0 5 x ❢ ( ① ) = ❡①♣ [ − { ① + ❡①♣ ( − ① ) } ] ✶✽✾✶✕✶✾✻✻ ❊♠✐❧ ❏✉❧✐✉s ●✉♠❜❡❧ ♦♥ ❇❇■✿ ❇❇■ ✲ ❇✐♦❣r❛♣❤✐❝❛❧ ❇❛❝❦❣r♦✉♥❞ ■♥❢♦r♠❛t✐♦♥
▼♦t✐✈❛t✐♦♥ ✶✲✸ ❙✐♠é♦♥ P♦✐ss♦♥✱ ▲❛❞✐s❧❛✉s ✈♦♥ ❇♦rt❦✐❡✇✐❝③ 0.6 f(k; 0.61) 0.4 0.2 0 5 0 1 2 3 4 k ❢ ( ❦ ; λ ) = ❡①♣ {− λ } λ ❦ ✶✼✽✶✲✶✽✹✵ ✶✽✻✽✲✶✾✸✶ ❦ ! ❙✐♠é♦♥ ❉❡♥✐s P♦✐ss♦♥ ❛♥❞ ▲❛❞✐s❧❛✉s ✈♦♥ ❇♦rt❦✐❡✇✐❝③ ♦♥ ❇❇■✿ ❇❇■ ✲ ❇✐♦❣r❛♣❤✐❝❛❧ ❇❛❝❦❣r♦✉♥❞ ■♥❢♦r♠❛t✐♦♥
▼♦t✐✈❛t✐♦♥ ✶✲✹ ❇❇■ ✭✐✮ ❉❛t❛❜❛s❡ ✲ ❇✐♦❣r❛♣❤✐❝ ■♥❢♦r♠❛t✐♦♥ ◮ ❙❝✐❡♥t✐sts✱ str✉❝t✉r❡ ❛♥❞ ✐♥t❡r❢❛❝❡ ◮ ❈r✐t❡r✐❛ ❛♥❞ ♣r✐♥❝✐♣❧❡s✱ ❛❝❛❞❡♠✐❝ ❝♦♥tr✐❜✉t✐♦♥s ✭✐✐✮ ❘❡s❡❛r❝❤ ❛♥❞ ❚❡❛❝❤✐♥❣ ◮ ❙❡❧❡❝t❡❞ ❜✐♦❣r❛♣❤✐❡s ♦❢ st❛t✐st✐❝✐❛♥s ❛♥❞ ♠❛t❤❡♠❛t✐❝✐❛♥s ◮ ❇❇■ ✐♥ ♣r❛❝t✐❝❡✿ ♣r♦❥❡❝ts ❛♥❞ ❝♦✉rs❡s ❇❇■ ✲ ❇✐♦❣r❛♣❤✐❝❛❧ ❇❛❝❦❣r♦✉♥❞ ■♥❢♦r♠❛t✐♦♥
❖✉t❧✐♥❡ ✶✳ ▼♦t✐✈❛t✐♦♥ � ✷✳ ❇❇■ Pr♦❥❡❝t ✸✳ ❙❡❧❡❝t❡❞ ❇✐♦❣r❛♣❤✐❡s ✹✳ ❇❇■ ✐♥ Pr❛❝t✐❝❡ ✺✳ ❈♦♥❝❧✉s✐♦♥s ❇❇■ ✲ ❇✐♦❣r❛♣❤✐❝❛❧ ❇❛❝❦❣r♦✉♥❞ ■♥❢♦r♠❛t✐♦♥
❇❇■ Pr♦❥❡❝t ✷✲✶ ❇❇■ ❙tr✉❝t✉r❡ ⊡ ✶✶✻ ❜✐♦❣r❛♣❤✐❡s ❆❧♣❤❛❜❡t✐❝❛❧ ✴ ❚✐♠❡ ✐♥❞❡① ◮ ❇✐♦❣r❛♣❤✐❝❛❧ ✐♥❢♦r♠❛t✐♦♥ ❛♥❞ ♣❤♦t♦✱ ❡❞✉❝❛t✐♦♥✱ ❝❛r❡❡r ♣❛t❤ ◮ ❆❝❛❞❡♠✐❝ ❝♦♥tr✐❜✉t✐♦♥✱ ✐♠♣♦rt❛♥t ♣✉❜❧✐❝❛t✐♦♥s✱ ♥❡t✇♦r❦ ❜✉✐❧❞✐♥❣ η ❚■ ❝ ❦♥♦✇❧❡❞❣❡ ❞❛t❛❜❛s❡ ⊡ ▼ ´ ▲✐♥❦ ❇❇■ ✲ ❇✐♦❣r❛♣❤✐❝❛❧ ❇❛❝❦❣r♦✉♥❞ ■♥❢♦r♠❛t✐♦♥
