On the ARL of CUSUM in multinomial models

Shangchen Yao; Mohammad Khan

Makale detayları

On the ARL of CUSUM in multinomial models

Yazarlar:

Shangchen Yao | Mohammad Khan

Yayıncı:

Hacettepe University

Ana Başlıklar:

Statistical Analysis

Dergi:

Hacettepe Journal of Mathematics and Statistics Vol.53 Issue 5, pp.1484-1496

Belge Tipi:

Makale

Yayın Tarihi:

10/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001329423

pISSN:

2651-477X

Anahtar kelimeler:

Özet:

 There is no known closed form expression for the average sample number, also known as average run length, of a multivariate CUSUM procedure N  min M_1, M_2,cdots, M_m for mgeq 3, where M_i are univariate CUSUM procedures. The problem is generally considered to be hopelessly complicated for any model. In this paper, for the multinomial model we show, however, that there is a rather simple closed form expression for the average run length of N with an elementary proof. A bit surprisingly, we further show that the average run length of N is related to the average run lengths of M_i the same way as the capacitance of a series network of capacitors is related to the capacitances of its own components.

 There is no known closed form expression for the average sample number, also known as average run length, of a multivariate CUSUM procedure N  min M_1, M_2,cdots, M_m for mgeq 3, where M_i are univariate CUSUM procedures. The problem is generally considered to be hopelessly complicated for any model. In this paper, for the multinomial model we show, however, that there is a rather simple closed form expression for the average run length of N with an elementary proof. A bit surprisingly, we further show that the average run length of N is related to the average run lengths of M_i the same way as the capacitance of a series network of capacitors is related to the capacitances of its own components.

 There is no known closed form expression for the average sample number, also known as average run length, of a multivariate CUSUM procedure N  min M_1, M_2,cdots, M_m for mgeq 3, where M_i are univariate CUSUM procedures. The problem is generally considered to be hopelessly complicated for any model. In this paper, for the multinomial model we show, however, that there is a rather simple closed form expression for the average run length of N with an elementary proof. A bit surprisingly, we further show that the average run length of N is related to the average run lengths of M_i the same way as the capacitance of a series network of capacitors is related to the capacitances of its own components.

 There is no known closed form expression for the average sample number, also known as average run length, of a multivariate CUSUM procedure N  min M_1, M_2,cdots, M_m for mgeq 3, where M_i are univariate CUSUM procedures. The problem is generally considered to be hopelessly complicated for any model. In this paper, for the multinomial model we show, however, that there is a rather simple closed form expression for the average run length of N with an elementary proof. A bit surprisingly, we further show that the average run length of N is related to the average run lengths of M_i the same way as the capacitance of a series network of capacitors is related to the capacitances of its own components.

Makale detayları

On the ARL of CUSUM in multinomial models

Yazarlar:

Shangchen Yao | Mohammad Khan

Yayıncı:

Hacettepe University

Ana Başlıklar:

Statistical Analysis

Dergi:

Hacettepe Journal of Mathematics and Statistics Vol.53 Issue 5, pp.1484-1496

Belge Tipi:

Makale

Yayın Tarihi:

10/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001329423

pISSN:

2651-477X

Average run length

multivariate CUSUM

Markov chain

sequential change point detection

Sayı

Makale detayları

On the ARL of CUSUM in multinomial models

Yazarlar: Shangchen Yao | Mohammad Khan

Yayıncı: Hacettepe University

Ana Başlıklar: Statistical Analysis

Dergi: Hacettepe Journal of Mathematics and Statistics Vol.53 Issue 5, pp.1484-1496

Belge Tipi: Makale

Yayın Tarihi: 10/2024

Belge Dili: İngilizce

Document ID (Org No.): 2001329423

pISSN: 2651-477X

Average run length

multivariate CUSUM

Markov chain

sequential change point detection

Sayı

Yazarlar:

Shangchen Yao | Mohammad Khan

Yayıncı:

Hacettepe University

Ana Başlıklar:

Statistical Analysis

Dergi:

Hacettepe Journal of Mathematics and Statistics Vol.53 Issue 5, pp.1484-1496

Belge Tipi:

Makale

Yayın Tarihi:

10/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001329423

pISSN:

2651-477X