PARAMETER ESTIMATION AND APPLICATIONS FOR A GENERALISATION OF THE BETA‐BINOMIAL DISTRIBUTION

Research output: Contribution to journalArticleResearchpeer-review

Abstract

A three‐parameter generalisation of the beta‐binomial distribution (BBD) derived by Chandon (1976) is examined. We obtain the maximum likelihood estimates of the parameters and give the elements of the information matrix. To exhibit the applicability of the generalised distribution we show how it gives an improved fit over the BBD for magazine exposure and consumer purchasing data. Finally we derive an empirical Bayes estimate of a binomial proportion based on the generalised beta distribution used in this study.

Original languageEnglish
Pages (from-to)263-275
Number of pages13
JournalAustralian Journal of Statistics
Volume30
Issue number3
DOIs
Publication statusPublished - 1 Jan 1988
Externally publishedYes

Keywords

  • >Binomial
  • beta‐binomial
  • effective reach.
  • empirical Bayes
  • magazine reach
  • modified beta‐binomial

Cite this

@article{db19c31ee18443918e70274146b8e8e7,
title = "PARAMETER ESTIMATION AND APPLICATIONS FOR A GENERALISATION OF THE BETA‐BINOMIAL DISTRIBUTION",
abstract = "A three‐parameter generalisation of the beta‐binomial distribution (BBD) derived by Chandon (1976) is examined. We obtain the maximum likelihood estimates of the parameters and give the elements of the information matrix. To exhibit the applicability of the generalised distribution we show how it gives an improved fit over the BBD for magazine exposure and consumer purchasing data. Finally we derive an empirical Bayes estimate of a binomial proportion based on the generalised beta distribution used in this study.",
keywords = ">Binomial, beta‐binomial, effective reach., empirical Bayes, magazine reach, modified beta‐binomial",
author = "Danaher, {P. J.}",
year = "1988",
month = "1",
day = "1",
doi = "10.1111/j.1467-842X.1988.tb00621.x",
language = "English",
volume = "30",
pages = "263--275",
journal = "Australian Journal of Statistics",
issn = "0004-9581",
publisher = "Blackwell Publishing Ltd Oxford, UK",
number = "3",

}

PARAMETER ESTIMATION AND APPLICATIONS FOR A GENERALISATION OF THE BETA‐BINOMIAL DISTRIBUTION. / Danaher, P. J.

In: Australian Journal of Statistics, Vol. 30, No. 3, 01.01.1988, p. 263-275.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - PARAMETER ESTIMATION AND APPLICATIONS FOR A GENERALISATION OF THE BETA‐BINOMIAL DISTRIBUTION

AU - Danaher, P. J.

PY - 1988/1/1

Y1 - 1988/1/1

N2 - A three‐parameter generalisation of the beta‐binomial distribution (BBD) derived by Chandon (1976) is examined. We obtain the maximum likelihood estimates of the parameters and give the elements of the information matrix. To exhibit the applicability of the generalised distribution we show how it gives an improved fit over the BBD for magazine exposure and consumer purchasing data. Finally we derive an empirical Bayes estimate of a binomial proportion based on the generalised beta distribution used in this study.

AB - A three‐parameter generalisation of the beta‐binomial distribution (BBD) derived by Chandon (1976) is examined. We obtain the maximum likelihood estimates of the parameters and give the elements of the information matrix. To exhibit the applicability of the generalised distribution we show how it gives an improved fit over the BBD for magazine exposure and consumer purchasing data. Finally we derive an empirical Bayes estimate of a binomial proportion based on the generalised beta distribution used in this study.

KW - >Binomial

KW - beta‐binomial

KW - effective reach.

KW - empirical Bayes

KW - magazine reach

KW - modified beta‐binomial

UR - http://www.scopus.com/inward/record.url?scp=84985535093&partnerID=8YFLogxK

U2 - 10.1111/j.1467-842X.1988.tb00621.x

DO - 10.1111/j.1467-842X.1988.tb00621.x

M3 - Article

VL - 30

SP - 263

EP - 275

JO - Australian Journal of Statistics

JF - Australian Journal of Statistics

SN - 0004-9581

IS - 3

ER -