, . n. , .
xi . xi ni. xi.
, . (8.1)
x 1, x 2, , xm , .
x 1 | x 2 | xm | |
n 1 | n 2 | nm |
. ..
, . ( ) . x 1, x 2, , xn n. I ( [min{ xi }, max{ xi }], , ). I z 0, z 1, , zk. D 1=[ z 0, z 1[, D 2= [ z 1 z 2[, , Dk =[ zk 1 zk ]. z 0 zk I . ni i - Di , Di (i =1,2,, k).
D 1 | D 2 | Dk | |
n 1 | n 2 | nk |
, (8.1).
( )
.
. F (x) .., x e >0
.
, , .. ..
.. .
, . D 1,, Dk. n i / h, h . , , .
, .
.
. , .., .. ..
8.1.
(1, 3) | (3, 5) | (5, 7) | (7, 9) | (9, 11) |
. , , ..
|
|
n =100. h 2. n 1=10/100=0.1, n 2=32/100=0.32, n 3=0.2, n 4=0.24, n 5=0.14.
:
8.1 .
F *(x) (x) F (x) 8.1 8.2 |
: 0.1/2=0.05, 0.32/2=0.16, 0.1,0.12, 0.07. 8.2 .
() .
. , .
8.2 .., , 10, .. . , .
. , .. . , , l = 1/10. , .
.. , .
( ) H 0 . ( ) , , , . . , .. 10, : .. 10, .. 9.
. K , H 0. Z=Z (X 1, , Xn), , . Z .
K . a ( a = 0.1, 0.05, 0.01), . : ( a) . V Z Vk, , Z Î Vk , H 0 , ( a): P (Z Î V k / H 0 ) = a. Vk . z Z. z Î Vk, , . H 0 . z Î V \ Vk, H 0 . V \ Vk .
|
|
H 0 : q = q 0 H 1: q <q 0. p (z / H 0 ) Z. [ z 1, +¥), P (Z ³ z 1/ H 0 ) = 1 a, P (Z < z 1/ H 0 ) = a (. 8.3).
, z 1= za Z a.
8.3 |
, (¥, za),
[ za, +¥).
. .. z Z. ( ) za. z ³ za, q = q 0 . z < za, q = q 0 ( q <q 0).
8.3 m =10 . 100 . 25 . 100 . X c , H 0 : m =10 a = 0.05 H 1 : m <10.
, m =10 , .. X m =10 . [ ], . . U a = 0.05 N [ ] u 0.05 = u 0.95 = 1.645.
U: .
u = 1.75< ua = 1.645, u , m =10 m <10. , : 0.95 , .
, . , . .
, .. P (Z Î Vk / H 0 ) = a. , .
, .. P (Z Î V\Vk / H 1 ) = b.
8.3 2
.. .. X : .. X ( ..) . H 0.
2 ( --).
.. X , , F , l ³1. .
n k = [1+3.32 lg n ] +1 (. . 8.1).
|
|
.
. (8.2)
( ).
(8.3)
.
, n
(8.4)
-- s = k l 1, k , l , , mi i - . , npi ni, . . a , . . , -- 1 a s = k l 1.
, , .
..
1) , (8.2).
2) .
3) npi (i = 1, , k) (8.3). npi ³ 5. , ( pi ). npi ³ 5.
4) (8.4) .
5) -- 1 a s = k l 1, k 3, l , 2.
6) < , a; ³ , .