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I | III | IV | IV | V | VI | VII | VII | VI | IV | II | I |
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:
M = ∑ u()r / n,
M - ; ∑ - u; - ; r - ; n - .
, , .
u | r | u()r |
n = 50 | ∑ = 679 |
M =.679: 50 = 13,58
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(χ2) F(x) (n ≥ 100). F(x), , . .
χ2 () nj e . .
. : n = 100 e = 10 ÷ 15, n = 200 e = 15 ÷ 20, n = 400 e = 25 ÷ 30, n = 1000 e = 35 ÷ 40.
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, , . , 20 % , nj ≥ 2.
, (3.91)
pj - j- , F(x). pj , . , -∞, - +∞.
F(x) (3.91) χ2α, . VI α k = e 1 - m - 1. e 1 - ; m - , .
χ2 ≤ χ2α (3.92)
. .
, . χ2 . (n ≈ 100).
3.18. χ2 . 2.3 2.4. α = 0.05.
. 3.18, . 2.4. 1- 2- 9- 10- 11-.
4- ,
x s - . 2.2, x = lg(N) = 6.515 s = 0.315. . I (1.29) (1.27) 5- . (6- ) . , . pj, 6 . 7- , pj n =100. 7- 3- .
3.18. | |||||||||
j | xj | nj | z j | Φ(z j) | pj | npj | nj-npj | (nj-npj)2/npj | |
5.825; 5.975 | -∞; -1.71 | 0.0000; 0.0436 | 0.1075 | 10.75 | 3.25 | 0.984 | |||
5.975; 6.125 | -1.71; -1.24 | 0.0436; 0.1075 | |||||||
6.125; 6.275 | -1.24; -0.76 | 0.1075; 0.2236 | 0.1161 | 11.61 | -1.61 | 0.223 | |||
6.275; 6.425 | -0.76; -0.29 | 0.2236; 0.3859 | 0.1623 | 16.23 | -3.23 | 0.643 | |||
6.425; 6.575 | -0.29; 0.19 | 0.3859; 0.5753 | 0.1894 | 18.94 | 2.06 | 0.224 | |||
6.575; 6.725 | 0.19; 0.67 | 0.5753; 0.7486 | 0.1733 | 17.33 | -0.33 | 0.006 | |||
6.725; 6.875 | 0.67; 1.14 | 0.7486; 0.8729 | 0.1243 | 12.43 | 1.57 | 0.198 | |||
6.875; 7.025 | 1.14; 1.61 | 0.8729; 0.9463 | 0.0734 | 7.34 | -1.34 | 0.244 | |||
7.025; 7.175 | 1.61; 2.09 | 0.9463; 0.9817 | 0.0537 | 5.37 | -0.37 | 0.025 | |||
7.175; 7.325 | 2.09; 2.57 | 0.9817; 0.9949 | |||||||
7.325; 7.475 | 2.57; +∞ | 0.9949; 1.0000 | |||||||
1.0000 | χ2 = 2.547 |
9- χ2. χ2 = 2.547.
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. VI α = 0.05 k = 8 - 2 - 1 = 5 (8 - , 2 - , , (x, s) χ20.05 = 11.1. (3.92) , , . . . (. . 2.4).
χ2 = 2.547 α ≈ 0.75 (. VI ). , n = 100 , χ2 ≥ 2.547 75 %.
3.19. - (1.46) α = 0.06 . 2.3 2.8.
(1.46) 2.4 (b = 0.721; x H = 0.736106 c = 3.235106 ).
χ2 . 3.19. χ2 = 35.091.
. VI α = 0.05 k = 11 - 3 - 1 =7 (11 - , 3 - ) χ20.05 = 14.1. (3.92) , - (1.46), . . . α = 0.001, χ20.001 = 24.3.
(. . 2.5).
3.19 - | ||||||||
j | , . | nj | (1.46) | , pj | npj | nj - npj | (nj - npj)2/npj | |
0.736; 1.4 | 0.0000; 0.2733 | 0.2733 | 27.33 | -13.33 | 6.502 | |||
1.4; 2.1 | 0.2733; 0.4152 | 0.1419 | 14.19 | -3.19 | 0.717 | |||
2.1; 2.8 | 0.4152; 0.5148 | 0.0996 | 9.96 | +3.04 | 0.928 | |||
2.8; 3.5 | 0.5148; 0.5905 | 0.0757 | 7.57 | +5.43 | 3.895 | |||
3.5; 4.2 | 0.5905; 0.6503 | 0.0598 | 5.98 | +6.02 | 6.060 | |||
4.2; 4.9 | 0.6503; 0.6987 | 0.0484 | 4.84 | +1.16 | 0.278 | |||
4.9; 5.6 | 0.6987; 0.7386 | 0.0399 | 3.99 | +6.01 | 9.053 | |||
5.6; 6.3 | 0.7386; 0.7720 | 0.0334 | 3.34 | +1.66 | 0.822 | |||
6.3; 7.0 | 0.7720; 0.8242 | 0.0522 | 5.22 | -0.25 | 0.012 | |||
7.0; 7.7 | ||||||||
7.7; 8.4 | 0.8242; 0.8624 | 0.0382 | 3.82 | +2.18 | 1.244 | |||
8.4; 9.1 | ||||||||
9.1; +∞ | 0.8624; 1.0000 | 0.1376 | 13.76 | -8.76 | 5.574 | |||
1.0000 | χ2 = 35.091 |
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