• Corpus ID: 251564101

On the recent-$k$-record of discrete random variables

@inproceedings{Li2022OnTR,
  title={On the recent-\$k\$-record of discrete random variables},
  author={Anshui Li},
  year={2022}
}

• A. Li
• Published 14 August 2022
• Mathematics

Let X 1 , X 2 , · · · be a sequence of i.i.d random variables which are supposed to be observed in sequence. The n th value in the sequence is a k − record value if exactly k of the first n values (including X n ) are at least as large as it. Let R k denote the ordered set of k -record values. The famous Ignatov’s Theorem states that the random sets R k ( k = 1 , 2 , · · · ) are independent with common distribution. We introduce one new record named recent − k − record (RkR in short) in this paper: X n is a j -RkR if there are exactly j values at least as large as X n in X n − k , X n − k +1 , · · · , X n − 1 . It turns out that RkR brings many interesting problems and some novel properties such as prediction rule and Poisson approximation which are proved in this paper. One application named ”No Good Record” via the Lov´asz Local Lemma is also provided. We conclude this paper with some possible connection with scan statistics.