❇❇■ Pr♦❥❡❝t ✷✲✷ ❈r✐t❡r✐❛ ❛♥❞ ♣r✐♥❝✐♣❧❡s ⊡ ❆❝❛❞❡♠✐❝ ❈♦♥tr✐❜✉t✐♦♥s ▼❛t❤❡♠❛t✐❝s ◮ ◮ ▼❛t❤❡♠❛t✐❝❛❧ st❛t✐st✐❝s ◮ ❱❛r✐♦✉s ✜❡❧❞s ♦❢ st❛t✐st✐❝s✱ ❡✳❣✳ ✜♥❛♥❝✐❛❧ st❛t✐st✐❝s ❇❇■ ✲ ❇✐♦❣r❛♣❤✐❝❛❧ ❇❛❝❦❣r♦✉♥❞ ■♥❢♦r♠❛t✐♦♥
❇❇■ Pr♦❥❡❝t ✷✲✸ ❙♦✉r❝❡s ⊡ ❉✐❝t✐♦♥❛r✐❡s ❛♥❞ ❡♥❝✐❝❧♦♣❡❞✐❛s ⊡ ❆r❝❤✐✈❡s ❯♣♣s❛❧❛ ◮ ❆♠st❡r❞❛♠ ◮ ❇❡r❧✐♥ ◮ ❇❇■ ✲ ❇✐♦❣r❛♣❤✐❝❛❧ ❇❛❝❦❣r♦✉♥❞ ■♥❢♦r♠❛t✐♦♥
❙❡❧❡❝t❡❞ ❇✐♦❣r❛♣❤✐❡s ✸✲✶ ▲❛❞✐s❧❛✉s ✈♦♥ ❇♦rt❦✐❡✇✐❝③ ❇✐♦❣r❛♣❤② ▲❛❞✐s❧❛✇ ❏♦s❡♣❤♦✇✐ts❝❤ ❇♦rt❦✐❡✇✐ts❝❤ ✼ ❆✉❣✳ ✶✽✻✽ ❙t P❡t❡rs❜✉r❣ ✲ ✶✺ ❏✉❧② ✶✾✸✶ ❇❡r❧✐♥ ❇❇■ ✲ ❇✐♦❣r❛♣❤✐❝❛❧ ❇❛❝❦❣r♦✉♥❞ ■♥❢♦r♠❛t✐♦♥
❙❡❧❡❝t❡❞ ❇✐♦❣r❛♣❤✐❡s ✸✲✷ ❲❧❛❞✐♠✐r ❙❛✈❡❧②❡✈✐❝❤ ❲♦②t✐♥s❦② ❇✐♦❣r❛♣❤② ❱❧❛❞✐♠✐r ❙✳ ❱♦❥t✐♥s❦✐❥ ✶✷ ◆♦✈✳ ✶✽✽✺ ❙t✳ P❡t❡rs❜✉r❣ ✲ ✶✶ ❏✉♥❡ ✶✾✻✵ ❲❛s❤✐♥❣t♦♥ ❇❇■ ✲ ❇✐♦❣r❛♣❤✐❝❛❧ ❇❛❝❦❣r♦✉♥❞ ■♥❢♦r♠❛t✐♦♥
❙❡❧❡❝t❡❞ ❇✐♦❣r❛♣❤✐❡s ✸✲✸ ❊r♥st ❲❛❣❡♠❛♥♥ ❇✐♦❣r❛♣❤② ✶✽ ❋❡❜r✳ ✶✽✽✹ ❈❤❛♥❛r❝✐❧❧♦ ✲ ✷✵ ▼❛r❝❤ ✶✾✺✻ ❇❛❞ ●♦❞❡s❜❡r❣ ❇❇■ ✲ ❇✐♦❣r❛♣❤✐❝❛❧ ❇❛❝❦❣r♦✉♥❞ ■♥❢♦r♠❛t✐♦♥
