, (7.3), (7.5), (7.6) (7.7), . .
n . , ε. , , Ρ (ε):
Ρ (ε) = Ρ (| - | < ε). (7.8)
- , ε +ε. + ε , I ε = ε - . , - [4]. m ( 1, 2), m N, , . , , . , , P [ Î ( 1, 2)] ( 1, 2),
P [ Î ( 1, 2)] ≈ m / N. (7.9)
, P [ Î ( 1, 2)] ( 1, 2), . , (- 1, 2) ( 1 > 0) [1]
P [ Î (- 1, 2)] = P [| | < 1] = 2 ( / σ) = 2 Φ (t) = (t), (7.10)
(t) :
(- t) = - (t); (7.11)
2 ( / σ) = 2 Φ (t) = (t) ( t = / σ) - . Ÿ t 7.6;
( / σ) = Φ (t) - ;
σ - .
, tσ, (t > 0),
Ρ [| | > tσ ] = 1 - 2 Φ (t). (7.12)
³ 3 σ (.. t ³ 3) Ρ[| | > tσ ] (Ρ [| | > 3 σ ] =1 - 2 (3) = 0,0027), . . (), | | > 3 σ, . σ , (7.5) σ ,
|
|
| | > 3 σ . (7.13)
7.6 - (t) = 2 Φ (t) [1, 4, 30] (- t) = - (t)
t | (t) | t | (t) | t | (t) |
0.00 | 0.0000 | 0.75 | 0.5467 | 1.50 | 0.8864 |
0.05 | 0.0399 | 0.80 | 0.5763 | 1.55 | 0.8789 |
0.10 | 0.0797 | 0.85 | 0.6047 | 1.60 | 0.8904 |
0.15 | 0.1192 | 0.90 | 0.6319 | 1.65 | 0.9011 |
0.20 | 0.1585 | 0.95 | 0.6579 | 1.70 | 0.9109 |
0.25 | 0.1974 | 1.00 | 0.6827 | 1.75 | 0.9199 |
0.30 | 0.2357 | 1.05 | 0.7063 | 1.80 | |0.9281 |
0.35 | 0.2737 | 1.10 | 0.7287 | 1.85 | 0.9357 |
0.40 | 0.3108 | 1.15 | 0.7419 | 1.90 | 0.9426 |
0.45 | 0.3473 | 1.20 | 0.7699 | 1.95 | 0.9488 |
0.50 | 0.3829 | 1.25 | 0.7887 | 2.00 | 0.9545 |
0.55 | 0.4177 | 1.30 | 0.8064 | 2.25 | 0.9756 |
0.60 | 0.4515 | 1.35 | 0.8230 | 2.50 | 0.9876 |
0.65 | 0.4843 | 1.40 | 0.8385 | 3.00 | 0.9973 |
0.70 | 0.5161 | 1.45 | 0.8529 | 4.00 | 0.9999 |
7.6, , Ρ [| |> tσ ] 5% ( (t) = 2 (t) = 0,95), > 1,96 σ (t > 1,96). , Ρ [| |> tσ ] 1% ( (t) = 2 (t) = 0,99), > 2,576 σ (t > 2,576). , Ρ [| |> tσ ] 0,1% ( (t) = 2 (t) = 0,999), > 3,291 σ (t > 3,291). t [1]. σ (7.5) , .
, , . . λ, [10]
λ = ( 2 - 1) / σ (7.14 )
λ = ( n - n-1) / σ , (7.14)
, . 7.7 n α = 0,95 λ = 0,95. λ ≤ λ (a = 0,95), . λ > λ (a = 0,95), ( ), . x σ . [10] .
|
|
7.7 - λ(a = 0,95) α = 0,95 n [10]
n | ||||||
λ(a = 0,95) | 1,3 | 1,2 | 1,1 | 1,0 | 0,9 | 0,8 |