Bias-corrected maximum likelihood estimation for the beta distribution

Journal of Statistical Computation and Simulation

Volumn 58, Issue 1, 1997, Pages 21-35

  Cordeiro, Gauss M ^a   Da Rocha, Enivaldo C ^a   Da Rocha, Jacira Guiro C ^a   Cribari Neto, Francisco ^b  

^a FEDERAL UNIVERSITY OF PERNAMBUCO   (Brazil)

^b SOUTHERN ILLINOIS UNIVERSITY   (United States)

Author keywords

Asymptotic approximation; Beta distribution; Bias correction; Maximum likelihood estimation

Indexed keywords

EID: 0031333164     PISSN: 00949655     EISSN: None     Source Type: Journal    
DOI: 10.1080/00949659708811820     Document Type: Article

References (25)

1. Abell, M. L. and Braselton, J. P. (1994) The Maple V Hanbook. A. P. Professional, New York.
2. Beckman, R. J. and Tietjen, G. L. (1978) Maximum likelihood estimation for the beta distribution. Journal of Statistical Computation and Simulation, 7, 253-258.
3. Bernardo, J. M. (1976) Psi (digamma) function: algorithm AS103. Applied Statistics, 25, 315-317.
4. Bowman, K. and Shenton, L. (1992) Parameter estimation for the beta distribution. Journal of Statistical Computation and Simulation, 43, 217-228.
5. Box, M. J. (1971) Bias in nonlinear estimation (with discussion). Journal of the Royal Statistical Society B, 33, 171-201.
6. Cook, R. D., Tsai, C. -L. and Wei, B. C. (1986) Bias in nonlinear regression. Biometrika, 74, 265-274.
7. Cordeiro, G. M. and McCullagh, P. (1991) Bias correction in generalized linear models. Journal of the Royal Statistical Society B, 53, 629-43.
8. Cordeiro, G. M. (1993) Bartlett corrections and bias correction for two heteroscedastic regression models. Communications in Statistics, Theory and Methods, 22, 169-188.
9. Cordeiro, G. M. and Klein, R. (1994) Bias correction ARMA models. Statistics and Probability Letters, 19, 169-176.
10. Cox, D. R. and Snell, E. J. (1968) A general definition of residuals (with discussion). Journal of the Royal Statistical Society B, 30, 248-275.
11. DiCiccio, T. J. (1984) On parameter transformations and interval estimation. Biometrika, 71, 447-485.
12. Doornik, J. A. (1996) Object-Oriented Matrix Programming Using Ox. London: International Thompson Business Press and Oxford: http://www.nuff.ox.ac.uk/Users/ Doornik/.
13. Firth, D. (1993) Bias reduction of maximum likelihood estimates. Biometrika, 80, 27-38.
14. Gnanadesikan, R., Pinkham, R. and Hughes L. (1967) Maximum likelihood estimation of the parameters of the beta distribution from the smallest order statistics. Technometrics, 9, 607-620.
15. Lau, H. -S. and Lau, A. H. -L. (1991) Effective procedures for estimating beta distribution's parameters and their confidence intervals. Journal of Statistical Computation and Simulation, 38, 139-150.
16. Lawley, D. N. (1956) A general method for approximating to the distribution of the likelihood ratio criteria. Biometrika, 71, 233-244.
17. McCullagh, P. (1980) A rapidly convergent series for computing ψ(z) and its derivatives. Mathematics of Computation, 36, 247-250.
18. McLachlan, G. J. (1980) A note on bias correction in maximum likelihood estimation with logistic discrimination. Technometrics, 22, 621-627.
19. Paula, G. A. (1992) Bias correction for exponential family nonlinear models. Journal of Statistical Computation and Simulation, 40, 43-54.
20. Rubinstein, Y. (1991) Generating from beta distribution. Cahiers de Centre d'Etude de Recherche Operationnelle, 23, 81-86.
21. Schneider, B. E. (1978) Trigamma function: algorithm AS121. Applied Statistics, 27, 97-99.
22. Sowden, R. R. (1971) Bias and accuracy of parameter estimates in a quantal response model. Biometrika, 58, 595-603.
23. Stafford, J. E., Andrews, D.F. and Wang, Y. (1994) Symbolic computation: a unified approach to studying likelihood. Statistics and Computing, 4, 235-245.
24. Wolfram, S. (1991) Mathematics: A System for Doing Mathematics by Computer, 2nd ed. Addison-Wesley, New York.
25. Young, D. H. and Bakir, S. T. (1987) Bias correction for a generalized log-gamma regression model. Technometrics, 29, 183-191.