Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

THE BIVARIATE F3-BETA DISTRIBUTION

  • Published : 2006.04.01
Download PDF
⟨ Previous Next ⟩

Abstract

A new bivariate beta distribution based on the Appell function of the third kind is introduced. Various representations are derived for its product moments, marginal densities, marginal moments, conditional densities and conditional moments. The method of maximum likelihood is used to derive the associated estimation procedure as well as the Fisher information matrix.

Keywords

References

  1. D. A-Grivas and A. Asaoka, Slope safety prediction under static and seismic loads, Journal of the Geotechnical Engineering Division, Proceedings of the American Society of Civil Engineers, 108 (1982), 713-729
  2. F. J. Apostolakis and P. Moieni, The foundations of models of dependence in probabilistic safety assessment, Reliability Engineering 18 (1987), 177-195 https://doi.org/10.1016/0143-8174(87)90097-7
  3. B. C. Arnold, E. Castillo, and J. M. Sarabia, Conditional Specification of Statistical Models, New York, Springer Verlag, 1999
  4. C. Chatfield, A marketing application of a characterization theorem, In A Modern Course on Distributions in Scientific Work, volume 2, Model Building and Model Selection (editors G. P. Patil, S. Kotz, and J. K. Ord), pp. 175-185. Dordrecht, Reidel, 1975
  5. R. W. Hoyer and L. S. Mayer, The equivalence of various objective functions in a stochastic model of electoral competition, Technical Report No. 114, Series 2, Department of Statistics, Princeton University, 1976
  6. T. P. Hutchinson and C. D. Lai, The Engineering Statistician's Guide to Continuous Bivariate Distributions, Adelaide, Australia, Rumsby Scientific Publishing, 1991
  7. S. Kotz, N. Balakrishnan, and N. L. Johnson, Continuous Multivariate Distributions, volume 1, Models and Applications(second edition), New York, John Wiley and Sons, 2000
  8. D. L. Libby and M. R. Novick, Multivariate generalized beta-distributions with applications to utility assessment, Journal of Educational Statistics 7 (1982), 271-294 https://doi.org/10.2307/1164635
  9. I. Olkin and R. Liu, A bivariate beta distribution, Statistics and Probability Letters 62 (2003), 407-412 https://doi.org/10.1016/S0167-7152(03)00048-8
  10. A. P. Prudnikov, Y. A. Brychkov, and O. I. Marichev, Integrals and Series (volumes 1, 2, and 3), Amsterdam, Gordon and Breach Science Publishers, 1986

Cited by

  1. Generalized bivariate beta distributions involving Appell’s hypergeometric function of the second kind vol.64, pp.8, 2012, https://doi.org/10.1016/j.camwa.2012.06.006
  2. Bivariate Kumaraswamy distribution: properties and a new method to generate bivariate classes vol.47, pp.6, 2013, https://doi.org/10.1080/02331888.2012.694446
  3. A Measure of Dependence Between Two Compositions vol.54, pp.4, 2012, https://doi.org/10.1111/j.1467-842X.2012.00688.x
  4. A new bivariate beta distribution vol.51, pp.2, 2017, https://doi.org/10.1080/02331888.2016.1240681
  5. A new bivariate beta distribution of Kind-1 of Type-A vol.22, pp.1, 2019, https://doi.org/10.1080/09720510.2018.1537593