Multivariate aging properties of epoch times of nonhomogeneous processes
Journal of Multivariate Analysis
Stochastic Properties Of p-Spacings Of Generalized Order Statistics
Probability in the Engineering and Informational Sciences
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Stochastic Orderings Between p-Spacings Of Generalized Order Statistics From Two Samples
Probability in the Engineering and Informational Sciences
Multivariate Stochastic Comparisons Of Sequential Order Statistics
Probability in the Engineering and Informational Sciences
Order restricted inference for sequential k-out-of-n systems
Journal of Multivariate Analysis
Multivariate dependence of spacings of generalized order statistics
Journal of Multivariate Analysis
Ordering p-spacings of generalized order statistics revisited
Probability in the Engineering and Informational Sciences
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In the model of sequential order statistics, prior distributions are considered for the model parameters, which, for example, describe increasing load put on remaining components. Gamma priors are examined as well as priors out of a class of extended truncated Erlang distributions (ETED), which is introduced along with some properties. The choice of independent priors in both set-ups leads to respective independent, conjugate posterior distributions for the model parameters of sequential order statistics. Since, in practical applications, the model parameters will often be increasingly ordered, a multivariate prior is applied being the joint distribution of common ETED-order statistics. Whatever baseline distribution of the sequential order statistics is chosen, the joint posterior distribution turns out to be a Weinman multivariate exponential distribution. Posterior moments are given explicitly, and HPD credible sets for the model parameters are stated.