Bayesian Estimation of n in a Binomial Distribution

Abstract

Let X Sub 1,X Sub 2,...,X, be a random sample of size r from a binomial distribution b(n, 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.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1987
Accession Number
ADA196623

Entities

People

  • Raymond M. Shirven
  • Ronald B. Sindler
  • Victor K. Tang

Organizations

  • Center for Naval Analyses

Tags

Communities of Interest

  • Ground and Sea Platforms

DTIC Thesaurus Topics

  • Availability
  • Bayesian Networks
  • Binomials
  • Classification
  • Coefficients
  • Computational Science
  • Computer Programs
  • Equations
  • Estimators
  • Intervals
  • Navy
  • Probability
  • Probability Distributions
  • Random Variables
  • Security
  • Statistical Samples
  • Virginia

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Statistical inference.

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference