Large Sample Properties of the Bayes' Sequential Procedure for Estimating the Arrival Rate of a Poisson Process with Invariant Loss.

Abstract

Let W sub n, n=0,1,..., be the time until the nth arrival of a Poisson process with rate Theta. Using invariant loss L(Theta, Theta bar) =1/theta (Theta-Theta bar) squared and sampling costs involving cost per arrival and cost per unit time, the Bayes' sequential procedure (N*, Theta bar sub N*) is derived. The large sample properties of the procedure are then studied in the classical framework, and N*, the stopping time, is shown to be asymptotically equivalent to n*, the best fixed sample size procedure when Theta is known. Asymptotically normality of the sequential estimator Theta bar sub N* is also shown. (Author)

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1977
Accession Number
ADA042726

Entities

People

  • C. P. Shapiro
  • Robert Wardrop

Organizations

  • University of Wisconsin–Madison

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Communities of Interest

  • Materials and Manufacturing Processes

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  • Asymptotic Normality
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  • Random Variables
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Fields of Study

  • Mathematics

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  • Statistical inference.