The Continuous Time Bayes' Sequential Procedure for Estimating the Arrival Rate of a Poisson Process and Large Sample Properties.

Abstract

Let X(t), t > or = 0, be a homogeneous Poisson process with arrival rate Theta. Sequential estimation procedures (sigma, Theta bar sub sigma) are considered with loss due to estimation of L(Theta, Theta bar) = 1/Theta (Theta-Theta bar)squared, and sampling costs involving both time and arrival costs. In this context the Bayes', sequential procedure is obtained in a simple computable form. The large sample properties of the procedure are then studied when Theta is fixed but unknown, and the Bayes' stopping rule tau is shown to be asymptotically equivalent to the best fixed sample size procedure when Theta is known. Asymptotic normality of the Bayes' sequential estimator Theta bar sub tau of Theta is also shown. (Author)

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1977
Accession Number
ADA042729

Entities

People

  • C. P. Shapiro
  • Robert Wardrop

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Asymptotic Normality
  • Computations
  • Identities
  • Inequalities
  • Markov Processes
  • Mathematics
  • Normality
  • North Carolina
  • Probability
  • Random Variables
  • Sampling
  • Sequences
  • Statistical Algorithms
  • Statistical Analysis
  • Statistics
  • United States
  • Wisconsin

Fields of Study

  • Mathematics

Readers

  • Statistical inference.