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Transcription:

k ) λ ) k λ ) λk k! e λ ) π/!. e α + α) /α e k ) λ ) k λ )! λ k! k)! ) λ k λ k! λk e λ k! λk e λ. k! ) k λ ) k k + k k k ) k ) k e k λ e k ) k EX EX V arx) X Nα, σ ) Bp) Eα) Πλ) U, θ) X Nα, σ ) E ) X α σ E X α ) σ EX α V arx) σ EX EX) + V arx) α + σ X Bp) EX P X ) p EX P X ) p V arx) EX EX) p p X Eα) EX xαe αx dx yαx α ye y dy α Γ) α, EX x αe αx dx α y e y dy α Γ3) α V arx) EX EX) α X Πλ) EX λ k k k )! e λ λ k λk k! e λ λ EX k kλ k k )! e λ k k )λ k k )! e λ + V arx) EX EX) λ + λ λ λ X U, θ) EX θ x θ dx θ EX θ k x θ λ k k )! e λ λ k λ k k! e λ + EX λ + λ, θ θ dx 3 V arx) 3 θ 4 θ θ U[, θ] fx θ) θ x θ, < θ <

m θ) E θ X θ m θ) E θ X θ 3 θ m X) X, θ m X ) 3 X. θ θ V ar θ X) m θ )) ) θ. θ E θ X 4 X θ E θ e tx e tx tθ dx etθ ) k θ tθ k + )!. E θ e tx k tk k! E θ X k E θ X k θk k+ E θ X 4 θ4 5 V ar θ X 4 θ ) m θ )) θ > 5 θ 3 4 9 θ 45 7 k 9 θ 3 4. λ Πλ) φλ) i d d φλ) λ + λ dλ dλ px i λ) λ i X i i X i! e λ. ) i X i X i! + X i. λ i λ < i X i φx) λ > i X i φx) φλ) λ i X i λ Πλ) λ i X i α Eα) φα) px i α) [, ) X i ) α e α i Xi [, ) Y ), i Y X,, X } φα) φα) i i d d φα) dα dα α α X i ) α d dα φα) α <. φα) α α / X i Xi i X i X α Eα)

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fx p) p x p) x e x p p p) ap)bx)e cp)dx), ap) p bx) cp) p p dx) x S i dx i) i X i X E p S p X p Nα, σ ) σ σ α α fx α) πσ e x σ e α σ e αx σ fx α) aα) e α x σ bx) e σ πσ cα) α σ dx) x S i dx i) i X i X E α S α X α p p p X X p ξp) Bα, β) E[p] α α+β.5 E[p X,, X ].9 α β p ξx X x,, X x ) P p x X x,, X x ) P X x,, X x p x)p p x) P X x,, X x p y)p p y)dy Cx i x i x) i x i) x α x) β Cx i xi+α x) β+ i xi) C ξp x X x,, X x ) x Γ + α + β) C Γ i x i + α)γ i x i) + β), α 7 E[p X,, X ] β 9 7 xp p x X X )dx Γ + α + β) x Γα)Γ + β) xα x) +β dx α + α + β +. α α+β.5 α+ α+β+.9,

p p ξ.).7 ξ.).3. p ξ. X x,, X x ) P p. X x,, X x ) P X x,, X x p.)p p.) P X x,, X x p.)p p.) + P X x,, X x p.)p p.)..9 6.7..9 6.7 +..8 6.3.548. ξ. X x,, X x ).548.458 θ θ θ Γα, β) E[θ] α β V arθ) α β α β α β 5, α β Eα) α α α ξx) α Γa, b) E[α] a b. V arα) a b a 5 b 5 ξx X x,, X x ) P X x,, X x α x)p α x) P X x,, X x α y)p α y)dy x e x i x i b a Γa) xa e bx Costat b + i x i) +a x +a e b+ i xi)x Γ + a) +a b + X) x +a e b+ X)x. Γ + a) X 3.8 a 5 b 5 α p p α 5 β p

