Title: Asymptotic generalized bivariate extreme with random index,
Abstract: In many biological, agricultural, military activity problems and in some
quality control problems, it is almost impossible to have a fixed sample size,
because some observations are always lost for various reasons. Therefore, the
sample size itself is considered frequently to be a random variable (rv). The
class of limit distribution functions (df's) of the random bivariate extreme
generalized order statistics (GOS) from independent and identically distributed
RV's are fully characterized. When the random sample size is assumed to be
independent of the basic variables and its df is assumed to converge weakly to
a non-degenerate limit, the necessary and sufficient conditions for the weak
convergence of the random bivariate extreme GOS are obtained. Furthermore, when
the interrelation of the random size and the basic rv's is not restricted,
sufficient conditions for the convergence and the forms of the limit df's are
deduced. Illustrative examples are given which lend further support to our
theoretical results.