Abstract
Let , be independent copies of bivariate random vector
with joint cumulative distribution function
and probability density function
. For
, the vector of order statistics of
and
, respectively, is denoted by
. Let
,
, be a new sample from
, which is independent from
. Let
be the rank of order statistics
in a new sample
and
be the rank of order statistics
in a new sample
. We derive the joint distribution of discrete random vector
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.
Acknowledgements
The authors are grateful to the Editor and anonymous reviewers for their valuable comments and suggestions which resulted in improvement of the presentation of this paper.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Supplemental data and research materials
Supplemental data for this article can be accessed at http://dx.doi.org/10.1080/02664763.2015.102370510.1080/02664763.2015.1023705.