p Γα + β + ) ξx X,, X ) Γα + i X i)γβ + i X i) xα+ i Xi) x) β+ i X i). p p E[p X,, X ] x Γ35)x5 x) 8 dx 6 Γ6)Γ9) 35. Πλ) λ λ α 3 β λ λ ξx X,, X ) λ E[λ X,, X ] β + )α+ i Xi x α+ Γα + i X i) i Xi e β+)x x 3+3 x 3+3 e x dx 8. Γ3 + 3). Γα, β) β α Γα, β) β [ ] β α fx,, x α) x x ) α e β i x i x,,x Γα) } ux,, x )vt x,, x ), α), ux,, x ) e β [ ] i x i x,,x } vt, α) β α Γα) T α T x,, x ) i x i T X,, X ) i X i fx θ) aθ)bx)e cθ)dx) X X fx,, x θ) aθ) i bx i )e cθ) i dxi) ux,, x )vt x,, x ), θ), T x,, x ) i dx i) vt, θ) aθ) e tcθ) ux,, x ) i bx i) T X,, X ) i dx i)

Γα, β) β α fx,, x α, β) [ ] β α x x ) α e β i xi x,,x Γα) } ux,, x )vt x,, x ), T x,, x ), α, β), [ ] ux,, x ) x,,x } vt, t, α, β) β α Γα) t α e βt T x,, x ) i x i T x,, x ) i x i i X i, i X i) X X Eα) α α Eα) fx,, x α) α e α i xi x,,x }. x,, x } < fx,, x α) x,, x } α α fx,, x α) α α α i x x. i T x,, x ) x ux,, x ) x,,x } vt, α) α e α t fx,, x α) ux,, x )vt x,, x ), α) α α X α X X U[, θ] Y X,, X }. θ cy E θ cy θ). θ cy Y t t θ} E θ cy θ) θ ct θ) t dt + c ) + c + θ +. 86, 8, 76, 49, 84, 9, 58, 39, 75, 48, 5,, 4, 53, 9, 57, 3, 49, 35, 3 µ σ

X 56.85 X 588.95 X X) 487.3 c c c P χ 9 c ) P χ 9 c ) α.5 P t 9 c) P t 9 c) α.5 c 6.844 c 3.4 c.79 σ [ X X) ), X X) ] ) [33.8, 43.] c c µ [ ] X c X X) ), X + c X X) ) [48., 65.6]. f x) f x) x f x) f x) x x X fx) f x) f x) H : fx) f x), H : fx) f x). αδ) + βδ) αδ) + βδ) αδ) βδ) αδ) P δ H ) βδ) P δ H ) ξ) 3 ξ) 3 ξ)p δ H ) + ξ)p δ H ) f X) f ξ) X) X ξ) H : X < 4 δ H : X > 4 H H : X 4. δ H : X δ 4 H : X > 4. αδ ) + βδ ) P δ H ) + P δ H ) P X > 4 ) + P X 4 ) 4 4 dx + xdx 7 8.

αδ). βδ) βδ) c ) f X) P f X) < c.. c 5 9 ) ) f X) P f X) < c P X < c P X > c ) c } c ).. δ H : X 5 9 H : X < 5 9 αδ). βδ) βδ) P δ H ) P X 9.8. H H H P p. H P p.4 X X α.5 fx,, x p) p i x i p) i x i) f X, X ). X+X.8 X+X) f X, X ).4 X+X.6 X+X) f X, X ) f X, X ).5X +X ) X +X 4 ). 3 c P f X,X ) f X,X ) < c ) α.5 ) f X, X ) P f X, X ) < c 6 9 <c}.64 + 4 <c}.4 + 3 <c}.3. c p ) ) f X, X ) P f X, X ) < c f X, X ) + p)p f X, X ) c.5. ) P f X,X ) f X,X ) < c ) P f X,X ) f X,X ) c c 3.5 c 4, 3 ].4 + p)p X, X X, X ).5,

