The trivariate extremes based on a random sample size

Abstract EN

In this paper, the class of the limit distribution functions (d.f.’s) of the trivariate extreme order statistics (upper–upper–upper (u–u–u), or upper–upper–lower (u–u–l)) with random sample size, which is assumed to be independent of all basic random variables (r.v.’s), is fully characterized.

The necessary and sufficient conditions for the weak convergence ( ) of the distributions of the trinal vectors of the extremes with random sample sizes are obtained.

Finally, an illustrative example is given.