## The Annals of Statistics

### Bayes Sequential Estimation of a Poisson Rate: A Discrete Time Approach

#### Abstract

This paper provides explicit solutions to the problem of estimating the arrival rate $\lambda$ of a Poisson process using a Bayes sequential approach. The loss associated with estimating $\lambda$ by $d$ is assumed to be of the form $(\lambda - d)^2\lambda^{-p}$ and the cost of observation includes both a time cost and an event cost. A discrete time approach is taken in which decisions are made at the end of time intervals having length $t$. Limits of the procedures as $t$ approaches zero are discussed and related to the continuous time Bayes sequential procedure.

#### Article information

Source
Ann. Statist., Volume 8, Number 4 (1980), 840-844.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176345076

Digital Object Identifier
doi:10.1214/aos/1176345076

Mathematical Reviews number (MathSciNet)
MR572627

Zentralblatt MATH identifier
0463.62072

JSTOR