Generating Large Sequences of Normal Maxima via Record Values

Abstract

In our recent paper [4], algorithms for generating normal record values were developed. The developed algorithms were faster and more efficient than currently existing algorithms for generating normal record values. Algorithm 2.2, presented in this paper, is the most efficient algorithm among the algorithms studied in [4]. It allows generating “long” sequences of record values (up to two billion record values). In the present paper, two algorithms for generating normal maxima are proposed, one of which is based on algorithm 2.2. It also allows the generation of maxima taken from “large” samples. An algorithm for generating record times in a general continuous case is also proposed in the present paper.