@article {STMAZ.05880180, author = {Bairamov, I. and Stepanov, A.}, title = {Numbers of near bivariate record-concomitant observations.}, year = {2011}, journal = {Journal of Multivariate Analysis}, volume = {102}, number = {5}, issn = {0047-259X}, pages = {908-917}, publisher = {Elsevier Science (Academic Press), San Diego, CA}, doi = {10.1016/j.jmva.2011.01.007}, abstract = {Let $Z_1=(X_1,Y_1)$, $Z_2=(X_2,Y_2)$, \dots be independent copies of the bivariate random vector $Z=(X,Y)$ with continuous distribution function. The sequence of record values $X(n)$ and record times $L(n)$ is defined by $L(1)=1$, $L(n+1)=\min\{j:\,j>L(n), X_j>X_{L(n)}\}$, $X(n)=X_{L(n)}$, $n\ge 1$. The sequence of record values $X(n)$ induces the sequence of their concomitants $Y(n)=Y_i$ if $X_i=X(n)$. The bivariate record-concomitant observations are $Z(n)=(X(n),Y(n))$. $Z_j=(X_j,Y_j)$ is called a near $n$\,th bivariate record-concomitant observation if $L(n)0$. The number of near $n$\,th bivariate record-concomitant observations is denoted by $\xi_n$. In this paper the probability mass function $P(\xi_n=k)$, $k\ge 0$, is computed and the asymptotic behavior of $\xi_n$ as $n$ increases is determined under different conditions. Various examples are given. New simulation techniques for generating bivariate record-concomitant observations, the number of near record observations and the number of near bivariate record-concomitant observations conclude this article.}, reviewer = {Michael Falk (W\"urzburg)}, msc2010 = {62G32 (60G70)}, identifier = {1233.62109}, }