Skip to main content
Log in

Exact posterior computation for the binomial–Kumaraswamy model

  • Published:
Advances in Computational Mathematics Aims and scope Submit manuscript

Abstract

In Bayesian analysis, the well-known beta–binomial model is largely used as a conjugate structure, and the beta prior distribution is a natural choice to model parameters defined in the (0,1) range. The Kumaraswamy distribution has been used as a natural alternative to the beta distribution and has received great attention in statistics in the past few years, mainly due to the simplicity and the great variety of forms it can assume. However, the binomial–Kumaraswamy model is not conjugate, which may limit its use in situations where conjugacy is desired. This work provides the exact posterior distribution for the binomial–Kumaraswamy model using special functions. Besides the exact forms of the posterior moments, the predictive and the cumulative posterior distributions are provided. An example is used to illustrate the theory, in which the exact computation and the MCMC method are compared.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Andrade, J.A.A., Gosling, J.P.: Predicting rainy seasons: Quantifying the beliefs of prophets. J. Appl. Stat. 38, 183–193 (2011)

    Article  MathSciNet  Google Scholar 

  2. Andrade, J.A.A., Rathie, P.N.: On exact posterior distributions using H-functions. J. Comput. Appl. Math. 290, 459–475 (2015)

    Article  MathSciNet  Google Scholar 

  3. Andrade, J.A.A., Rathie, P.N.: Exact posterior computation in non-conjugate Gaussian location-scale parameters models. Commun. Nonlinear Sci. Numer. Simul. 53, 111–129 (2017)

    Article  MathSciNet  Google Scholar 

  4. Andrade, J.A.A., Rathie, P.N., Farias, R.B.A.: Exact Bayesian computation using H-functions. Comput. Appl. Math. 38, 2277–2293 (2018)

    Article  MathSciNet  Google Scholar 

  5. Braaksma, B.L.J.: Asymptotic expansions and analytic continuations for a class of Barnes-integrals. Compositio Math. 15, 239–341 (1964)

    MathSciNet  MATH  Google Scholar 

  6. Brychkov, Y.A., Prudnikov, A.P.: Integral Transformations of Generalized Functions. Gordon & Breach, Moscow (1989)

    MATH  Google Scholar 

  7. Fox, C.: The G and H functions as symmetrical Fourier kernels. Trans. Am. Math. Soc. 98, 395—429 (1961)

    MathSciNet  MATH  Google Scholar 

  8. Goyal, S.P.: A finite integral involving the H-function. Proc. Natl. Acad. Sci. India Sect. A 39, 201–203 (1969)

    MathSciNet  MATH  Google Scholar 

  9. Jones, M.C.: Kumaraswamy’s distribution: A beta-type distribution with some tractability advantages. Stat. Methodol. 6, 70–81 (2009)

    Article  MathSciNet  Google Scholar 

  10. Kumaraswamy, P.: A generalized probability density function for double-bounded random processes. J. Hydrol. 46(1–2), 79—88 (1980)

    Google Scholar 

  11. Luke, Y.L.: The Special Functions and Their Approximations. Academic Press, New York (1979)

    Google Scholar 

  12. Mathai, A.M., Saxena, R.K., Haubold, H.J.: The H-Function: Theory and Applications. Springer, New York (2010)

    Book  Google Scholar 

  13. O’Hagan, A., Buck, C.E., Daneshkhah, A., Eiser, J.E., Garthwaite, P.H., Jenkinson, D., Oakley, J.E. , Rakow, T.: Uncertain Judgements: Eliciting Expert Probabilities. Wiley , Chichester (2006)

    Book  Google Scholar 

  14. Springer, M.D.: The Algebra of Random Variables. Wiley, New York (1979)

    MATH  Google Scholar 

  15. Srivastava, H.M., Gupta, K.C., Goyal, S.P.: The H-Function of One and Two Variables with Applications. South Asian Publishers, New Delhi (1982)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to J. A. A. Andrade.

Additional information

Communicated by: Youssef Marzouk

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Andrade, J.A.A. Exact posterior computation for the binomial–Kumaraswamy model. Adv Comput Math 46, 80 (2020). https://doi.org/10.1007/s10444-020-09821-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10444-020-09821-y

Keywords

Mathematics Subject Classification (2010)

Navigation