619
Views
1
CrossRef citations to date
0
Altmetric
Articles

Bayesian analysis for the Lomax model using noninformative priors

, &
Pages 61-68 | Received 09 Nov 2021, Accepted 02 Oct 2022, Published online: 14 Oct 2022

References

  • Atkinson, A. B., & Harrison, A. J. (1978). Distribution of personal wealth in Britain. Cambridge University Press.
  • Bain, L. J., & Engelhardt, M. (1992). Introduction to probability and mathematical statistics. PWSKENT Publishing Company.
  • Berger, J. O., & Bernardo, J. M. (1992). Ordered group reference priors with application to the multinomial problem. Biometrika, 79(1), 25–37. https://doi.org/10.1093/biomet/79.1.25
  • Berger, J. O., Bernardo, J. M., & Sun, D. C. (2009). The formal definition of reference priors. The Annals of Statistics, 37(2), 905–938. https://doi.org/10.1214/07-AOS587
  • Bernardo, J. M. (1979). Reference posterior distributions for Bayesian inference (with discussion). Journal of the Royal Statistical Society: Series B (Methodological), 41(2), 113–147. https://doi.org/10.1111/j.2517-6161.1979.tb01066.x
  • Chakraborty, T. (2019). An analysis of the maximum likelihood estimates for the Lomax distribution. ArXiv: 1911.12612v2, 1–14.
  • Consonni, G., Fouskakis, D., Liseo, B., & Ntzoufras, I. (2018). Prior distributions for objective Bayesian analysis. Bayesian Analysis, 13(2), 627–679. https://doi.org/10.1214/18-BA1103
  • Datta, G. S., & Mukerjee, R. (2004). Probability matching priors: Higher order asymptotics. Lecture Notes in Statistics. Sringer.
  • Deville, Y. (2016). Renext: Renewal method for extreme values extrapolation (p. 25). https://cran.r-project.org/web/packages/Renext/Renext.pdf.
  • Ferreira, P. H., Gonzales, J. F. B., Tomazella, V. L. D., Ehlers, R. S., Louzada, F., & Silva, E. B. (2016). Objective Bayesian analysis for the Lomax distributionms. ArXiv: 1602.08450v1, 1–19.
  • Ferreira, P. H., Ramos, E., Ramos, P. L., Gonzales, J. F. B., Tomazella, V. L. D., R. S. Ehlers, Silva, E. B., & Louzad, F. (2020). Objective Bayesian analysis for the Lomax distribution. Statistics & Probability Letters, 159, Article 108677. https://doi.org/10.1016/j.spl.2019.108677
  • Holland, O., Golaup, A., & Aghvami, A. H. (2006). Traffic characteristics of aggregated module downloads for mobile terminal reconfiguration. IEEE Proceedings: Communications, 153(5), 683–690. https://doi.org/10.1049/ip-com:20045155
  • Jeffreys, H. (1961). Theory of probability (3rd ed.). Oxford University Press.
  • Kang, S. G., Lee, W. D., & Kim, Y. (2021). Posterior propriety of bivariate lomax distribution under objective priors. Communication in Statistics – Theory and Methods, 50(9), 2201–2209. https://doi.org/10.1080/03610926.2019.1662049
  • Lemonte, A. J., & Cordeiro, G. M. (2013). An extended Lomax distribution. Statistics, 47(4), 800–816. https://doi.org/10.1080/02331888.2011.568119
  • Lindley, D. V. (1956). On a measure of the information provided by an experiment. The Annals of Mathematical Statistics, 27(4), 986–1005. https://doi.org/10.1214/aoms/1177728069
  • Lomax, K. (1954). Business failures: Another example of the analysis of failure data. Journal of the American Statistical Association, 49(268), 847–852. https://doi.org/10.1080/01621459.1954.10501239
  • Marshall, A. W., & Olkin, I. (2007). Life distributions: Structure of nonparametric, semiparametric, and parametric families. Springer.
  • Nadarajah, S. (2005). Sums, products, and ratios for the bivariate Lomax distribution. Computational Statistics & Data Analysis, 49(1), 109–129. https://doi.org/10.1016/j.csda.2004.05.003
  • Nayak, T. K. (1987). Multivariate Lomax distribution: Properties and usefulness in reliability theory. Journal of Applied Probability, 24(1), 170–177. https://doi.org/10.2307/3214068
  • Peers, H. W. (1965). On confidence sets and Bayesian probability points in the case of several parameters. Journal of the Royal Statistical Society: Series B (Methodological), 27(1), 9–16. https://doi.org/10.1111/j.2517-6161.1965.tb00581.x
  • Ramos, P. L., Louzada, F., & Ramos, E. (2018). Posterior properties of the Nakagami-m distribution using non-informative priors and applications in reliability. IEEE Transactions on Reliability, 67(1), 105–117. https://doi.org/10.1109/TR.24
  • Roberts, G. O., Gelman, A., & Gilks, W. R. (1997). Weak convergence and optimal scaling of random walk metropolis algorithms. Annals of Applied Probability, 7(1), 110–120 . http://doi.org/10.1214/aoap/1034625254
  • Roy, D., & Gupta, R. P. (1996). Bivariate extension of Lomax and finite range distributions through characterization approach. Journal of Multivariate Analysis, 59(1), 22–33. https://doi.org/10.1006/jmva.1996.0052
  • Zellner, A. (1977). Maximal data information prior distributions. In A. Aykac & C. Brumat (Eds.), New developments in the applications of Bayesian methods (pp. 211–232). North-Holland.