N4.
a(x1,...,xn) ; , .. , . , , , , -
a (2¸4) 
.
(x1,...,xn) º x - n F (z / a), a, .
1. a1 (x1,...,xn) (, ) a ( 1), 
P { a1 (x1,...,xn)£ a }³ P
2. a2 (x1,...,xn) ( ) 
,
P { a2 (x1,...,xn)³ a }³ P.
3. ( )
I (x) = (a1 (x), a2 (x)),
, a , a
P { I (x)' a } º P{ a1 (x1,...,xn)£ a £ a2 (x1,...,xn)} ³ P,
.. ( a) I (x) a - : .
. ( ) z=z (x1,...,xn), ( z = a (x1,...,xn)). . , j = j(z, a), z a ,
1) 
a;
2) j(z, a) .
- 
, :
P { f1 £j(z, a) £ f2 }³ P, (1)
(1- )/2 (1+ )/2 . (1) , a; (, ):
P { g (z, f1)£ a £ g (z, f2) }³ P.
a ( (1)), , ,
(g (z, f1), g (z, f2))
a . , (g (z, f2), g (z, f1)).
a ,
P {j(z, a) ³ f1 }³ P, f1=Q (1 - P)
|
|
|
P {j(z, a) £ f2 }³ P , f2 = Q (P),
- 
. a.
. a s 
.
x 
,..., xn - N (a, s 
).
a = a (x 
,...,xn) = 
,
N (a, 
); ,
, (2)
N (0, 1) .
j [- fp, fp ] ,
, (3)
.. fp - (1+ )/2 N (0,1); , j , (3) . (3) j (2) (3) ;
, (4)
.
, 
( 5)
I (x1,..., xn) =(a1 (x1,..., xn), a2 (x1,..., xn)), (5a)
(4) , , , , .
j (1) . F (z / a) z (F, , ). z j (z, ) º F(z / a), , [0, 1] ; f1= (1- P)/ 2, f2 = (1+P)/ 2, (4)
P { f 1 £ F (z / a) £ f 2} = P.
z .
: [ z 1(a), z 2(a)] ,
P{ z1 (a)£ z £ z2 (a)} ³ ; (6)
, z1 z2 , ..
F (z !/ a)=(1- )/ 2, F (z 2/ a)=(1+ )/ 2.
z1 (a) z2 (a) , , (6) , z 1(a) < z 2(a),:
P { z 2-1(z) £ a £ z1-1(z) } ³ ,
; , (z2-1 (z), z1-1 (z)), z, .
, , 1, , 1 . , ( 1- ) .
. (5) I(x1,..., xn), :
{ I (x1,...,xn) ' a } = ,
, a Ï I, (1- ), a Î I(x1,...,xn) , .. , x1,...,xn I .
(5) 50 n= 10 : 0.9, 0.99, 0.999 (, fp).
|
|
|
= 0.9 k =50 5,
k (1- ) = 5;
=0.99 k =50 :
1- k=1-0.9950 0.61;
=0.999 :
1- k=1-0.99950 0.05.
.
1. , k =50 ;. . =0.9 =0.99 . . . 2 - 4.
2. 50 (7) - (9) .
