Abstract
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.
Highlights
Bayesian estimation is presented for the stationary rate of disappointments, D∞, for two models of intermittently used systems
Inference about D∞ is being restrained in both models by the complex and non-linear definition of D∞
A numerical example where Bayes estimates and the highest posterior density (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
Summary
Daar is sekere stelsels waar kontinue falingsvrye verrigting van die stelsel nie ’n vereiste is nie en sodanige stelsels word stelsels wat afwisselend gebruik word, genoem. Dit kan maklik bepaal word deur die verdeling van die tydsduur van ’n teleurstelling te verkry. In hierdie artikel word die Bayes-beraming van die stasionêre tempo van teleurstellings vir bogenoemde twee modelle voorgestel deur Jeffrey se a priori-verdeling vir die onbekende parameters te gebruik. Objektiewe priors word in Bayes statistiese analise gebruik om neutrale kennis voor te stel van die onbekende parameters in die model. Afdeling 2 gee ’n kort beskrywing van twee verskillende modelle van ’n eeneenheidstelsel wat afwisselend gebruik word, die nodige notasie en die maksimumaanneemlikheidsberamers vir die stasionêre tempo van teleurstellings, soos afgelei deur Yadavalli en Botha (2002). Die voorwaardelike verdeling van die stasionêre tempo vir die twee modelle, gegee die data, word bepaal. Hieruit word die hoogste a posteriori-digtheidsintervalle (HPD) en ander puntberamers bepaal
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