ON THE LIMIT DISTRIBUTION OF THE EXTREMES OF A RANDOM NUMBER OF INDEPENDENT RANDOM-VARIABLES

This paper deals with the weak convergence of the r-th ((n - r)-th) order statistics of n independent identically distributed (i.i.d.) random variables (r.v.'s) X1,X2,...,Xn, where the sample size n is a positive integer valued r.v.vn and r is a positive fixed integer. When the interrelation of the basic variables X1,X2,... and vn is not restricted and the normalizing constants do not contain the random size vn, sufficient conditions of convergence and the limit forms of the distribution functions (d.f.'s) are obtained. © 1990.