p 3 3 α.5 H :.5 X+X 4 X+X ) 3) > 3 δ H :.5 X+X 4 X+X ) 3) < 3 H H :.5 X+X 4 X+X ) 3) H p 3 3 H p 3 ) ) f X, X ) P δ H ) P f X, X ) < c f X, X ) + p)p f X, X ) c P X X ) + 3 P X, X X, X ).6 + 3.48.75. 3, X X µ σ H : µ H : µ δ α δ).5 } f X,, X ) f X,, X ) i [X i µ ) X i µ ) ] σ ) f X,, X P f X,, X ) < c P i X i < c) i e X i. ) i P X i ) c < σ σ ) c Φ. ) Φ c.5 c.88 δ i H : e X i.88 δ i H : e X i <.88. ) i P δ H ) P e X i < c ) c + Φ.94.

α.5 Aa /4 AA / Aa /4 aa Aa AA Aa aa χ p P AA) p P Aa) p 3 P aa) H : p p, p p, p 3 p 3 H :, p, p p 3 4 v i X i AA} v i X i Aa} v 3 i X i aa} T 3 k v k p k ) p k 3 3.667. χ δ H : T c H : T > c, c.5 α χ 3 c, ) c 5.99 T

.8..45.35.7.3.8.66.39.38.38.6.49.4.85.33.34.96.64.3.4.64 3.44.67.85.4..67.3.4.49.36.4.4..5.4.76.6.4.35.8.46.63.6.64.56..3.8 χ x.84 x.53 x 3.53 x 4.84 Φx k ).k k,, 3, 4) B,.84] B.84,.53] B 3.53,.53] B 4.53,.84] B 5.84, ) p k P X B k ) k,, 3, 4, 5) H : p p p 3 p 4 p 5. H :. v k i X i B k } k,, 3, 4, 5) v 5 v v 3 7 v 4 v 5 6 5 v k 5.) T 5. k 5.4. χ δ H : T c H : T > c, c.5 α χ 5 c, ) c 9.488 H N N 6 θ θ H N, N 36, N 3 4, N 4 36, N 5, N 6 4. Q H fθ, θ ) θ N θ N θ θ ) N 3 θ θ ) N 4 [θ θ θ )] N 5 [θ θ θ )] N 6. A <

fθ, θ ) N θ + N θ + N 3 θ θ ) + N 4 + θ + θ ) +N 5 [ + θ + θ θ )] + N 6 [ + θ + θ θ )]. fθ, θ ) θ θ N3+N5+N6 θ θ θ fθ, θ ) N+N4+N5 θ θ fθ, θ ) N +N 4 +N 6 θ N 3+N 5 +N 6 θ θ. θ θ N i θ θ θ. θ.5 T N 5. ) 5. + N 5.5 ) 5.5 + N 3 5.3 ) 5.3 + N 4 5.) + N 5 5.) + N 6 5.3) 5. 5. 5.3 4.37. T χ 6 χ 3 c 7.85 χ 3c, ).5 T c T 4.37 < c 7.85 33 67 66 3 5 4 9 θ < θ < ) p θ) 4, p 4θ θ) 3, p 6θ θ), p 3 4θ 3 θ), p 4 θ 4. H : p θ) 4, p 4θ θ) 3, p 6θ θ), p 3 4θ 3 θ), p 4 θ 4, θ, ) H :. fθ) 4 i i pn i i N i fθ) 4N θ) + N [ 4 + θ + 3 θ)] + N [ 6 + θ + θ)] +N 3 [ 4 + 3 θ + θ)] + 4N 4 θ.

