Asymptotic behavior of the ratio of weak kth records

Abstract

Let $W_0^{(k)},W_1^{(k)},\dots$ be weak kth records obtained from a sequence of independent variables with a common discrete distribution. In this paper, asymptotic properties of $W_{n+m}^{(k)}/W_n^{(k)}$ as $n\to \infty$ are discussed by using the theory of regular variation.

Keywords:

• Weak kth records
• Ratio of weak kth records
• Limit laws
• Theory of regular variation
• Discrete distributions