• Corpus ID: 251564101

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

  title={On the recent-\$k\$-record of discrete random variables},
  author={Anshui Li},
  • 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… 



On independence of $k$-record processes: Ignatov's theorem revisited

For an infinite sequence of independent and identically distributed Ž . i.i.d. random variables, the k-record process consists of those terms that are the kth largest at their appearance. Ignatov’s

Probabilities for a Generalized Birthday Problem

Abstract Let 1's and M- 0's be randomly arranged in a row. Saperstein [11] defines the random variable k* m to be the maximum number of 1's within any m consecutive positions in the arrangement, and

Record sequences and their applications

Two moments su ce for Poisson approx-imations: the Chen-Stein method

Convergence to the Poisson distribution, for the number of occurrences of dependent events, can often be established by computing only first and second moments, but not higher ones. This remarkable

Ignatov's theorem: a new and short proof

The present paper contains an elementary and short proof for the case where the underlying distribution function F is discrete, and then extends the result to general F.


A general set of distribution-free conditions is described under which an i.i.d. sequence of random variables is preserved under optional skipping. This work is motivated by theorems of J. L. Doob

Longest increasing subsequences: from patience sorting to the Baik-Deift-Johansson theorem

We describe a simple one-person card game, patience sorting. Its analysis leads to a broad circle of ideas linking Young tableaux with the longest increasing subsequence of a random permutation via

Scan statistics on graphs

Scan statistics are used in spatial statistics and image analysis to detect regions of unusual or anomalous activity. A scan statistic is a maximum (or minimum) of a local statistic—one computed on a

Spatial Scan Statistics: Models, Calculations, and Applications

A common problem in spatial statistics is whether a set of points are randomly distributed or if they show signs of clusters or clustering. When the locations of clusters are of interest, it is