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• Ranked Set Sampling (RSS)
(Patil
RSS
(Mc Intyre 1952)
RSS
Takahasi-Wakimoto(1968)
RSS
X1,X2, …,Xn
X1,x2, …,Xn are i.i.d. f(x)
•
x11 x21 . . . xm1
. . . . . .
. . . . . .. . . . . .
x1m x2m . . . xmm
•
•
x(1)1 x(2)1 . . . . . . x(m)1
x(1)2 x(2)2 . . . . . . x(m)2
. . . . . . ..... . . ...
x(1)m x(2)m . . x(m)m
x(1)1
x(2)1
x(2)2
. x(m)m
RSS
m
x(1)1 , x(2)2, x(3)3 ….. x(m)m
m
k
n=km
x1(1)1 , x1(2)2, x1(3)3 ….. x1(m)m
x2(1)1 , x2(2)2, x2(3)3 ….. x2(m)m
x3(1)1 , x3(2)2, x3(3)3 ….. x3(m)m
………………………………………………
xk(1)1 , xk(2)2, xk(3)3 ….. xk(m)m
.m
(balanced )
Mathematical Manipulations
variance