@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 $L(n)<j<L(n+1)$ and $Z_j$ belongs to the rectangle $(X(n)-a,X(n))\times (Y(n)-b_1,Y(n)+b_2)$, where $a\,,b_1,\,b_2>0$. 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},
}