Let
(
X
k
,Y
k
), k=1,2,…,n, be independent copies of bivariate random vector
(X,Y)
with joint cumulative distribution function
F(x,y)
and probability density function
f(x,y)
. For
1≤r,s≤n
, the vector of order statistics of
X
1:n
≤X
2:n
≤⋯≤X
n:n
and
Y
1:n
≤Y
2:n
≤⋯≤Y
n:n
, respectively, is denoted by
(
X
r:n
,Y
s:n
). Let
(
X
n+i
,Y
n+i
),
i=1,2,…,m
, be a new sample from
F(x,y)
, which is independent from
(
X
k
,Y
k
), k=1,2,…,n. Let
ξ
1
be the rank of order statistics
X
r:n
in a new sample
X
n+1
,X
n+2
,…,X
n+m
and
ξ
2
be the rank of order statistics
Y
s:n
in a new sample
Y
n+1
,Y
n+2
,…,Y
n+m
. We derive the joint distribution of discrete random vector
(
ξ
1
,ξ
2
) and a general scheme wherein the distributions of new and old samples are different is considered. Numerical examples for given well-known distribution are also provided.
