Unimodal Behavior of the Negative Beta Binomial Distribution

Authors

  • Cicero Carlos Felix Oliveira IFCE - CAMPUS CRATO e UFRPE
  • Claudio T Cristino UFRPE
  • Pedro F de Lima UFRPE

Keywords:

Negative binomial beta distribution, Negative Binomial Distribution, Mode

Abstract

This article presents a study on the behavior of the Negative Binomial Beta distribution regarding their mode. Applies this study that when the distribution is given by a hypergeometric distribution equivalent multiplied by the likelihood of the Negative Binomial distribution. This representation, which does not ordinarily appear in the literature, is an interesting view of the Negative Binomial Beta distribution, both in didactic terms, as computational. This distribution is obtained from a Bayesian considerations. Thus, two analyzes are done on a comparative basis: the first using the idea of Holgate (1970) which is also observed in Hassan and Bilal (2008) article, and the second using the idea that mode is a maximum point regarding the distribution,
this calculation is done using the software free R-software and at the same time is observed graphically.

Author Biography

Cicero Carlos Felix Oliveira, IFCE - CAMPUS CRATO e UFRPE

Professor de Estatística do IFCE - Campus Crato.

Aluno de doutorado de Biometria e Estatística Aplicada.

 

References

F. EGGENBERGER AND G. POLYA, Z. ANGEW. Math. Mech, Uber die Statistik verketteter vorgange, 1(1923), 279-289.

HASSAN, ANWAR AND BILAL, SHEIKH. On Estimation of Negative Polya-Eggenberger Distribution and Its Applications. J. Ksiam, vol. 12, $N^o$ 2, 81 - 95, 2008.

JOHNSON, N. L.; KOTZ, S. AND ADRIENNE, W. K. Univariate Discrete Distributions. Third edition, Wiley, New York, 2005.

MADEIRA, A. P. C. A Distribuição beta binomial negativa. 2009. 81 p. Dissertação (Mestrado em Estatística e Experimentação Agropecuária) - Universidade Federal de Lavras, Lavras, MG.

P. HOLGATE, B. Biometrika, The modality of compound Poisson distribution, 57 (1970), 665-667.

R CORE TEAM. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. 2013. ISBN 3-900051-07-0, URL http://www.R-project.org/

TEERAPABOLARN, K. (2008). Poisson approximation to the beta-negative binomial distribution}, International Journal of Contemporary Mathematical Sciences, vol. 3, Nº 3 457-461.

Published

11-11-2015

How to Cite

Oliveira, C. C. F., Cristino, C. T., & de Lima, P. F. (2015). Unimodal Behavior of the Negative Beta Binomial Distribution. Sigmae, 4(2), 1–5. Retrieved from https://publicacoes.unifal-mg.edu.br/revistas/index.php/sigmae/article/view/226

Issue

Section

Probability and Statistics