Research Articles (Statistics and Actuarial Science)

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Browsing Research Articles (Statistics and Actuarial Science) by Author "Bekker, A."

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    Bayesian highest posterior density intervals for the availability of a system with a 'rest-period' for the repair facility
    (SAIIE, 2001) Yadavalli, V. S. S.; Bekker, A.; Mostert, P. J.; Botha, M.
    In this paper Bayesian estimation for the steady state availability of a one-unit system with a rest-period for the repair facility is studied. The assumption is that the repair facility takes rest with probability p after each repair completion and the facility does not take the same with probability (l - p). The prior information is assumed to be vague and the Jeffreys' prior is used for the unknown parameters in the system. Gibbs sampling is used to derive the posterior distribution of the availability and subsequently the highest posterior density (HPD) intervals. A numerical example illustrates these results.
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    Berekening van a posteriori-verdeling in Bayes-analise : toepassing in 'n betroubareheidstelsel wat afwisselend gebruik word
    (AOSIS, 2002) Yadavalli, V. S. S.; Mostert, P. J.; Bekker, A.; Botha, M.
    Bayesian estimation is presented for the stationary rate of disappointments, D∞, for two models (with different specifications) of intermittently used systems. The random variables in the system are considered to be independently exponentially distributed. Jeffreys’ prior is assumed for the unknown parameters in the system. Inference about D∞ is being restrained in both models by the complex and non-linear definition of D∞. Monte Carlo simulation is used to derive the posterior distribution of D∞ and subsequently the highest posterior density (HPD) intervals. A numerical example where Bayes estimates and the HPD intervals are determined illustrates these results. This illustration is extended to determine the frequentistical properties of this Bayes procedure, by calculating covering proportions for each of these HPD intervals, assuming fixed values for the parameters.