# Bayes optimal stopping of a homogeneous poisson process under linex loss function and variation in the prior

Marek Męczarski; Ryszard Zieliński

Applicationes Mathematicae (1997)

- Volume: 24, Issue: 4, page 457-463
- ISSN: 1233-7234

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topMęczarski, Marek, and Zieliński, Ryszard. "Bayes optimal stopping of a homogeneous poisson process under linex loss function and variation in the prior." Applicationes Mathematicae 24.4 (1997): 457-463. <http://eudml.org/doc/219185>.

@article{Męczarski1997,

abstract = {A homogeneous Poisson process (N(t),t ≥ 0) with the intensity function m(t)=θ is observed on the interval [0,T]. The problem consists in estimating θ with balancing the LINEX loss due to an error of estimation and the cost of sampling which depends linearly on T. The optimal T is given when the prior distribution of θ is not uniquely specified.},

author = {Męczarski, Marek, Zieliński, Ryszard},

journal = {Applicationes Mathematicae},

keywords = {prior distribution uncertainty; homogeneous Poisson process; LINEX loss function; LINEX loss},

language = {eng},

number = {4},

pages = {457-463},

title = {Bayes optimal stopping of a homogeneous poisson process under linex loss function and variation in the prior},

url = {http://eudml.org/doc/219185},

volume = {24},

year = {1997},

}

TY - JOUR

AU - Męczarski, Marek

AU - Zieliński, Ryszard

TI - Bayes optimal stopping of a homogeneous poisson process under linex loss function and variation in the prior

JO - Applicationes Mathematicae

PY - 1997

VL - 24

IS - 4

SP - 457

EP - 463

AB - A homogeneous Poisson process (N(t),t ≥ 0) with the intensity function m(t)=θ is observed on the interval [0,T]. The problem consists in estimating θ with balancing the LINEX loss due to an error of estimation and the cost of sampling which depends linearly on T. The optimal T is given when the prior distribution of θ is not uniquely specified.

LA - eng

KW - prior distribution uncertainty; homogeneous Poisson process; LINEX loss function; LINEX loss

UR - http://eudml.org/doc/219185

ER -

## References

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- N. Ebrahimi, (1992), An optimal stopping time for a power law process, Sequential Anal. 11, 213-227. Zbl0766.62049
- M. Męczarski and R. Zieliński (1991), Stability of the Bayesian estimator of the Poisson mean under the inexactly specified gamma prior, Statist. Probab. Lett. 12, 329-333.
- M. Męczarski and R. Zieliński (1997), Stability of the posterior mean in linear models: an admissibility property of D-optimum and E-optimum designs, ibid., to appear. Zbl0902.62084
- S. Sivaganesan and J. O. Berger (1989), Ranges of posterior measures for priors with unimodal contaminations, Ann. Statist. 17, 868-889. Zbl0724.62032
- A. Zellner (1986), Bayesian estimation and prediction using asymmetric loss functions, J. Amer. Statist. Assoc. 81, 446-451. Zbl0603.62037

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