Weak kth records from geometric distribution and some characterizations

Abstract

Let $(W_n^{(k)}, n\ge 0)$ be weak kth records from the geometric distribution. For $k\ge 2,$ $s\ge 1$ we prove that the regression $\mathrm{E}(W_{n+s}^{(k)}-W_n^{(k)}|W_n^{(k)})$ is constant iff n = 0. We also obtain characterizations of the geometric distribution based on partial independence of $W_0^{(k)}$ and $W_s^{(k)}-W_0^{(k)}$.

Keywords:

• Weak kth records
• regression
• independence
• discrete distribution
• geometric distribution
• characterizations

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G30
• 62G08
• 62E10
• 60E05