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

Anshui Li

Makale detayları

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

Yazarlar:

Anshui Li

Yayıncı:

Hacettepe University

Ana Başlıklar:

Statistics

Dergi:

Hacettepe Journal of Mathematics and Statistics Vol.53 Issue 5, pp.1408-1418

Belge Tipi:

Makale

Yayın Tarihi:

10/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001329409

pISSN:

2651-477X

Anahtar kelimeler:

Özet:

 Let X_1,X_2,cdots be a sequence of independent and identically distributed random variables which are supposed to be observed in sequence. The nth 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 bf R_k denote the ordered set of k-record values. The famous Ignatovs Theorem states that the random sets bf R_kk1,2,cdots are independent with common distribution. We introduce one new record named recent-k-record in this paper: X_n is a j-recent-k-record if there are exactly j values at least as large as X_n in X_n-k,X_n-k1,cdots,X_n-1. It turns out that recent-k-record brings many interesting problems and some novel properties such as prediction rule and Poisson approximation are proved in this paper. One application named No Good Record via the Lovasz Local Lemma is also provided. We conclude this paper with some possible extensions for future work.

 Let X_1,X_2,cdots be a sequence of independent and identically distributed random variables which are supposed to be observed in sequence. The nth 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 bf R_k denote the ordered set of k-record values. The famous Ignatovs Theorem states that the random sets bf R_kk1,2,cdots are independent with common distribution. We introduce one new record named recent-k-record in this paper: X_n is a j-recent-k-record if there are exactly j values at least as large as X_n in X_n-k,X_n-k1,cdots,X_n-1. It turns out that recent-k-record brings many interesting problems and some novel properties such as prediction rule and Poisson approximation are proved in this paper. One application named No Good Record via the Lovasz Local Lemma is also provided. We conclude this paper with some possible extensions for future work.

 Let X_1,X_2,cdots be a sequence of independent and identically distributed random variables which are supposed to be observed in sequence. The nth 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 bf R_k denote the ordered set of k-record values. The famous Ignatovs Theorem states that the random sets bf R_kk1,2,cdots are independent with common distribution. We introduce one new record named recent-k-record in this paper: X_n is a j-recent-k-record if there are exactly j values at least as large as X_n in X_n-k,X_n-k1,cdots,X_n-1. It turns out that recent-k-record brings many interesting problems and some novel properties such as prediction rule and Poisson approximation are proved in this paper. One application named No Good Record via the Lovasz Local Lemma is also provided. We conclude this paper with some possible extensions for future work.

 Let X_1,X_2,cdots be a sequence of independent and identically distributed random variables which are supposed to be observed in sequence. The nth 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 bf R_k denote the ordered set of k-record values. The famous Ignatovs Theorem states that the random sets bf R_kk1,2,cdots are independent with common distribution. We introduce one new record named recent-k-record in this paper: X_n is a j-recent-k-record if there are exactly j values at least as large as X_n in X_n-k,X_n-k1,cdots,X_n-1. It turns out that recent-k-record brings many interesting problems and some novel properties such as prediction rule and Poisson approximation are proved in this paper. One application named No Good Record via the Lovasz Local Lemma is also provided. We conclude this paper with some possible extensions for future work.

Makale detayları

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

Yazarlar:

Anshui Li

Yayıncı:

Hacettepe University

Ana Başlıklar:

Statistics

Dergi:

Hacettepe Journal of Mathematics and Statistics Vol.53 Issue 5, pp.1408-1418

Belge Tipi:

Makale

Yayın Tarihi:

10/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001329409

pISSN:

2651-477X

Ignatov’s theorem

recent-k-record

Poisson approximation

the Lovász Local LemmaRecent-$k$-record

Poisson Approximation

Ignatov's theorem

the Lovàsz Local Lemma

Sayı

Makale detayları

Yazarlar: Anshui Li

Yayıncı: Hacettepe University

Ana Başlıklar: Statistics

Dergi: Hacettepe Journal of Mathematics and Statistics Vol.53 Issue 5, pp.1408-1418

Belge Tipi: Makale

Yayın Tarihi: 10/2024

Belge Dili: İngilizce

Document ID (Org No.): 2001329409

pISSN: 2651-477X

Sayı

Yazarlar:

Anshui Li

Yayıncı:

Hacettepe University

Ana Başlıklar:

Statistics

Dergi:

Hacettepe Journal of Mathematics and Statistics Vol.53 Issue 5, pp.1408-1418

Belge Tipi:

Makale

Yayın Tarihi:

10/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001329409

pISSN:

2651-477X