Generalized Sooner Waiting Time Problems in a Sequence of Trinary Trials

Abstract

Let {xi(n), n >= 1} be a sequence of independent trials with three possible outcomes 0, 1, 2 labeled as failure, success of type I and success of type II, respectively. Suppose that at each time a success of type I (type II) occurs in {xi(n), n >= 1} a random reward of type I (type II) is received. We obtain distributions of the number of trials until either the sum of consecutive rewards of type I is equal to or exceeds the level k(1) or the sum of consecutive rewards of type II is equal to or exceeds the level k(2) under two different schemes. (C) 2016 Elsevier B.V. All rights reserved.