Monograph ΚΑΤΑΝΟΜΕΣ ΖΩΗΣ
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Transcript of Monograph ΚΑΤΑΝΟΜΕΣ ΖΩΗΣ
, (Survival Analysis). , (censored data), , , , . , ( / life or failure or survival time), ., : , Weibull, Pareto, , . : .
- . : ( ), (, , , ), .. survival, failure life time. , . , . . , .
. , , ., , () . , . . , 100 , . , , , .
(), , (). , 60 . . . (life distributions) (, Weibull, , ..). , , .
, (life distributions) :
Weibull Pareto
, : (, , , ...) , . , , . (reliability theory).
. , , 0. ( .. 1, 2 ,, ) ( (0,)). , , . , :
: .. , .
: .. (, , ), . : .. , , , , . U (censoring time), ( ).
(censored failure time random variable), = min{,U}. , .
. , .
Hald (1949). .1.
2.
3. (failure time) 4.
(exact data). (staggered entry). (censored failure data). 3, (censoring time), 4, / . (survival data)=
T =
(right censored data) (left censored data) (interval censored data)
(Right Censored Data) . , . , Ui ( ). .. Xi = min{Ti,Ui} (failure indicator) :i =
. , (censoring indicator) :ci =
(Left Censored Data) , . , Ui ( ). .. Xi = max{Ti, Ui} (failure indicator) :i =
.
: ( ). Stanford ( ). , . (left-censored observations). ( ). , , (right-censored observations).
(Interval Censored Data)
. , . , . Li, Ri (Li < Ri), Ti (Li, Ri).
1: . 2: ( ) . 3 .
(Truncated Data)
, ( ), . : : ( , . : , . , , . : ( - failure) , . : , , . .
n :(T1, U1), (T2, U2), , (Tn, Un) Ui ( ) Ti i . 3 () :
(Type I Censoring)
(Type II Censoring)
(Random Censoring)
T (Type I Censoring)
Ui . .. , 2 (Ui=2). , U=Ui ( i). ( ), / . , , U ( ). : ( - ). 100 (U = 10). ( > U =10 ). .
, , ( ) Ui. .
: ( ??? - ).
( D.J. Bartholomew) : ( ). 31 . 31 . :/ // i Ui
111-13-281
221---71
322-12-5170
42---60
521-23-3341
631-27-2731
731-14-1431
81-25-2430
92-6-429
1010---21
1 () U1=81 , ).
(31-) 81 . 2 U2=71 ( ). .. Xi = min{Ti,Ui} (failure indicator) :i =
. , 10 , :
X1 = min{T1,U1} = min{2,81} = 2 1=1X2 = min{T2,U2} = min{-,71} = 71 1=0X3 = min{T3,U3} = min{51,70} = 51 1=1X4 = min{T4,U4} = min{-,60} = 60 1=0X5 = min{T5,U5} = min{33,41}= 33 1=1X6 = min{T6,U6} = min{27,31}= 27 1=1X7 = min{T7,U7} = min{14,31}= 14 1=1X8 = min{T8,U8} = min{24,30}= 24 1=1X9 = min{T9,U9} = min{4,29} = 4 1=1X10 = min{T10,U10}= min{-,21} = 21 1=0 :
2, 71+, 51, 60+, 33, 27, 14, 24, 4, 21+ I (Type I Censoring)
Ui = T(r), r . .. 4/6 . . . , rN, r0, (t=T2) , (t=T2+). , 3, t>0, (t=T3), (t=T3+).
, . , . & :
( ) Ui, Ti. 1 : Ui ( 2 ), Ti ( ).
2 : Ui / , Ui Ti .
, . . , , .. , Ui Ti. . U U : U , , U . & (informative censoring) : ( ) Ui Ti.
& :
, , , . , , . Weibull, , ..
( )
0
( )
T
T
T
T
..
2+
3+
1
t=0
..
:
Ui Ti
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