θ θ θ.4 p θ).96 p θ).3456 p θ).3456 p 3 θ).536 p 4 θ).56 T χ 33.96) 67.3456) + +.96.3456 5.536) 9.56) + +.536.56 47.8. 66.3456).3456 T χ 5 χ 3 α c χ 3c, ) α H : T c δ H : T > c α c 7.85 χ 3c, ).5 T > c 7 6 5 3 3 9 N 7 N 6 N 3 5 N 3 N 3 N 3 9 N + 7 N + 5 N + 47 N + 9 N +3 4 χ T [7 7 47/478) /7 47) + 6 7 9/478) /7 9) +5 7 4/478) /7 4) + 3 5 47/478) /5 47) +3 5 9/478) /5 9) + 9 5 4/478) /5 4)] 478.46. α : T c δ : T > c, c χ )3 )c, ) α δ α c 5.99 χ c, ).5 T > 5.99 T

O A B AB Rh O A B AB Rh 8 89 54 9 Rh 3 7 7 9 N 8 N 89 N 3 54 N 4 9 N 3 N 7 N 3 7 N 4 9 N + 44 N + 56 N + 95 N + 6 N +3 6 N +4 8 χ T 8.6. [8 44 95/3) /44 95) + 89 44 6/3) /44 6) + 54 44 6/3) /44 6) +9 44 8/3) /44 8) + 3 56 95/3) /56 95) + 7 56 6/3) /56 6) +7 56 6/3) /56 6) + 9 56 8/3) /56 8)] 3 α : T c δ : T > c, c χ )4 )c, ) α δ α c 7.85 χ 3c, ).5 T > 7.85 57 4 5 87 4 3 6 49

N 57 N 4 N 3 5 N 87 N N 3 4 N 3 3 N 3 6 N 33 49 N + 49 N + 5 N 3+ 78 N + 47 N + 9 N +3 4 T α : T c δ : T > c, c χ 3 )3 )c, ) α δ α c 9.488 χ 4c, ).5 T > 9.488 [, ].4.6.88.4.9.38.78.7.57.66.48.35.6..8..9.79.75.8.3.3..4.9 H : H : F x) F x) x. H : D.35 δ H : D >.35 D x F x) x 5 D A

x.4 F x) F x) D 5.8.9 H fx) 3 < x fx) < x <. fx) x 3 F x) x < x x+ < x < x. H : H : F x) F x). H : D.35 δ H : D >.35 D

x.66 F x) F x) D 5.5.75 H / [, ] / θ θ [, ] θ θ P θ ) P θ ).5 P θ X x,, X 5 x 5 ) P X x,, X 5 x 5 θ )P θ ) P X x,, X 5 x 5 θ )P θ ) + P X x,, X 5 x 5 θ )P θ ) P X x,, X 5 x 5 θ ) P X x,, X 5 x 5 θ ) + P X x,, X 5 x 5 θ ) +.5 5 i <x i.5} +.5 5 i.5<x i<} + 8.5.34. β β σ y x.5 β i x i y i i x i y i.3.4 6..8.4.9 7..7 3..4 8..4 4.3.3 9.7. 5..3.7.7 β β σ β XY XȲ.54.386 X X).6.764.435, β Ȳ β X.47, σ Y i β β X i ).45. i α. α α χ, c ) α.5 χ c, ) α.5 c.736 c 5.573 σ [ σ c, σ c ] [.9,.65] β c t c, c) α.9 c.8595 β [ ] β c [.88,.5876]. σ ) X X) ), β + c σ ) X X) )

β [ σ β c + X) ) X X), β + c σ + X) )] [.64,.38]. X X) x.5 ŷ y β + β.5.8 y x.5 [ σ Ŷ c + + X ) X) X X), Ŷ + c σ + + X )] X) [.386,.94]. X X) H : β H : β <, β N ) X X) β β ) σ σ σ β X X) ) T ) β β σ σ σ ) X X) ) ) σ β, X X) ) χ β β t β T T H : T > c δ H : T c, c t 8, c). c.3968 T 5.3 > c H σ )