Geometric Distribution of Order <i>k</I> With a Reward

Abstract

In this paper, we introduce and study geometric distribution of order k with a reward. In a sequence of binary trials, suppose that each time a success occurs a random reward is received. The distribution of the number of trials until the sum of consecutive rewards is equal to or exceeds the level k is called geometric distribution of order k with a reward. We obtain expressions for the probability mass function of this distribution. (C) 2014 Elsevier B.V. All rights reserved.