Second order approximations in sequential point estimation of the probability of zero in Poisson distribution

Eisa MAHMOUDI; Mohammad HATAMI KAMIN

Makale detayları

Second order approximations in sequential point estimation of the probability of zero in Poisson distribution

Yazarlar:

Eisa MAHMOUDI | Mohammad HATAMI KAMIN

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2013 Vol.37 Issue 4, pp.719-731

Belge Tipi:

Makale

Yayın Tarihi:

3/2013

Belge Dili:

Türkçe

Document ID (Org No.):

2000747585

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Anahtar kelimeler:

Özet:

 

In the analysis of the count data, the Poisson model becomes  overtly restrictive in the case of over-dispersed or under-dispersed  data.  When count data are under-dispersed, specific models such as  generalized linear models (GLM) are proposed.  Other examples are the  zero-inflated Poisson model (ZIP) and zero-truncated Poisson model  (ZTP), which have been used in literature to deal with an excess or  absence of zeros in count data.  Thus having a knowledge of the  probability of zeros and its estimation in Poisson distribution can be  significant and useful.    Some estimation problems with unknown parameter cannot attain minimum  risk where the sample size is fixed.  To resolve this captivity,  working with a sequential sampling procedure can be useful.  In this  paper, we consider sequential point estimation of the probability of  zero in Poisson distribution.  Second order approximations to the  expected sample size and the risk of the sequential procedure are  derived as the cost per observations tends to zero.  Finally, a  simulation study is given.

 

In the analysis of the count data, the Poisson model becomes  overtly restrictive in the case of over-dispersed or under-dispersed  data.  When count data are under-dispersed, specific models such as  generalized linear models (GLM) are proposed.  Other examples are the  zero-inflated Poisson model (ZIP) and zero-truncated Poisson model  (ZTP), which have been used in literature to deal with an excess or  absence of zeros in count data.  Thus having a knowledge of the  probability of zeros and its estimation in Poisson distribution can be  significant and useful.    Some estimation problems with unknown parameter cannot attain minimum  risk where the sample size is fixed.  To resolve this captivity,  working with a sequential sampling procedure can be useful.  In this  paper, we consider sequential point estimation of the probability of  zero in Poisson distribution.  Second order approximations to the  expected sample size and the risk of the sequential procedure are  derived as the cost per observations tends to zero.  Finally, a  simulation study is given.

Makale detayları

Second order approximations in sequential point estimation of the probability of zero in Poisson distribution

Yazarlar:

Eisa MAHMOUDI | Mohammad HATAMI KAMIN

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2013 Vol.37 Issue 4, pp.719-731

Belge Tipi:

Makale

Yayın Tarihi:

3/2013

Belge Dili:

Türkçe

Document ID (Org No.):

2000747585

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Poisson distribution

regret

second-order approximations

sequential estimation

Sayı

Makale detayları

Second order approximations in sequential point estimation of the probability of zero in Poisson distribution

Yazarlar: Eisa MAHMOUDI | Mohammad HATAMI KAMIN

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2013 Vol.37 Issue 4, pp.719-731

Belge Tipi: Makale

Yayın Tarihi: 3/2013

Belge Dili: Türkçe

Document ID (Org No.): 2000747585

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

Poisson distribution

regret

second-order approximations

sequential estimation

Sayı

Yazarlar:

Eisa MAHMOUDI | Mohammad HATAMI KAMIN

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2013 Vol.37 Issue 4, pp.719-731

Belge Tipi:

Makale

Yayın Tarihi:

3/2013

Belge Dili:

Türkçe

Document ID (Org No.):

2000747585

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098