- . ,
= +
:
= +
, :
= +
m ,
- m .
2 = 2 + 2 + 2
+ :
D ( + ) = D = M 2 = M 2 + M 2 + 2 M =
= D + D + 2 M ( ) (1)
M ( ) (, ). (, ). ,
(, ) = M ( ).
(1) :
D ( + ) = D () + D () + 2 K ( ) (2)
- .
, , ( correlation , ), . .
, .
, . ,
, . , : M ( ) = M M = = 0.
: (, ) ≠ 0, . , .
, .
, , , : , () .
, ,
K ( ) = M ( ) = M (( - m ) ( - )),
m - . ,
K (, ) = M ( ) - m ;
,
( - m )( - ) = - m - + m
.
, . (, ) .
, , . , . , , : , , ( ).
. , ; = 2. = 0
K (, ) = M ( ) = M () = 3 dx = 0.
, , ; , = 5 2, , 1 , = 5106 2. . , - .
|
|
.
- .
, ( , r (, ) ). .
.
. -1 1:
-1 r 1
, r = 1, :
= a + b (a, b = const),
a >0; r = -1 c a <0.
.
( + t )2,
= - , = - m , t . :
M ( + )2 = M ( 2 + 2 t + t 2 2) = M 2 +2 t M ( ) + + t 2 M 2 = D + 2 tK (, ) + t 2 D .
M ( + )2 = t 2 + 2 t + (3)
= D , = K (, ), = D . , , t ( , ). , , . .
2 - ,
. ,
2(, ) D D 0,
r 2 1, , r 1 -1.
, r 2 1, . . r -1 1.
. , , . . t = - a t 2 + 2 t + . (3) :
M ( + )2 = 0
:
- a = 0
= a + b.
, , . ( r), , b = 0, . . = a . , , r -1, a < 0, 1, a > 0.
, : r 2 , . r > 0, , ; r < 0, ( ).