❙❡❧❡❝t❡❞ ❇✐♦❣r❛♣❤✐❡s ✸✲✹ ❑❛r❧ P❡❛rs♦♥ ❇✐♦❣r❛♣❤② ✷✼ ▼❛r❝❤ ✶✽✺✼ ▲♦♥❞♦♥ ✲ ✷✼ ❆♣r✐❧ ✶✾✸✻ ❈♦❧❞❤❛r❜♦✉r ❙✉rr❡② ❇❇■ ✲ ❇✐♦❣r❛♣❤✐❝❛❧ ❇❛❝❦❣r♦✉♥❞ ■♥❢♦r♠❛t✐♦♥
❙❡❧❡❝t❡❞ ❇✐♦❣r❛♣❤✐❡s ✸✲✺ ❊❣♦♥ P❡❛rs♦♥ ❇✐♦❣r❛♣❤② ✶✶ ❆✉❣✳ ✶✽✾✺ ❍❛♠st❡❛❞ ✲ ✶✷ ❏✉♥❡ ✶✾✽✵ ❙✉ss❡① ❇❇■ ✲ ❇✐♦❣r❛♣❤✐❝❛❧ ❇❛❝❦❣r♦✉♥❞ ■♥❢♦r♠❛t✐♦♥
❙❡❧❡❝t❡❞ ❇✐♦❣r❛♣❤✐❡s ✸✲✻ ❍❡r♠❛♥♥ ❖tt♦ ❍✐rs❝❤❢❡❧❞ ❇✐♦❣r❛♣❤② ❍❡r♠❛♥♥ ❖tt♦ ❍❛rt❧❡② ✶✸ ❆♣r✐❧ ✶✾✶✷ ❇❡r❧✐♥ ✲ ✸✵ ❉❡❝✳ ✶✾✽✵ ❉✉r❤❛♠ ❇❇■ ✲ ❇✐♦❣r❛♣❤✐❝❛❧ ❇❛❝❦❣r♦✉♥❞ ■♥❢♦r♠❛t✐♦♥
❇❇■ ✐♥ Pr❛❝t✐❝❡ ✹✲✶ ❇❇■ ✐♥ Pr❛❝t✐❝❡ ❆❞✈❛♥❝❡❞ ▼❛t❤❡♠❛t✐❝s ✲ ❚♦♣♦❧♦❣② ❛♥❞ ❈♦♥✈❡① ❖♣t✐♠✐③❛t✐♦♥ ❇❇■ ✲ ❇✐♦❣r❛♣❤✐❝❛❧ ❇❛❝❦❣r♦✉♥❞ ■♥❢♦r♠❛t✐♦♥
❇❇■ ✐♥ Pr❛❝t✐❝❡ ✹✲✷ ❇❇■ ✐♥ Pr❛❝t✐❝❡ ❆❞✈❛♥❝❡❞ ▼❡t❤♦❞s ✐♥ ◗✉❛♥t✐t❛t✐✈❡ ❋✐♥❛♥❝❡ ✲ ▼♦❞❡❧✐♥❣ ❉❡♣❡♥❞❡♥❝✐❡s ✇✐t❤ ❈♦♣✉❧❛❡ ❇❇■ ✲ ❇✐♦❣r❛♣❤✐❝❛❧ ❇❛❝❦❣r♦✉♥❞ ■♥❢♦r♠❛t✐♦♥
❇❇■ ✐♥ Pr❛❝t✐❝❡ ✹✲✸ ❇❇■ ✐♥ Pr❛❝t✐❝❡ ▼❡t✐s ❦♥♦✇❧❡❞❣❡ ❞❛t❛❜❛s❡ ✲ ❇❛❤❛❞✉r ❘❡♣r❡s❡♥t❛t✐♦♥✱ ❊❞❣❡✇♦rt❤ ❊①♣❛♥s✐♦♥ ❛♥❞ ❈♦r♥✐s❤✲❋✐s❤❡r ❊①♣❛♥s✐♦♥ ❇❇■ ✲ ❇✐♦❣r❛♣❤✐❝❛❧ ❇❛❝❦❣r♦✉♥❞ ■♥❢♦r♠❛t✐♦♥
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