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# Accession Number:

## ADA196623

# Title:

## Bayesian Estimation of n in a Binomial Distribution

# Descriptive Note:

## Final rept.

# Corporate Author:

## CENTER FOR NAVAL ANALYSES ALEXANDRIA VA STRIKE AND AMPHIBIOUS WARFARE RESEARCH DEPT

# Report Date:

## 1987-10-01

# Pagination or Media Count:

##
27.0

# Abstract:

## Let X Sub 1,X Sub 2,...,X, be a random sample of size r from a binomial distribution bn, p. Let x Sub 1,x Sub 2,...,x Sub r, be r-observed success counts. A method has been developed to estimate the total number of trials n from a Bayesian perspective when the probability of success p is either known or unknown. The prior distribution for n is assumed to be the discrete uniform distribution. In the case when p is unknown, p is assumed to have a beta prior distribution. The estimate for n is then the mode of the posterior distribution. Additionally, guidelines for selecting shape parameters for the beta distributions are discussed.

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#