Estimation of Beta Regression Model with Applied Study
DOI:
https://doi.org/10.24297/jam.v12i11.10Keywords:
Beta distribution, Maximum likelihood estimation, Bayesian estimation, Regression.Abstract
This paper proposes a regression model where the dependent variable is beta distributed. Therefore the observations of the dependent variable must fall within (0,1) interval. This beta regression model produces two regression coefficients: one for the model of the mean and one for the model of the dispersion. Parameter estimation is performed by maximum likelihood and Bayesian method. Finally, numerical study is presented.Downloads
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Applied Statistics vol. 42, issue 2.
2. Bury, K. (1999) Statistical Distributions in Engineering. New York: Cambridge University Press.
3. Cepeda, E. &Gamerman, D. (2005), Bayesian methodology for modeling parameters in the two parameter
exponential family, Estadistica 57, 93-105.
4. CoxeStefany (2012) Regression Analysis of Grouped Counts and Frequencies using the Generalized Linear
Model, ph.D, Arizona State University.
5. El-Eqully L., Measuring of Financial Risk to Off-Balance Sheet Activities and the Effecting on Auditors Going
Concern Opinions, Unpublished PhD, Tanta University, Faculty of Commerce, 2009.
6. Ferrari S. L. P., Cribari-Neto, F. (2004) Beta regression for modeling rates and proportions, Journal of applied
statistics, 31(7), 799-815.
7. Figueroa-Zuniga, J., Arellano-Valle, R.B. &S.L.p., F. (2013), Beta mixed regression: a Bayesian perspective,
Computational statistics and Data Analysis. 61, 137-147.
8. Gelman, A., Carlin, J.B., Stern, H. S., Dunson, D.B., (2014) Bayesian Data Analysis 3rd edn. CRC press, London.
9. Hviid M, Villadsen B (1995) Beta distributed market shares in a spatial model with an application to the market for
audit services. Review of industrial Organization, 10 ,737-747.
10. Johnson NL, Kotz S, Balakrishnan N (1995) Continuous univariate distributions, volumes 1 and 2. New York:
John Wiley & Sons, Inc.
11. Krishnamoorhy, K., (2006) Handbook of statistical Distributions with Applications, Chapman & Hall. CRC, Florida.
12. Patel, S. Balic, A. ,and Bwakira, L., Measuring Transparency and Disclosure at Firm-Level in Emerging
Markets,Emerging Markets Review,3, (2002), 325-337.
13. Patel. S. and Dallas G., Transparency and Disclosure: Overview of Methodology and Study Results-United
States, Standard & poor's Transparency and Disclosure, 2002.
14. Silva, G. L., Soares P., Marques S., Dias, M. I., Oliveira M. M., and Borges J. G., (2015) A Bayesian Modeling of
wildfires in Portugal. Dynamics, Games and science, ch. 37, sprin international publishing Switzerland, editors:
J.P. Bourguignon et al (eds, pp.723-733)
15. Simas, A., Barreto-Souza, W.& Rocha, A.(2010), Improved estimators for a general class of beta regression
models, Computational statistics & Data Analysis 54(2), 348-366.
16. Yan, X. and Su, X., G., (2009) Regression Analysis, theory and computing, world scientific publishing co., Uk.
Published
2016-12-30
How to Cite
Salem, H. A. E. R. (2016). Estimation of Beta Regression Model with Applied Study. JOURNAL OF ADVANCES IN MATHEMATICS, 12(11), 6773–6777. https://doi.org/10.24297/jam.v12i11.10
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